Fuzzy-Model-Based Sliding Mode Control of Nonlinear Descriptor Systems

Event-triggered adaptive optimal tracking control for nonlinear stochastic systems with dynamic state constraints

This paper investigates the issue of event-triggered adaptive optimal tracking control for uncertain nonlinear systems with stochastic disturbances and dynamic state constraints. To handle the dynamic state constraints, a novel unified tangent-type nonlinear mapping function is proposed. A neural networks (NNs)-based identifier is designed to cope with the stochastic disturbances. By utilizing adaptive dynamic programming (ADP) of identifier-actor-critic architecture and event triggering mechanism, the adaptive optimized event-triggered control (ETC) approach for the nonlinear stochastic system is first proposed. It is proven that the designed optimized ETC approach guarantees the robustness of the stochastic systems and the semi-globally uniformly ultimately bounded in the mean square of the NNs adaptive estimation error, and the Zeno behavior can be avoided. Simulations are offered to illustrate the effectiveness of the proposed control approach.

Safety Flight Control Design of a Quadrotor UAV With Capability Analysis

This article considers the safety control problem of a quadrotor unmanned aerial vehicle (UAV) subject to actuator faults and external disturbances, based on the quantization of system capability and safety margin. First, a trajectory function is constructed online with backpropagation of system dynamics. Therefore, a degraded trajectory is gracefully regenerated, via the tradeoff between the remaining system capability and the expected derivatives (velocity, jerk, and snap) of the trajectory. Second, a control-oriented model is established into a form of strict feedback, integrating actuator malfunctions and disturbances. Therefore, a retrofit dynamic surface control (DSC) scheme based on the control-oriented model is developed to improve the tracking performance. When comparing to the existing control methods, the compensation ability is analyzed to determine whether the faults and disturbances can be handled or not. Finally, simulation and experimental studies are conducted to highlight the efficiency of the proposed safety control scheme.

Fuzzy-Affine-Model-Based Sliding-Mode Control for Discrete-Time Nonlinear 2-D Systems via Output Feedback

This work investigates the issue of output-feedback sliding-mode control (SMC) for nonlinear 2-D systems by Takagi-Sugeno fuzzy-affine models. Via combining with the sliding surface, the sliding-mode dynamical properties are depicted by a singular piecewise-affine system. Through piecewise quadratic Lyapunov functions, new stability and robust performance analysis of the sliding motion are carried out. An output-feedback dynamic SMC design approach is developed to guarantee that the system states can converge to a neighborhood of the sliding surface. Simulation studies are given to verify the validity of the proposed scheme.

H∞ Proportional-Integral State Estimation for T-S Fuzzy Systems Over Randomly Delayed Redundant Channels With Partly Known Probabilities

In this article, we consider the H_∞ proportional-integral (PI) state estimation (SE) problem for discrete-time T-S fuzzy systems subject to transmission delays, external disturbances, and redundant channels. Multiple redundant communication channels are utilized between the sensors and the remote estimator to enhance the reliability of data transmissions. In order to characterize the transmission delays in network-based communication, a family of random variables with partly known probabilities, which are independent and identically distributed, is adopted to describe the random behavior of the transmission delays with the redundant channels. The objective of this work is to put forward a PI state estimator such that the dynamics of the estimation error is exponentially mean-square stable and satisfies the prescribed H_∞ performance index of the disturbance attenuation/rejection. By employing the stochastic analysis approach, the error dynamics of the SE under the proposed state estimator is analyzed and sufficient conditions are obtained to ensure the existence of the required PI state estimator. Furthermore, the desired estimator parameters are derived by solving a nonlinear optimization problem. Finally, two simulation examples are exploited to demonstrate the validity of the proposed SE scheme.

Stabilization of Positive Systems With Time Delay via the Takagi-Sugeno Fuzzy Impulsive Control

In this study, the Takagi-Sugeno (T-S) fuzzy impulsive control problem is investigated for a class of nonlinear positive systems with time delay. The time delay under consideration is both in the continuous-time dynamics and at the impulsive instants, which can model practical systems more accurately. An impulse-time-dependent copositive Lyapunov function (IDCLF) is constructed, and the Razumikhin technique is adopted to develop conditions that ensure the globally exponential stability of T-S fuzzy positive systems with delayed impulses. The size constraint between the impulse delay and the bound of impulsive intervals is removed. A T-S fuzzy impulsive controller is designed in terms of the solutions to certain vector inequalities that are readily solvable. Numerical examples and a practical example of lipoprotein metabolism and potassium ion transfer model are given to demonstrate the effectiveness, advantages, and practicality of the proposed results.

Two-dimensional event-triggered sliding mode control for Roesser model with time delays

This paper is concerned with the event-triggered sliding mode control (SMC) strategy for the discrete-time two-dimensional (2-D) systems represented by Roesser model with time delays. Firstly, the linear sliding surface functions combined with the event-triggered scheme are constructed for the 2-D Roesser model. Then sufficient conditions are established for the asymptotic stability of the reduced-order sliding mode dynamics and the existence of linear sliding surface functions in terms of linear matrix inequality. Subsequently, the event-triggered sliding mode control law is designed by the Lyapunov function approach to drive the state trajectories of the resultant closed-loop system into a bounded region and maintain there for subsequent time. Finally, a numerical example is given to illustrate the effectiveness of the proposed SMC design method.

On design of robust sliding mode observer for nonlinear networked time-delay systems with communication constraints

For a class of nonlinear discrete-time networked systems with time-delay and communication constraints, this paper is concerned with the design of robust sliding mode observer (SMO), where only one sensor node is allowed to transmit information to remote observer. We focus on the design of SMO to guarantee the exponentially stable of estimation error system and have a desired H_∞ disturbance attenuation level in presence of communication constraints. Firstly, a sensor selector is introduced such that only one sensor node is chosen and its measurement can be transmitted to remote SMO at each time instant. Then, a sufficient condition is derived by introducing a piece-wise Lyapunov functional and using the Jensen's Inequality, which ensures the prescribed performance of estimation error system in the sliding mode surface that we have defined. Moreover, the observer gain matrices can be obtained through solving some matrix inequalities given in the main results. Finally, a simulation study performed on the F404 aircraft engine state monitoring is introduced to validate the robust SMO design.

Event-triggered observer-based H∞ sliding mode control of nonlinear systems

The problem of sliding mode control for a class of Takagi-Sugeno fuzzy model-based nonlinear one-sided Lipschitz systems is investigated in the paper. Due to the state components are not available, a state observer is designed based on an event-triggering mechanism. Meanwhile, the output measurements transmitted through the communication channels suffer from signal delays. Based on the estimated state, an integral sliding surface is proposed. Then, the sliding mode dynamics is obtained by virtue of equivalent control principle. Further, by constructing appropriate sliding mode controller, the finite-time reachability of predefined sliding surface is surely guaranteed. Moreover, the stability with an H_∞ performance analysis of sliding mode dynamics is undertaken via Lyapunov function theory and the criteria are established in terms of LMI. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method.

Fixed-time terminal sliding mode tracking protocol design for high-order multiagent systems with directed communication topology

This paper presents a novel fixed-time consensus tracking protocol for high order multi-agent system (MAS) with directed communication topology. A new distributed observer is proposed such that fixed-time leader's state estimation can be achieved, which overcomes the difficulty arising from asymmetry of communication topology. A series of terminal sliding surfaces are constructed and a singularity-free sliding mode fixed-time tracking protocol is developed. It is proved that the proposed tracking protocol achieves fixed-time consensus tracking. Particularly, we can obtain the controller gain from the pre-specified time, which helps to tune the gain in accordance with consensus time requirement. Moreover, a less conservative convergence time bound estimation is attained. Simulation examples demonstrate the effectiveness of the presented scheme.

Design and implementation of finite time sliding mode controller for fuzzy overhead crane system

This paper considers the problem of fuzzy overhead crane system modelling and finite-time stability/boundedness via sliding mode control (SMC) method. Due to the strong coupling of control input, the fuzzy technique is utilized to linearize the overhead crane system and a fuzzy overhead crane model is established with appropriate membership functions. Considering the bad effect, including the swing of hook and plates, the external disturbances of the friction and air resistances, is inevitable during the transportation of copper electrode plates, the SMC method is adopted to stabilize the fuzzy system and robust to these interference signals. Furthermore, taking the time cost of actual industry into account, the finite-time stability/boundedness is introduced to achieve the state of system could be stable in a specified finite time. Moreover, the reaching law of sliding mode dynamics is analysed and the sufficient conditions for finite-time stability/boundedness of system state are formulated, respectively. Finally, the simulation results of the control strategy put forward in this article with the comparisons on some existing algorithms are provided to verify the effectiveness of the control strategy in the copper electrolytic overhead crane system.

Dynamic Event-Triggered Control for Interval Type-2 Fuzzy Systems Under Fading Channel

This article is to tackle the event-based state-feedback control problem for interval type-2 (IT2) fuzzy systems subject to the fading channel. For saving communication resources, a dynamic event-triggered (ET) mechanism is utilized to decide the data transmission from sensors to the controller. A time-varying random process is employed to characterize the fading phenomenon in the unpredictable communication network. By considering the effect of channel fading, a nonparallel distribution compensation (non-PDC) IT2 fuzzy controller is synthesized and its number of rules and membership functions (MFs) can be freely selected. As a consequence, the closed-loop fuzzy system possesses imperfectly matched MFs. By taking the global membership boundary information into stability analysis, the membership-function-dependent analysis method is employed to handle these imperfectly matched MFs and to obtain relaxed criteria. Besides, sufficient criteria are obtained so that the resulting closed-loop IT2 fuzzy system can achieve stochastic stability despite fading measurements. The effectiveness of the proposed method is illustrated by a mass-spring-damper system and a numerical example.

Co-Design of 2-D Event Generator and Sliding Mode Controller for 2-D Roesser Model via Genetic Algorithm

The co-design problem of 2-D event generators and sliding mode controller (SMC) is studied in this article for the discrete-time 2-D Roesser model to reduce the communication usage between the plant and the controller. First, by resorting to the 2-D reaching law conditions, the event-based 2-D SMC schemes are proposed and a kind of horizonal/vertical independent event generator is designed. Then, the stability of the sliding-mode dynamics is analyzed and a nonlinear matrix inequality condition associated with the horizontal/vertical sliding matrices is obtained. In order to solve the derived nonlinear matrix inequality condition without introducing conservatism, a binary genetic algorithm (GA) is applied by considering a multiobjective optimization problem, which reflects the tradeoff between the convergence of the sliding-mode dynamics and the scheduling performance of the designed horizontal/vertical event generators. Finally, a simulation example is exploited to demonstrate the effectiveness of the proposed co-design approach with GA.

Nonlinear Nonsingular Fast Terminal Sliding Mode Control Using Deep Deterministic Policy Gradient

Background: As a control strategy of industrial robots, sliding mode control has the advantages of fast response and simple physical implementation, but it still has the problems of chattering and low tracking accuracy caused by chattering. This paper proposes a new sliding mode control strategy for the application of industrial robot control, which effectively solves these problems. Methods: In this paper, a deep deterministic policy gradient–nonlinear nonsingular fast terminal sliding mode control (DDPG–NNFTSMC) strategy is proposed for industrial robot control. In order to improve the tracking control accuracy and anti-interference ability, DDPG is used to approach the uncertainties of the system in real time, which ensures the robustness of the system in various uncertain environments. Lyapunov function is used to prove the stability and finite time convergence of the system. Compared with the nonsingular terminal sliding mode control (NTSMC), the time to reach the equilibrium point is shorter. With the help of MATLAB/Simulink, the tracking accuracy and control effects are compared with traditional terminal sliding mode control (TSMC), NTSMC and radial basis function–sliding mode control (RBF–SMC), the results showed that it had the advantages of nonsingularity, finite time convergence, small tracking error. The motion accuracy and anti-interference ability of the uncertain manipulator system was further improved, and the chattering problem of the system in the motion process is effectively eliminated.

Memory-Based Integral Sliding-Mode Control for T-S Fuzzy Systems With PMSM via Disturbance Observer

In this article, the disturbance observer (DOB)-based memory integral sliding-mode control (ISMC) is designed for the permanent magnet synchronous motor (PMSM) model subject to mismatched disturbance through the Takagi-Sugeno (T-S) fuzzy approach. Different from the previous studies, a memory-based ISMC scheme that has a constant delay is taken for the first time to design the ISMC for the T-S fuzzy systems. The DOB is given to estimate the disturbances, which are incorporated in the controller design to counteract the disturbance. To fully abide by the model characteristics of the PMSM-based T-S fuzzy systems and DOB, an integral-type fuzzy switching surface function (IFSSF), which involves state-dependent input matrix and memory parameter simultaneously, is defined. From the IFSSF, the fuzzy ISMC is designed to ensure the reachability condition in finite time. Besides that, the designed fuzzy ISMC can effectively attenuate the mismatched disturbances based on the H_∞ control theory. Also, a set of sufficient conditions is derived to ensure the global asymptotic stability for the sliding-mode dynamics by the proposed controller. Finally, the applicability of designed DOB-based memory fuzzy ISMC methodology is demonstrated by a controller design for the PMSM model.

State-estimation-based adaptive sliding mode control of uncertain switched systems: A novel linear sliding manifold approach

A new sliding mode observer design scheme is developed with a novel linear sliding manifold for the exponential stabilization problem of a class of uncertain switched systems in this note. Firstly, the linear sliding manifold is constructed based on a modified observer, through which a new technical approach of the underlying system analysis is exploited to devise a novel exponential stability criteria. Moreover, an associated adaptive switching controller is presented, by which the arrival condition of the designated sliding manifold is fulfilled. Ultimately, illustrative examples are conducted to confirm the feasibility of the proposed scheme.

A novel high order sliding mode control method

In this article, we develop an original high order sliding mode control (SMC) method which can be used to control single input single output (SISO) system and multi-variable system. The method has the benefit of resisting unmodelled dynamics and external disturbance. However, there exist the chattering effect in the conventional control methods. For decreasing the chattering phenomenon, a new high order SMC method is raised. Firstly, the new methodology is designed. Secondly, the method is employed to control the single input single output system with two examples. Thirdly, this new scheme is applied to control the multi-variable system. At the same time, two examples are presented to testify the validity of the raised control method, then the raised new control method has been utilized to the load frequency control. Additionally, in comparison with other recently existed high order control method, the raised control method has demonstrated better control performance in terms of fast convergence and chattering phenomenon.

Neural-Network-Based Sliding-Mode Control of an Uncertain Robot Using Dynamic Model Approximated Switching Gain

In this article, a new neural-network-based sliding-mode control (SMC) of an uncertain robot is presented. The distinguishing characteristic of the proposed control scheme is that the switching gain is designed as a dynamic model approximated value, which is handled by using the neural-network strategy to adapt the unknown dynamics and disturbances. In the presented control scheme, the modeling information of the robotic system is not required and only one parameter is required to be estimated in each joint of the robotic system. Subsequently, the Lyapunov method is utilized to prove that the trajectory tracking errors will eventually converge to a neighborhood of zero. Finally, the contrast simulation studies reveal that with the proposed control scheme, the problems of chattering and high-speed switching of control input, which takes place in a conventional SMC, can be addressed, and a satisfactory control precision is guaranteed.

Neural Network-Based Adaptive Control for Spacecraft Under Actuator Failures and Input Saturations

In this article, we develop attitude tracking control methods for spacecraft as rigid bodies against model uncertainties, external disturbances, subsystem faults/failures, and limited resources. A new intelligent control algorithm is proposed using approximations based on radial basis function neural networks (RBFNNs) and adopting the tunable parameter-based variable structure (TPVS) control techniques. By choosing different adaptation parameters elaborately, a series of control strategies are constructed to handle the challenging effects due to actuator faults/failures and input saturations. With the help of the Lyapunov theory, we show that our proposed methods guarantee both finite-time convergence and fault-tolerance capability of the closed-loop systems. Finally, benefits of the proposed control methods are illustrated through five numerical examples.

Fuzzy Output Tracking Control and Filtering for Nonlinear Discrete-Time Descriptor Systems Under Unreliable Communication Links

In this paper, the problems of output tracking control and filtering are investigated for Takagi-Sugeno fuzzy-approximation-based nonlinear descriptor systems in the discrete-time domain. Especially, the unreliability of the communication links between the sensor and actuator/filter is taken into account, and the phenomenon of packet dropouts is characterized by a binary Markov chain with uncertain transition probabilities, which may reflect the reality more accurately than the existing description processes. A novel bounded real lemma (BRL), which ensures the stochastic admissibility with H_∞ performance for fuzzy discrete-time descriptor systems despite the uncertain Markov packet dropouts, is presented based on a fuzzy basis-dependent Lyapunov function. By resorting to the dual conditions of the obtained BRL, a solution for the designed fuzzy output tracking controller is given. A design method for the full-order fuzzy filter is also provided. Finally, two examples are finally adopted to show the applicability of the achieved design strategies.

Observer Design of Discrete-Time Fuzzy Systems Based on an Alterable Weights Method

This paper proposes an improvement on observer design of discrete-time fuzzy systems based on an alterable weights method. Different from the recent result, a more effective ranking-based switching mechanism is developed by introducing a bank of alterable weights for the sake of making use of the size difference information of the normalized fuzzy weighting functions more freely than before. Therefore, a positive result can be provided in this paper, that is, less conservative conditions of designing feasible fuzzy observers can be obtained than those existing results, while the computational cost of designing feasible fuzzy observers is even less than the up-to-date one. Finally, two numerical examples are given to show the progressiveness of the proposed method.