Extended state observer-based backstepping control for nonlinear systems under FDI attacks

In this paper, a novel extended state observer-based backstepping control scheme is proposed for strict-feedback nonlinear systems with unmeasured states suffering from false data injection (FDI) attacks. An extended state observer is designed to achieve simultaneous online estimation of system states and FDI attacks. A secure output feedback tracking control scheme with an attack compensation method is proposed to reduce the influence of FDI attacks. It is proven that the proposed scheme can guarantee that the closed-loop system is semi-global uniformly ultimately bounded. Moreover, it is shown that the observation errors can be as small as desired with an adjustable parameter and the tracking error can converge to a small neighborhood of the origin. Finally, two simulation examples verify the efficiency of the proposed approach.

LPVS guidance and adaptive event-triggered control for an underactuated surface vessel with the prevention of obstacle's vicious maneuvering

This paper investigates the adaptive neural event-triggered control for an underactuated surface vessel (USV), considering constraints of the obstacle's vicious maneuvering and the limited communication channel. In the algorithm, a novel logical phantom virtual ship (LPVS) guidance principle is developed to generate the global path following reference and the obstacle avoidance order in the simulation results, where the corresponding operation comply to the suggestion in international regulations for prevention collision at sea (COLREGs). The improved design of velocity obstacle (VO) method can guarantee its predictive capability to prevent the obstacle's vicious maneuvering. As for the control module, the adaptive event-triggered control algorithm is proposed by employing the robust neural damping technique and the input event-triggered mechanism. And the derived adaptive law can effectively solve perturbations from the gain uncertainty and the external disturbances. Through the theoretical analysis, all signals of the closed-loop control system are with the semi-globally uniform ultimate bounded (SGUUB) stability. The simulation experiments have been presented to verify the obstacle avoidance effectiveness and the burden-some superiority of the algorithm.

Adaptive Learning Control Algorithms for Infinite-Duration Tracking

Learning control is applicable to systems that operate periodically or over finite time intervals. Currently, there is a lack of research results about learning control approaches to infinite-duration tracking, without requiring periodicity or repeatability. This article addresses the problem of adaptive learning control (ALC) for systems performing infinite-duration tasks. Instead of using integral adaptation, incremental adaptive mechanisms are exploited, by which the numerical integration for implementation can be avoided. The comparison with the conventional integral adaptive mechanisms indicates that the suggested methodology can be an alternative to the adaptive system designs. Using an error-tracking approach, the approximation-based backstepping design is carried out for systems in the strict-feedback form, where a novel integral Lyapunov function is shown to be efficient in the treatment of state-dependent control gain. Theoretical results for the performance analysis are presented in detail. In particular, the robust convergence of the tracking error is established, while the boundedness of the variables of the closed-loop system is characterized, with the aid of a key technical lemma. It is shown that the proposed control method can provide satisfactory tracking performance and simplify the controller designs. Numerical results are presented to demonstrate effectiveness of the learning control schemes.

Adaptive NN Tracking Control for Uncertain MIMO Nonlinear System With Time-Varying State Constraints and Disturbances

In this article, an adaptive neural network (NN) tracking control scheme is proposed for uncertain multi-input-multi-output (MIMO) nonlinear system in strict-feedback form subject to system uncertainties, time-varying state constraints, and bounded disturbances. The radial basis function NNs (RBFNNs) are adopted to approximate the system uncertainties. By constructing the intermediate variables, the external disturbances that cannot be directly measured are approximated by the disturbance observers. The time-varying barrier Lyapunov function (TVBLF) is constructed to guarantee the boundedness of the errors lie in the sets. To overcome the potential singularity problem that the denominator of the barrier function term approaches zero in controller design, the adaptive NN tracking control scheme with time-varying state constraints is proposed. Based on the TVBLF, the controller will be designed to guarantee tracking performance without violating the appropriate error constraints. The analysis of TVBLF shows that all closed-loop signals remain semiglobally uniformly ultimately bounded (SGUUB). The simulation results are performed to validate the validity of the proposed scheme.

Predictor-Based Neural Dynamic Surface Control for Bipartite Tracking of a Class of Nonlinear Multiagent Systems

This article is concerned with bipartite tracking for a class of nonlinear multiagent systems under a signed directed graph, where the followers are with unknown virtual control gains. In the predictor-based neural dynamic surface control (NDSC) framework, a bipartite tracking control strategy is proposed by the introduction of predictors and the minimal number of learning parameters (MNLPs) technology along with the graph theory. Different from the traditional NDSC, the predictor-based NDSC utilizes prediction errors to update the neural network for improving system transient performance. The MNLPs technology is employed to avoid the problem of "explosion of learning parameters". It is proved that all closed-loop signals steered by the proposed control strategy are bounded, and the system achieves bipartite consensus. Simulation results verify the efficiency and effectiveness of the strategy.

Prescribed Performance Adaptive Neural Compensation Control for Intermittent Actuator Faults by State and Output Feedback

Due to the existing effects of intermittent jumps of unknown parameters during operation, effectively establishing transient and steady-state tracking performances in control systems with unknown intermittent actuator faults is very important. In this article, two prescribed performance adaptive neural control schemes based on command-filtered backstepping are developed for a class of uncertain strict-feedback nonlinear systems. Under the condition of system states being available for feedback, the state feedback control scheme is investigated. When the system states are not directly measured, a cascade high-gain observer is designed to reconstruct the system states, and in turn, the output feedback control scheme is presented. Since the projection operator and modified Lyapunov function are, respectively, used in the adaptive law design and stability analysis, it is proven that both schemes can not only ensure the boundedness of all closed-loop signals but also confine the tracking errors within prescribed arbitrarily small residual sets for all the time even if there exist the effects of intermittent jumps of unknown parameters. Thus, the prescribed system transient and steady-state performances in the sense of the tracking errors are established. Furthermore, we also prove that the tracking performance under output feedback is able to recover the tracking performance under state feedback as the observer gain decreases. Simulation studies are done to verify the effectiveness of the theoretical discussions.

Robust Intelligent Control of SISO Nonlinear Systems Using Switching Mechanism

In this article, a robust adaptive learning control strategy for uncertain single-input-single-output systems in strict-feedback form and controllability canonical form (CCF) is studied. For the strict-feedback system, the dynamic surface control is introduced while for the controllability canonical system, sliding-mode control is further constructed. The finite-time design is introduced for fast convergence. Under the switching mechanism, the intelligent design and the robust technique work together to obtain robust tracking performance. Once the states run out of the domain of intelligent control, the robust item will pull the states back while inside the neural working domain, the composite learning is developed to achieve higher approximation precision by building the prediction error for the weight update. The closed-loop system stability is analyzed via the Lyapunov approach. Especially for the CCF, the finite-time convergence is achieved while the system signals are globally uniformly ultimately bounded. Simulation studies on the general nonlinear systems and the flight dynamics show that the new design scheme obtains better tracking performance with higher precision and stronger robustness.

Indirect adaptive robust control of nonstrict feedback nonlinear systems by a fuzzy approximation strategy

To solve the control problem of nonstrict feedback nonlinear systems, a backstepping technique based controller design method is developed by integrating a robust control law with the excellent parameter identification algorithm of indirect adaptive framework. Each of unknown system functions that contain whole states is approximated by adding together a bounded time-varying parameter and a fuzzy approximator related to the current step and previous states only in the backstepping design procedure, which solves the algebraic loop problem existing in nonstrict feedback systems. Then the command filter is combined with the adaptive backstepping to construct the robust control law by which the differentiation operation of the virtual control signal can be avoided. Subsequently the swapping scheme is used to convert the studied system into a linear time-varying form. Both the weight vector of the fuzzy logic system and the bounded time-varying parameter are estimated by a least-squares identification algorithm under relaxed excitation conditions, so that the accurate value of system functions can be obtained. All signals in the closed-loop system are proved to be bounded. A simulation example is put forward to verify effectiveness of the presented method.

Event-Triggered Adaptive Fuzzy Tracking Control With Guaranteed Transient Performance for MIMO Nonlinear Uncertain Systems

This paper investigates an event-triggered adaptive tracking control problem of multi-input and multi-output (MIMO) triangular structure nonlinear systems with nonparametric uncertainties. The implementation of this paper can be roughly classified into two steps: 1) solving the existing rate-limited communication constraints and 2) guaranteeing perfect tracking control performance. By using the relative threshold event-triggered strategy, the communication resource constraint is availably resolved, while the Zeno behavior can be avoided. In addition, by constructing a series of novel Lyapunov functions, an effective adaptive fuzzy control method is developed. The proposed fuzzy control scheme contains fewer calculations by the operation of addressing the square of the norm of the fuzzy weight vector for the entire MIMO system. It is proved that all of the closed-loop signals are global bounded, and the proposed method is not only capable of guaranteeing output tracking performance but is also available to ensure preserved transient performance. Simulation studies show the effectiveness of our approach and verify our established theory.

Adaptive Tracking Control of Surface Vessel Using Optimized Backstepping Technique

In this paper, a tracking control approach for surface vessel is developed based on the new control technique named optimized backstepping (OB), which considers optimization as a backstepping design principle. Since surface vessel systems are modeled by second-order dynamic in strict feedback form, backstepping is an ideal technique for finishing the tracking task. In the backstepping control of surface vessel, the virtual and actual controls are designed to be the optimized solutions of corresponding subsystems, therefore the overall control is optimized. In general, optimization control is designed based on the solution of Hamilton-Jacobi-Bellman equation. However, solving the equation is very difficult or even impossible due to the inherent nonlinearity and complexity. In order to overcome the difficulty, the reinforcement learning (RL) strategy of actor-critic architecture is usually considered, of which the critic and actor are utilized for evaluating the control performance and executing the control behavior, respectively. By employing the actor-critic RL algorithm for both virtual and actual controls of the vessel, it is proven that the desired optimizing and tracking performances can be arrived. Simulation results further demonstrate effectiveness of the proposed surface vessel control.

Robust Control for a Two DOF Robot Manipulator

In this paper, we present robust control techniques applied on a manipulator robot system: modified sliding mode control (MSMC) and backstepping control (BSC). The purpose is to evaluate SMC and BSC performances, taking into account the model uncertainties. Then, the obtained results of MSMC technique are compared with those of the adaptive sliding mode. Both methods have comparable simulation results which show a good quality of robustness. However, simulation results prove that the modified SMC is more robust, mostly under the effect of external variations and uncertainties.

Adaptive Intelligent Control for Nonlinear Strict-Feedback Systems With Virtual Control Coefficients and Uncertain Disturbances Based on Event-Triggered Mechanism

This paper investigates the problem of adaptive fuzzy control on the basis of an event-triggered mechanism for nonlinear strict-feedback systems with time-varying external disturbances and virtual control coefficients in the presence of actuator failures. Virtual control coefficients are correlated with the designed adaptive law and control signal. In the backstepping technique procedure, fuzzy logic systems are utilized to approximate an unknown nonlinear function, and the tuning function is implemented to cope with the destabilizing problem of the control design. To save communication resources, an adaptive fuzzy event-triggered control strategy is developed to update the control input when the triggering condition is satisfied. Then, all of the closed-loop signals can remain semi-globally uniformly ultimately bounded. The Zeno behavior can be excluded. Finally, a numerical example and a real system are provided to illustrate the effectiveness of the proposed approach.

Adaptive Asymptotic Neural Network Control of Nonlinear Systems With Unknown Actuator Quantization

In this paper, we propose an adaptive neural-network-based asymptotic control algorithm for a class of nonlinear systems subject to unknown actuator quantization. To this end, we exploit the sector property of the quantization nonlinearity and transform actuator quantization control problem into analyzing its upper bounds, which are then handled by a dynamic loop gain function-based approach. In our adaptive control scheme, there is only one parameter required to be estimated online for updating weights of neural networks. Within the framework of Lyapunov theory, it is shown that the proposed algorithm ensures that all the signals in the closed-loop system are ultimately bounded. Moreover, an asymptotic tracking error is obtained by means of introducing Barbalat's lemma to the proposed adaptive law.

Neural Observer and Adaptive Neural Control Design for a Class of Nonlinear Systems

This paper addresses the problem of adaptive neural tracking control for nonlinear nonstrict-feedback systems. The state variables are immeasurable and only the system output is available. A neural observer is constructed to estimate these unknown system state variables. An observer-based adaptive neural tracking control scheme is developed via backstepping approach. It is shown that the designed controller guarantees that the system output well follows the desired reference signal, and meanwhile, other closed-loop signals remain bounded. Finally, two simulation examples are used to test our results.

Observer-Based Fuzzy Adaptive Output-Feedback Control of Stochastic Nonlinear Multiple Time-Delay Systems

This paper is concerned with the observer-based fuzzy output-feedback control for stochastic nonlinear multiple time-delay systems. On the basis of the consistent form of virtual input signals and increasing characteristics of the system upper bound functions, a variable splitting technique is employed to surmount the difficulty occurred in the nonlower-triangular form. In the controller design procedure, a state observer is first designed, and then an adaptive fuzzy output-feedback control method is presented by combining backstepping design together with fuzzy systems' universal approximation capability. The proposed adaptive controller guarantees the semi-global boundedness of closed-loop system trajectories in terms of fourth-moment. Two simulation examples are displayed to demonstrate the feasibility of the suggested controller.

Adaptive Fuzzy Output-Feedback Stabilization Control for a Class of Switched Nonstrict-Feedback Nonlinear Systems

This paper proposes an fuzzy adaptive output-feedback stabilization control method for nonstrict feedback uncertain switched nonlinear systems. The controlled system contains unmeasured states and unknown nonlinearities. First, a switched state observer is constructed in order to estimate the unmeasured states. Second, a variable separation approach is introduced to solve the problem of nonstrict feedback. Third, fuzzy logic systems are utilized to identify the unknown uncertainties, and an adaptive fuzzy output feedback stabilization controller is set up by exploiting the backstepping design principle. At last, by applying the average dwell time method and Lyapunov stability theory, it is proven that all the signals in the closed-loop switched system are bounded, and the system output converges to a small neighborhood of the origin. Two examples are given to further show the effectiveness of the proposed switched control approach.

Dynamic Learning From Neural Control for Strict-Feedback Systems With Guaranteed Predefined Performance

This paper focuses on dynamic learning from neural control for a class of nonlinear strict-feedback systems with predefined tracking performance attributes. To reduce the number of neural network (NN) approximators used and make the convergence of neural weights verified easily, state variables are introduced to transform the state-feedback control of the original strict-feedback systems into the output-feedback control of the system in the normal form. Then, using the output error transformation based on performance functions, the constrained tracking control problem of the normal systems is transformed into the stabilization problem of an equivalent unconstrained one. By combining the backstepping method, a high-gain observer with radial basis function (RBF) NNs, a novel adaptive neural control (ANC) scheme is proposed to guarantee the predefined tracking error performance as well as the ultimate boundedness of all other closed-loop signals. In particular, only one NN is employed to approximate the lumped unknown system dynamics during the controller design. Under the satisfaction of the partial persistent excitation condition for RBF NNs, the proposed stable ANC scheme is shown to be capable of achieving knowledge acquisition, expression, and storage of unknown system dynamics. The stored knowledge is reused to develop a neural learning controller for improving the control performance of the closed-loop system. When the initial condition satisfies the predefined performance, the proposed neural learning control can still guarantee the predefined tracking performance. Simulation results on a third-order one-link robot are given to show the effectiveness of the proposed method.

Neuro-adaptive backstepping control of SISO non-affine systems with unknown gain sign

This paper presents two neuro-adaptive controllers for a class of uncertain single-input, single-output (SISO) nonlinear non-affine systems with unknown gain sign. The first approach is state feedback controller, so that a neuro-adaptive state-feedback controller is constructed based on the backstepping technique. The second approach is an observer-based controller and K-filters are designed to estimate the system states. The proposed method relaxes a priori knowledge of control gain sign and therefore by utilizing the Nussbaum-type functions this problem is addressed. In these methods, neural networks are employed to approximate the unknown nonlinear functions. The proposed adaptive control schemes guarantee that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB). Finally, the theoretical results are numerically verified through simulation examples. Simulation results show the effectiveness of the proposed methods.

Adaptive Neural Control of MIMO Nonstrict-Feedback Nonlinear Systems With Time Delay

In this paper, an adaptive neural output-feedback tracking controller is designed for a class of multiple-input and multiple-output nonstrict-feedback nonlinear systems with time delay. The system coefficient and uncertain functions of our considered systems are both unknown. By employing neural networks to approximate the unknown function entries, and constructing a new input-driven filter, a backstepping design method of tracking controller is developed for the systems under consideration. The proposed controller can guarantee that all the signals in the closed-loop systems are ultimately bounded, and the time-varying target signal can be tracked within a small error as well. The main contributions of this paper lie in that the systems under consideration are more general, and an effective design procedure of output-feedback controller is developed for the considered systems, which is more applicable in practice. Simulation results demonstrate the efficiency of the proposed algorithm.

Adaptive Fuzzy Tracking Control for a Class of MIMO Nonlinear Systems in Nonstrict-Feedback Form

This paper focuses on the problem of fuzzy adaptive control for a class of multiinput and multioutput (MIMO) nonlinear systems in nonstrict-feedback form, which contains the strict-feedback form as a special case. By the condition of variable partition, a new fuzzy adaptive backstepping is proposed for such a class of nonlinear MIMO systems. The suggested fuzzy adaptive controller guarantees that the proposed control scheme can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking errors eventually converge to a small neighborhood around the origin. The main advantage of this paper is that a control approach is systematically derived for nonlinear systems with strong interconnected terms which are the functions of all states of the whole system. Simulation results further illustrate the effectiveness of the suggested approach.

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.

Approximation-based adaptive neural control design for a class of nonlinear systems

This paper focuses on approximation-based adaptive neural control of a class of nonlinear non-strict-feedback systems. Based on the structural characteristic and the monotonously increasing property of the system bounding functions, a variable separation method is first developed. By this method, an approximation-based adaptive backstepping approach is proposed for a class of nonlinear non-strict-feedback systems. It is shown that the proposed controller guarantees semi-global boundedness of all the signals in the closed-loop systems. Three examples are used to illustrate the effectiveness of the proposed approach.

Fuzzy Relational Control of an Uncertain System

The paper considers the usefulness of a control strategy based on a fuzzy relational model of the controller to counteract uncertainties caused by measurement noise and unmeasured disturbances. The fuzzy relational model is identified using a combination of feedback error learning and fuzzy identification. An important feature of the resulting fuzzy relational model is that it will generate a fuzzy output in the presence of uncertainties. Two causes of uncertainty are considered separately, the first cause of uncertainty is due to the noise on the sensor measuring the controlled variable and the second one is an unmeasured input disturbance. Results are presented that show that the fuzzy control signal is representative of the uncertainties and that conditional defuzzification can then be used to improve the control performance by reducing the control activity.

ADAPTIVE FUZZY TRACKING CONTROL FOR A CLASS OF PERTURBED NONLINEAR TIME-VARYING DELAYS SYSTEMS WITH UNKNOWN CONTROL DIRECTION

An adaptive fuzzy control scheme with only one adjusted parameter is developed for a class of nonlinear time-varying delays systems. Three kinds of uncertainties: time-varying delays, control directions, and nonlinear functions are all assumed to be completely unknown, which is different from the previous work. During the controller design procedure, appropriate Lyapunov-Krasovskii functionals are used to compensate the unknown time-varying delays terms and the Nussbaum-type function is used to detect the unknown control direction. It is proved that the proposed controller guarantees that all the signals in the closed-loop system are bounded and the tracking errors converge to a small neighborhood around zero. The two main advantages of the developed scheme are that (i) by combining the appropriate Lyapunov-Krasovskii functionals with the Nussbaum-gain technique, the control scheme is proposed for a class of nonlinear time-varying delays systems with unknown control directions, (ii) only one parameter needs to be adjusted online in controller design procedure, which reduces the computational burden greatly. Finally, two examples are used to show the effectiveness of the proposed approach.

Observer-based adaptive neural network control for nonlinear stochastic systems with time delay

This paper considers the problem of observer-based adaptive neural network (NN) control for a class of single-input single-output strict-feedback nonlinear stochastic systems with unknown time delays. Dynamic surface control is used to avoid the so-called explosion of complexity in the backstepping design process. Radial basis function NNs are directly utilized to approximate the unknown and desired control input signals instead of the unknown nonlinear functions. The proposed adaptive NN output feedback controller can guarantee all the signals in the closed-loop system to be mean square semi-globally uniformly ultimately bounded. Simulation results are provided to demonstrate the effectiveness of the proposed methods.