Coordinated control of a 3DOF cartesian robot and a shape memory alloy-actuated flexible needle for surgical interventions: a non-model-based control method

Success of any needle-based medical procedures depends on accurate placement of the needle at the target location. However, accurate targeting and control of flexible self-actuating (active) needle are challenging. We have developed a shape memory alloy-actuated flexible needle steered by a 3D Cartesian robot and performed a comparative study of four, non-model-based, coordinated control methodologies for the combined robot steering and flexible-needle insertion process for surgical interventions. Investigated four controllers are: proportional–integral–derivative (PID), PID with the cubic of positional error term (PID-P3), static PID sliding mode controller, and robust adaptive PID sliding mode controller (RAPID-SMC). Relative efficacies of these controllers are demonstrated by performing experiements using a tissue-mimicking soft material phantom. Results from experiments have reavealed that RAPID-SMC is superior to other three controllers.

Robust Stable Limit Cycle Generation in Multi-Input Mechanical Systems

This paper proposes a robust controller for the generation of stable limit cycles in multi-input mechanical systems subjected to model uncertainties. The proposed idea is based on Port-Controlled Hamiltonian (PCH) model and energy-based control by considering the Hamiltonian function as the Lyapunov function. For this purpose, first, a nominal controller is designed by shaping the energy function of the system according to the structure of the desired limit cycle. Then, an additional robustifying control term is designed based on the integral sliding mode method with the selection of an appropriate sliding surface. Finally, computer simulations for two practical case studies are provided to confirm the effectiveness of the proposed controller in the generation of stable limit cycles in the presence of uncertainties.

Neural Adaptive Backstepping Control of a Robotic Manipulator With Prescribed Performance Constraint

This paper presents an adaptive neural network (NN) control of a two-degree-of-freedom manipulator driven by an electrohydraulic actuator. To restrict the system output in a prescribed performance constraint, a weighted performance function is designed to guarantee the dynamic and steady tracking errors of joint angle in a required accuracy. Then, a radial-basis-function NN is constructed to train the unknown model dynamics of a manipulator by traditional backstepping control (TBC) and obtain the preliminary estimated model, which can replace the preknown dynamics in the backstepping iteration. Furthermore, an adaptive estimation law is adopted to self-tune every trained-node weight, and the estimated model is online optimized to enhance the robustness of the NN controller. The effectiveness of the proposed control is verified by comparative simulation and experimental results with Proportional-integral-derivative and TBC methods.

Robotic Impedance Learning for Robot-Assisted Physical Training

Impedance control has been widely used in robotic applications where a robot has physical interaction with its environment. However, how the impedance parameters are adapted according to the context of a task is still an open problem. In this paper, we focus on a physical training scenario, where the robot needs to adjust its impedance parameters according to the human user's performance so as to promote their learning. This is a challenging problem as humans' dynamic behaviors are difficult to model and subject to uncertainties. Considering that physical training usually involves a repetitive process, we develop impedance learning in physical training by using iterative learning control (ILC). Since the condition of the same iteration length in traditional ILC cannot be met due to human variance, we adopt a novel ILC to deal with varying iteration lengthes. By theoretical analysis and simulations, we show that the proposed method can effectively learn the robot's impedance in the application of robot-assisted physical training.

Design and Adaptive Control for an Upper Limb Robotic Exoskeleton in Presence of Input Saturation

This paper addresses the control design for an upper limb exoskeleton in the presence of input saturation. An adaptive controller employing the neural network technology is proposed to approximate the uncertain robotic dynamics. Also, an auxiliary system is designed to deal with the effect of input saturation. Furthermore, we develop both the state feedback and the output feedback control strategies, which effectively estimates the uncertainties online from the measured feedback errors, instead of the model-based control. In addition to the proposed control, a disturbance observer is designed to reject the unknown disturbance online for achieving the trajectory tracking. The method requires a minimal amount of a priori knowledge of system dynamics. Subsequently, the principle of Lyapunov synthesis ensures the stability of the closed-loop system. Finally, the experimental studies are carried out on this robotic exoskeleton.

Neural-Learning-Based Control for a Constrained Robotic Manipulator With Flexible Joints

Nowadays, the control technology of the robotic manipulator with flexible joints (RMFJ) is not mature enough. The flexible-joint manipulator dynamic system possesses many uncertainties, which brings a great challenge to the controller design. This paper is motivated by this problem. In order to deal with this and enhance the system robustness, the full-state feedback neural network (NN) control is proposed. Moreover, output constraints of the RMFJ are achieved, which improve the security of the robot. Through the Lyapunov stability analysis, we identify that the proposed controller can guarantee not only the stability of flexible-joint manipulator system but also the boundedness of system state variables by choosing appropriate control gains. Then, we make some necessary simulation experiments to verify the rationality of our controllers. Finally, a series of control experiments are conducted on the Baxter. By comparing with the proportional-derivative control and the NN control with the rigid manipulator model, the feasibility and the effectiveness of NN control based on flexible-joint manipulator model are verified.

Adaptive Neural Control for Robotic Manipulators With Output Constraints and Uncertainties

This paper investigates adaptive neural control methods for robotic manipulators, subject to uncertain plant dynamics and constraints on the joint position. The barrier Lyapunov function is employed to guarantee that the joint constraints are not violated, in which the Moore-Penrose pseudo-inverse term is used in the control design. To handle the unmodeled dynamics, the neural network (NN) is adopted to approximate the uncertain dynamics. The NN control based on full-state feedback for robots is proposed when all states of the closed loop are known. Subsequently, only the robot joint is measurable in practice; output feedback control is designed with a high-gain observer to estimate unmeasurable states. Through the Lyapunov stability analysis, system stability is achieved with the proposed control, and the system output achieves convergence without violation of the joint constraints. Simulation is conducted to approve the feasibility and superiority of the proposed NN control.

A New Varying-Parameter Recurrent Neural-Network for Online Solution of Time-Varying Sylvester Equation

Solving Sylvester equation is a common algebraic problem in mathematics and control theory. Different from the traditional fixed-parameter recurrent neural networks, such as gradient-based recurrent neural networks or Zhang neural networks, a novel varying-parameter recurrent neural network, [called varying-parameter convergent-differential neural network (VP-CDNN)] is proposed in this paper for obtaining the online solution to the time-varying Sylvester equation. With time passing by, this kind of new varying-parameter neural network can achieve super-exponential performance. Computer simulation comparisons between the fixed-parameter neural networks and the proposed VP-CDNN via using different kinds of activation functions demonstrate that the proposed VP-CDNN has better convergence and robustness properties.

Reference Adaptation for Robots in Physical Interactions With Unknown Environments

In this paper, we propose a method of reference adaptation for robots in physical interactions with unknown environments. A cost function is constructed to describe the interaction performance, which combines trajectory tracking error and interaction force between the robot and the environment. It is minimized by the proposed reference adaptation based on trajectory parametrization and iterative learning. An adaptive impedance control is developed to make the robot be governed by the target impedance model. Simulation and experiment studies are conducted to verify the effectiveness of the proposed method.

Adaptive Control of Semi-Autonomous Teleoperation System With Asymmetric Time-Varying Delays and Input Uncertainties

This paper addresses the adaptive task-space bilateral teleoperation for heterogeneous master and slave robots to guarantee stability and tracking performance, where a novel semi-autonomous teleoperation framework is developed to ensure the safety and enhance the efficiency of the robot in remote site. The basic idea is to stabilize the tracking error in task space while enhancing the efficiency of complex teleoperation by using redundant slave robot with subtask control. To unify the study of the asymmetric time-varying delays, passive/nonpassive exogenous forces, dynamic parameter uncertainties and dead-zone input in the same framework, a novel switching technique-based adaptive control scheme is investigated, where a special switched error filter is developed. By replacing the derivatives of position errors with their filtered outputs in the coordinate torque design, and employing the multiple Lyapunov-Krasovskii functionals method, the complete closed-loop master (slave) system is proven to be state-independent input-to-output stable. It is shown that both the position tracking errors in task space and the adaptive parameter estimation errors remain bounded for any bounded exogenous forces. Moreover, by using the redundancy of the slave robot, the proposed teleoperation framework can autonomously achieve additional subtasks in the remote environment. Finally, the obtained results are demonstrated by the simulation.

Adaptive Neural Network Control of a Flapping Wing Micro Aerial Vehicle With Disturbance Observer

The research of this paper works out the attitude and position control of the flapping wing micro aerial vehicle (FWMAV). Neural network control with full state and output feedback are designed to deal with uncertainties in this complex nonlinear FWMAV dynamic system and enhance the system robustness. Meanwhile, we design disturbance observers which are exerted into the FWMAV system via feedforward loops to counteract the bad influence of disturbances. Then, a Lyapunov function is proposed to prove the closed-loop system stability and the semi-global uniform ultimate boundedness of all state variables. Finally, a series of simulation results indicate that proposed controllers can track desired trajectories well via selecting appropriate control gains. And the designed controllers possess potential applications in FWMAVs.

Adaptive Neural Network Control of an Uncertain Robot With Full-State Constraints

This paper studies the tracking control problem for an uncertain n -link robot with full-state constraints. The rigid robotic manipulator is described as a multiinput and multioutput system. Adaptive neural network (NN) control for the robotic system with full-state constraints is designed. In the control design, the adaptive NNs are adopted to handle system uncertainties and disturbances. The Moore-Penrose inverse term is employed in order to prevent the violation of the full-state constraints. A barrier Lyapunov function is used to guarantee the uniform ultimate boundedness of the closed-loop system. The control performance of the closed-loop system is guaranteed by appropriately choosing the design parameters. Simulation studies are performed to illustrate the effectiveness of the proposed control.

Optimized Assistive Human-Robot Interaction Using Reinforcement Learning

An intelligent human-robot interaction (HRI) system with adjustable robot behavior is presented. The proposed HRI system assists the human operator to perform a given task with minimum workload demands and optimizes the overall human-robot system performance. Motivated by human factor studies, the presented control structure consists of two control loops. First, a robot-specific neuro-adaptive controller is designed in the inner loop to make the unknown nonlinear robot behave like a prescribed robot impedance model as perceived by a human operator. In contrast to existing neural network and adaptive impedance-based control methods, no information of the task performance or the prescribed robot impedance model parameters is required in the inner loop. Then, a task-specific outer-loop controller is designed to find the optimal parameters of the prescribed robot impedance model to adjust the robot's dynamics to the operator skills and minimize the tracking error. The outer loop includes the human operator, the robot, and the task performance details. The problem of finding the optimal parameters of the prescribed robot impedance model is transformed into a linear quadratic regulator (LQR) problem which minimizes the human effort and optimizes the closed-loop behavior of the HRI system for a given task. To obviate the requirement of the knowledge of the human model, integral reinforcement learning is used to solve the given LQR problem. Simulation results on an x - y table and a robot arm, and experimental implementation results on a PR2 robot confirm the suitability of the proposed method.

Optimal critic learning for robot control in time-varying environments

In this paper, optimal critic learning is developed for robot control in a time-varying environment. The unknown environment is described as a linear system with time-varying parameters, and impedance control is employed for the interaction control. Desired impedance parameters are obtained in the sense of an optimal realization of the composite of trajectory tracking and force regulation. Q -function-based critic learning is developed to determine the optimal impedance parameters without the knowledge of the system dynamics. The simulation results are presented and compared with existing methods, and the efficacy of the proposed method is verified.

Learning from adaptive neural dynamic surface control of strict-feedback systems

Learning plays an essential role in autonomous control systems. However, how to achieve learning in the nonstationary environment for nonlinear systems is a challenging problem. In this paper, we present learning method for a class of n th-order strict-feedback systems by adaptive dynamic surface control (DSC) technology, which achieves the human-like ability of learning by doing and doing with learned knowledge. To achieve the learning, this paper first proposes stable adaptive DSC with auxiliary first-order filters, which ensures the boundedness of all the signals in the closed-loop system and the convergence of tracking errors in a finite time. With the help of DSC, the derivative of the filter output variable is used as the neural network (NN) input instead of traditional intermediate variables. As a result, the proposed adaptive DSC method reduces greatly the dimension of NN inputs, especially for high-order systems. After the stable DSC design, we decompose the stable closed-loop system into a series of linear time-varying perturbed subsystems. Using a recursive design, the recurrent property of NN input variables is easily verified since the complexity is overcome using DSC. Subsequently, the partial persistent excitation condition of the radial basis function NN is satisfied. By combining a state transformation, accurate approximations of the closed-loop system dynamics are recursively achieved in a local region along recurrent orbits. Then, the learning control method using the learned knowledge is proposed to achieve the closed-loop stability and the improved control performance. Simulation studies are performed to demonstrate the proposed scheme can not only reuse the learned knowledge to achieve the better control performance with the faster tracking convergence rate and the smaller tracking error but also greatly alleviate the computational burden because of reducing the number and complexity of NN input variables.

Neural network-based motion control of an underactuated wheeled inverted pendulum model

In this paper, automatic motion control is investigated for one of wheeled inverted pendulum (WIP) models, which have been widely applied for modeling of a large range of two wheeled modern vehicles. First, the underactuated WIP model is decomposed into a fully actuated second order subsystem Σa consisting of planar movement of vehicle forward and yaw angular motions, and a nonactuated first order subsystem Σb of pendulum motion. Due to the unknown dynamics of subsystem Σa and the universal approximation ability of neural network (NN), an adaptive NN scheme has been employed for motion control of subsystem Σa . The model reference approach has been used whereas the reference model is optimized by the finite time linear quadratic regulation technique. The pendulum motion in the passive subsystem Σb is indirectly controlled using the dynamic coupling with planar forward motion of subsystem Σa , such that satisfactory tracking of a set pendulum tilt angle can be guaranteed. Rigours theoretic analysis has been established, and simulation studies have been performed to demonstrate the developed method.

Contact-force distribution optimization and control for quadruped robots using both gradient and adaptive neural networks

This paper investigates optimal feet forces' distribution and control of quadruped robots under external disturbance forces. First, we formulate a constrained dynamics of quadruped robots and derive a reduced-order dynamical model of motion/force. Consider an external wrench on quadruped robots; the distribution of required forces and moments on the supporting legs of a quadruped robot is handled as a tip-point force distribution and used to equilibrate the external wrench. Then, a gradient neural network is adopted to deal with the optimized objective function formulated as to minimize this quadratic objective function subjected to linear equality and inequality constraints. For the obtained optimized tip-point force and the motion of legs, we propose the hybrid motion/force control based on an adaptive neural network to compensate for the perturbations in the environment and approximate feedforward force and impedance of the leg joints. The proposed control can confront the uncertainties including approximation error and external perturbation. The verification of the proposed control is conducted using a simulation.

A proof of the Ge–Lee statement on the inertia regressor of robot manipulators

This paper delivers a proof of a statement due to Ge and Lee. Specifically, these authors stated, without proof, that the entries of the inertia matrix may be completely parameterized by stacking elements of a regressor superset. This superset has the advantage of avoiding to derive the complete dynamics of a robot manipulator. On the basis of both mechanics and combinatorial arguments, we deliver a formal proof. In addition, we improve the estimations by sorting joint variables and partitioning the inertia matrix that results into the reduction of the regressor superset. The number of nonlinear functions in the regressor is also quantified. A 2 degrees of freedom revolute robot is presented to illustrate these ideas.

The Inverted Pendulum Benchmark in Nonlinear Control Theory: A Survey

Abstract For at least fifty years, the inverted pendulum has been the most popular benchmark, among others, in nonlinear control theory. The fundamental focus of this work is to enhance the wealth of this robotic benchmark and provide an overall picture of historical and current trend developments in nonlinear control theory, based on its simple structure and its rich nonlinear model. In this review, we will try to explain the high popularity of such a robotic benchmark, which is frequently used to realize experimental models, validate the efficiency of emerging control techniques and verify their implementation. We also attempt to provide details on how many standard techniques in control theory fail when tested on such a benchmark. More than 100 references in the open literature, dating back to 1960, are compiled to provide a survey of emerging ideas and challenging problems in nonlinear control theory accomplished and verified using this robotic system. Possible future trends that we can envision based on the review of this area are also presented.

SVM-Based Control System for a Robot Manipulator

Real systems are usually non-linear, ill-defined, have variable parameters and are subject to external disturbances. Modelling these systems is often an approximation of the physical phenomena involved. However, it is from this approximate system of representation that we propose - in this paper - to build a robust control, in the sense that it must ensure low sensitivity towards parameters, uncertainties, variations and external disturbances. The computed torque method is a well-established robot control technique which takes account of the dynamic coupling between the robot links. However, its main disadvantage lies on the assumption of an exactly known dynamic model which is not realizable in practice. To overcome this issue, we propose the estimation of the dynamics model of the nonlinear system with a machine learning regression method. The output of this regressor is used in conjunction with a PD controller to achieve the tracking trajectory task of a robot manipulator. In cases where some of the parameters of the plant undergo a change in their values, poor performance may result. To cope with this drawback, a fuzzy precompensator is inserted to reinforce the SVM computed torque-based controller and avoid any deterioration. The theory is developed and the simulation results are carried out on a two-degree of freedom robot manipulator to demonstrate the validity of the proposed approach.

Neural-network control of mobile manipulators

In this paper, a neural network (NN)-based methodology is developed for the motion control of mobile manipulators subject to kinematic constraints. The dynamics of the mobile manipulator is assumed to be completely unknown, and is identified online by the NN estimators. No preliminary learning stage of NN weights is required. The controller is capable of disturbance-rejection in the presence of unmodeled bounded disturbances. The tracking stability of the closed-loop system, the convergence of the NN weight-updating process and boundedness of NN weight estimation errors are all guaranteed. Experimental tests on a 4-DOF manipulator arm illustrate that the proposed controller significantly improves the performance in comparison with conventional robust control.

Robust GRBF static neurocontroller with switch logic for control of robot manipulators

A new Gaussian radial basis function static neurocontroller is presented for stable adaptive tracking control. This is a two-stage controller acting in a supervisory fashion by means of a switch logic and allowing arbitration between a neural network (NN) and a robust proportional-derivative controller. The structure is intended to reduce the effects of the curse of dimensionality in multidimensional systems by fully exploiting the mechanical properties of the robot manipulator. A new factorization of the Coriolis/centripetal matrix is used, leading to an NN model that is much smaller than the dynamic ones. By resorting to the extended multivariate Shannon theorem and the computation of the effective bandwidth of the revolute robot manipulators, the network parameters are tuned. Stability and convergence properties are analyzed. This provides the assurance of reliability and effectiveness to make such controller viable. A robot manipulator with two degrees of freedom is employed to study the adaptive features of the neural control algorithm. Finally, the effectiveness of the proposed method is compared to the nonadaptive case.

Performance Analysis of a Neuro-PID Controller Applied to a Robot Manipulator

The performance of robot manipulators with nonadaptive controllers might degrade significantly due to the open loop unstable system and the effect of some uncertainties on the robot model or environment. A novel Neural Network PID controller (NNP) is proposed in order to improve the system performance and its robustness. The Neural Network (NN) technique is applied to compensate for the effect of the uncertainties of the robot model. With the NN compensator introduced, the system errors and the NN weights with large dispersion are guaranteed to be bounded in the Lyapunov sense. The weights of the NN compensator are adaptively tuned.

The simulation results show the effectiveness of the model validation approach and its efficiency to guarantee a stable and accurate trajectory tracking process in the presence of uncertainties.

ADAPTIVE FUZZY CONTROL WITH OUTPUT FEEDBACK FOR H∞ TRACKING OF SISO NONLINEAR SYSTEMS

Observer-based adaptive fuzzy H∞ control is proposed to achieve H∞ tracking performance for a class of nonlinear systems, which are subject to model uncertainty and external disturbances and in which only a measurement of the output is available. The key ideas in the design of the proposed controller are (i) to transform the nonlinear control problem into a regulation problem through suitable output feedback, (ii) to design a state observer for the estimation of the non-measurable elements of the system's state vector, (iii) to design neuro-fuzzy approximators that receive as inputs the parameters of the reconstructed state vector and give as output an estimation of the system's unknown dynamics, (iv) to use an H∞ control term for the compensation of external disturbances and modelling errors, (v) to use Lyapunov stability analysis in order to find the learning law for the neuro-fuzzy approximators, and a supervisory control term for disturbance and modelling error rejection. The control scheme is tested in the cart-pole balancing problem and in a DC-motor model.

Projection-based adaptive neurocontrol with switching logic deadzone tuning

In this brief, an adaptive neural network (NN) controller is proposed for multiple-input-multiple-output (MIMO) nonlinear systems with triangular control structure and unknown control directions. Deadzones are employed in the projection-based NN weight learning laws and the Nussbaum parameter update laws with levels tuned by an innovative switching logic tuning mechanism. Detailed analysis using a family of Lyapunov-like integral functions and the function approximation capability of NNs proves that all the tracking errors are semiglobal uniform ultimate bounded in small neighborhoods of the origin while the closed-loop system variables (state vector, NN weights, Nussbaum parameters) and the control law remain bounded. A simulation study confirms the theoretical results and verifies the effectiveness of the proposed design.

Neural network control of multifingered robot hands using visual feedback

It is interesting to observe that humans are able to manipulate an object easily and skillfully without the exact knowledge of the object, contact points, or kinematics of our fingers. However, research so far on multifingered robot control has assumed that the kinematics and contact points of the fingers are known exactly. In many applications of multifingered robot hands, the kinematics and contact points of the fingers are uncertain and structures of the Jacobian matrices are unknown. In this paper, we propose an adaptive neural network (NN) Jacobian controller for multifingered robot hand with uncertainties in kinematics, Jacobian matrices, and dynamics. It is shown that using NNs, the uniform ultimate boundedness of the position error can be achieved in the presence of the uncertainties. Simulation results are presented to illustrate the performance of the proposed controller.

Adaptive-Fourier-neural-network-based control for a class of uncertain nonlinear systems

An adaptive Fourier neural network (AFNN) control scheme is presented in this paper for the control of a class of uncertain nonlinear systems. Based on Fourier analysis and neural network (NN) theory, AFNN employs orthogonal complex Fourier exponentials as the activation functions. Due to the clear physical meaning of the neurons, the determination of the AFNN structure as well as the parameters of the activation functions becomes convenient. One salient feature of the proposed AFNN approach is that all the nonlinearities and uncertainties of the dynamical system are lumped together and compensated online by AFNN. It can, therefore, be applied to uncertain nonlinear systems without any a priori knowledge about the system dynamics. Derived from Lyapunov theory, a novel learning algorithm is proposed, which is essentially a frequency domain method and can guarantee asymptotic stability of the closed-loop system. The simulation results of a multiple-input-multiple-output (MIMO) nonlinear system and the experimental results of an X - Y positioning table are presented to show the effectiveness of the proposed AFNN controller.

Discrete-Time Adaptive Backstepping Nonlinear Control via High-Order Neural Networks

This paper deals with adaptive tracking for discrete-time multiple-input-multiple-output (MIMO) nonlinear systems in presence of bounded disturbances. In this paper, a high-order neural network (HONN) structure is used to approximate a control law designed by the backstepping technique, applied to a block strict feedback form (BSFF). This paper also includes the respective stability analysis, on the basis of the Lyapunov approach, for the whole controlled system, including the extended Kalman filter (EKF)-based NN learning algorithm. Applicability of the scheme is illustrated via simulation for a discrete-time nonlinear model of an electric induction motor.

Adaptive Robust Motion/Force Control of Holonomic-Constrained Nonholonomic Mobile Manipulators

In this paper, adaptive robust force/motion control strategies are presented for mobile manipulators under both holonomic and nonholonomic constraints in the presence of uncertainties and disturbances. The proposed control is robust not only to parameter uncertainties such as mass variations but also to external ones such as disturbances. The stability of the closed-loop system and the boundedness of tracking errors are proved using Lyapunov stability synthesis. The proposed control strategies guarantee that the system motion converges to the desired manifold with prescribed performance and the bounded constraint force. Simulation results validate that the motion of the system converges to the desired trajectory, and the constraint force converges to the desired force.

An improved dynamic neurocontroller based on Christoffel symbols

In this paper, a dynamic neurocontroller for positioning of robots based on static and parametric neural networks (NNs) has been developed. This controller is based on Christoffel symbols of first kind in order to carry out coriolis/centripetal matrix. Structural properties of robots and Kronecker product has been taken into account to develop NNs to approximate nonlinearities. The weight updating laws have been obtained from a nonlinear strategy based on Lyapunov energy that guarantees both stability and boundedness of signals and weights. The NN weights are tuned online with no "offline learning phase" and are initialized to zero. The neurocontroller improves the implementation with respect to other dynamic NNs used in the literature.

Performance-Oriented Antiwindup for a Class of Linear Control Systems With Augmented Neural Network Controller

This paper presents a conditioning scheme for a linear control system which is enhanced by a neural network (NN) controller and subjected to a control signal amplitude limit. The NN controller improves the performance of the linear control system by directly estimating an actuator-matched, unmodeled, nonlinear disturbance, in closed-loop, and compensating for it. As disturbances are generally known to be bounded, the nominal NN-control element is modified to keep its output below the disturbance bound. The linear control element is conditioned by an antiwindup (AW) compensator which ensures performance close to the nominal controller and swift recovery from saturation. For this, the AW compensator proposed is of low order, designed using convex linear matrix inequalities (LMIs) optimization.

Design and analysis of a general recurrent neural network model for time-varying matrix inversion

Following the idea of using first-order time derivatives, this paper presents a general recurrent neural network (RNN) model for online inversion of time-varying matrices. Different kinds of activation functions are investigated to guarantee the global exponential convergence of the neural model to the exact inverse of a given time-varying matrix. The robustness of the proposed neural model is also studied with respect to different activation functions and various implementation errors. Simulation results, including the application to kinematic control of redundant manipulators, substantiate the theoretical analysis and demonstrate the efficacy of the neural model on time-varying matrix inversion, especially when using a power-sigmoid activation function.

Output Feedback Control of a Class of Discrete MIMO Nonlinear Systems With Triangular Form Inputs

In this paper, adaptive neural network (NN) control is investigated for a class of discrete-time multi-input-multi-output (MIMO) nonlinear systems with triangular form inputs. Each subsystem of the MIMO system is in strict feedback form. First, through two phases of coordinate transformation, the MIMO system is transformed into input-output representation with the triangular form input structure unchanged. By using high-order neural networks (HONNs) as the emulators of the desired controls, effective output feedback adaptive control is developed using backstepping. The closed-loop system is proved to be semiglobally uniformly ultimate bounded (SGUUB) by using Lyapunov method. The output tracking errors are guaranteed to converge into a compact set whose size is adjustable, and all the other signals in the closed-loop system are proved to be bounded. Simulation results show the effectiveness of the proposed control scheme.

Nonlinear control of a dynamic model of HIV-1

Highly active antiretroviral therapy (HAART) reduces the viral burden in human immunodeficiency virus type 1 (HIV-1) infected patients. The paper addresses the problem of controlling the predator-prey like model of the interaction among CD4+ T-cell, CD8+ T-cell, and HIV-1 by an external drug agency. By exploring the dynamic properties of the system, the original system is first regrouped into two subsystems, then a nonlinear global controller is presented by designing two controllers over two complementary zones: a local controller on a finite region and a global controller over its complement. The local controller is designed to guarantee nonnegativty, and avoids the problem of control singularity within the neighborhood of the origin omega. The complementary controller is designed via backstepping for both subsystems over the complementary region. The closed-loop system is globally stable at nominal values through the introduction of a novel bridging virtual control, and the resulting controller is singularity free and guarantees nonnegativity. In this paper, simulations are conducted in discrete-time with sampling time Ts to show the effectiveness of the proposed method.

A unified quadratic-programming-based dynamical system approach to joint torque optimization of physically constrained redundant manipulators

In this paper, for joint torque optimization of redundant manipulators subject to physical constraints, we show that velocity-level and acceleration-level redundancy-resolution schemes both can be formulated as a quadratic programming (QP) problem subject to equality and inequality/bound constraints. To solve this QP problem online, a primal-dual dynamical system solver is further presented based on linear variational inequalities. Compared to previous researches, the presented QP-solver has simple piecewise-linear dynamics, does not entail real-time matrix inversion, and could also provide joint-acceleration information for manipulator torque control in the velocity-level redundancy-resolution schemes. The proposed QP-based dynamical system approach is simulated based on the PUMA560 robot arm with efficiency and effectiveness demonstrated.

Adaptive neural network control for a class of MIMO nonlinear systems with disturbances in discrete-time

In this paper, adaptive neural network (NN) control is investigated for a class of multiinput and multioutput (MIMO) nonlinear systems with unknown bounded disturbances in discrete-time domain. The MIMO system under study consists of several subsystems with each subsystem in strict feedback form. The inputs of the MIMO system are in triangular form. First, through a coordinate transformation, the MIMO system is transformed into a sequential decrease cascade form (SDCF). Then, by using high-order neural networks (HONN) as emulators of the desired controls, an effective neural network control scheme with adaptation laws is developed. Through embedded backstepping, stability of the closed-loop system is proved based on Lyapunov synthesis. The output tracking errors are guaranteed to converge to a residue whose size is adjustable. Simulation results show the effectiveness of the proposed control scheme.

Robust adaptive neural network control of uncertain nonholonomic systems with strong nonlinear drifts

In this paper, robust adaptive neural network (NN) control is presented to solve the control problem of nonholonomic systems in chained form with unknown virtual control coefficients and strong drift nonlinearities. The robust adaptive NN control laws are developed using state scaling and backstepping. Uniform ultimate boundedness of all the signals in the closed-loop are guaranteed, and the system states are proven to converge to a small neighborhood of zero. The control performance of the closed-loop system is guaranteed by appropriately choosing the design parameters. The proposed adaptive NN control is free of control singularity problem. An adaptive control based switching strategy is used to overcome the uncontrollability problem associated with x0 (t0) = 0. The simulation results demonstrate the effectiveness of the proposed controllers.

Obstacle avoidance for kinematically redundant manipulators using a dual neural network

One important issue in the motion planning and control of kinematically redundant manipulators is the obstacle avoidance. In this paper, a recurrent neural network is developed and applied for kinematic control of redundant manipulators with obstacle avoidance capability. An improved problem formulation is proposed in the sense that the collision-avoidance requirement is represented by dynamically-updated inequality constraints. In addition, physical constraints such as joint physical limits are also incorporated directly into the formulation. Based on the improved problem formulation, a dual neural network is developed for the online solution to collision-free inverse kinematics problem. The neural network is simulated for motion control of the PA10 robot arm in the presence of point and window-shaped obstacle.