Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

This paper deals with the problem of adaptive fuzzy output feedback control for a class of stochastic nonlinear switched systems. The controlled system in this paper possesses unmeasured states, completely unknown nonlinear system functions, unmodeled dynamics, and arbitrary switchings. A state observer which does not depend on the switching signal is constructed to tackle the unmeasured states. Fuzzy logic systems are employed to identify the completely unknown nonlinear system functions. Based on the common Lyapunov stability theory and stochastic small-gain theorem, a new robust adaptive fuzzy backstepping stabilization control strategy is developed. The stability of the closed-loop system on input-state-practically stable in probability is proved. The simulation results are given to verify the efficiency of the proposed fuzzy adaptive control scheme.

Adaptive Fuzzy Control Design for Stochastic Nonlinear Switched Systems With Arbitrary Switchings and Unmodeled Dynamics

This paper investigates a robust adaptive fuzzy control stabilization problem for a class of uncertain nonlinear systems with arbitrary switching signals that use an observer-based output feedback scheme. The considered switched nonlinear systems possess the unstructured uncertainties, unmodeled dynamics, and without requiring the states being available for measurement. A state observer which is independent of switching signals is designed to solve the problem of unmeasured states. Fuzzy logic systems are used to identify unknown lumped nonlinear functions so that the problem of unstructured uncertainties can be solved. By combining adaptive backstepping design principle and small-gain approach, a novel robust adaptive fuzzy output feedback stabilization control approach is developed. The stability of the closed-loop system is proved via the common Lyapunov function theory and small-gain theorem. Finally, the simulation results are given to demonstrate the validity and performance of the proposed control strategy.

Adaptive Fuzzy Output Feedback Control for Switched Nonlinear Systems With Unmodeled Dynamics

In this paper, adaptive neural tracking control is proposed for a robotic manipulator with uncertainties in both manipulator dynamics and joint actuator dynamics. The manipulator joints are subject to inequality constraints, i.e., the joint angles are required to remain in some compact sets. Integral barrier Lyapunov functionals (iBLFs) are employed to address the joint space constraints directly without performing an additional mapping to the error space. Neural networks (NNs) are utilised to compensate for the unknown robot dynamics and external force. Adapting parameters are developed to estimate the unknown bounds on NN approximations. By the Lyapunov synthesis, the proposed control can guarantee the semi-global uniform ultimate boundedness of the closed-loop system, and the practical tracking of joint reference trajectory is achieved without the violation of predefined joint space constraints. Simulation results are given to validate the effectiveness of the proposed control scheme.

Adaptive neural control for an uncertain robotic manipulator with joint space constraints

A radial basis function (RBF) neural network control algorithm can effectively improve the robotic manipulators’ performance against a large amount of uncertainty. The adaptive law can be derived by using the Lyapunov method so that the stability of robotic manipulator control system and the weight self-adaptive convergence of RBF neural networks will be guaranteed. Meanwhile, system fluctuations and even overshot phenomenon under every start-up process, which are caused by the system’s convergence from the given nonoptimal initial weight value to the optimal weight value, can be avoided by using memristors to remember the optimal weight after the system’s first operation. According to the above analysis, this correspondence paper designs a kind of RBF neural network control algorithm based on spintronic memristors, and then analyzes its theoretical derivation process and core design idea. Finally, the system simulation model, which uses a two-link robotic manipulator as control object, is built to prove the algorithm’s validity and feasibility. Simulation results show that the proposed algorithm can satisfy the effect of presupposition.

A Spintronic Memristor-Based Neural Network With Radial Basis Function for Robotic Manipulator Control Implementation

This paper studies robust problems of a class of discrete-time positive switched systems with uncertainties. The uncertainties refer to interval and polytopic uncertainties. By means of the multiple linear copositive Lyapunov functions approach, the robust stability of autonomous systems with average dwell time is solved. Then, the control synthesis of non-autonomous systems with average dwell time is discussed. State-feedback and output-feedback controllers are designed to guarantee the robust stabilization of the considered systems, respectively. All present conditions are solvable in terms of linear programming. Finally, several simulation examples are given to illustrate the validity of the design.

Robust Stabilization of Discrete-Time Positive Switched Systems with Uncertainties and Average Dwell Time Switching

This brief deals with the interval observer design for a class of discrete-time switched systems. In order to reduce the constraints of design conditions and improve the accuracy of estimation, the zonotope method is used to estimate the bounds of the system states. First, an $H_{\infty }$ observer is constructed for discrete-time switched systems and sufficient conditions are derived to guarantee the existence of the $H_{\infty }$ observer. Then, zonotope method is employed to estimate the states based on the designed observer. Finally, a numerical example in the background of booster converter is simulated to demonstrate the efficiency of the proposed approach.

Further Result on Interval Observer Design for Discrete-Time Switched Systems and Application to Circuit Systems

In this paper, we present the robust adaptive neural switching control problem for the application of robotic manipulators with uncertainty and disturbances. The control scheme relaxes the hypothesis that the bounds of external disturbance and approximation errors of neural networks are known. RBF Neural Networks (Radial Basis Function NNs) are adopted to approximate unknown functions of robotic manipulators and an H ? $\infty $ controller is designed to enhance system robustness and stabilization due to the existence of the compound disturbance which consists of approximation errors of the neural networks and external disturbance. The adaptive updated laws and the admissible switching signals have been derived from switched multiple Lyapunov function method, so that both system tracking stability and error convergence can be guaranteed in the closed-loop system. Experimental results have demonstrated the improved performance of the proposed control scheme over PD (Proportional Differential) control strategy, which have shown good accuracy of position tracking.

Design of Robust Adaptive Neural Switching Controller for Robotic Manipulators with Uncertainty and Disturbances

Due to the existence of external disturbance which affects the systems’ robustness and stability, a robust sliding mode switching controller with disturbance observer method has been developed for the switching systems of the direct-drive servo control systems, which can eliminate the chatter and reduce the switching gain of the switching systems completely or alleviate it greatly. According to the Lyapunov stability method and the periodically switching law, the resulting closed-loop switched system is robustly stable such that all the signals in the resulting closed-loop switched system of the direct-drive servo control systems keep bounded and the sliding surface of the switching system can be well reached. Finally, the presented switching control scheme is easy to implement and simulation results illustrate the good control performance.

Robust Switching Control of the Direct-Drive Servo Control Systems Based on Disturbance Observer for Switching Gain Reduction

In this paper, we discuss the trajectory switching neural control problem for the switching model of a serial n-joint robotic manipulator. The key feature of this paper is to provide the dual design of the control law for the developed adaptive switching neural controller and the associated robust compensation control law. RBF Neural Networks (NNs) are employed to approximate unknown functions of robotic manipulators and a robust controller is designed to compensate the approximation errors of the neural networks and external disturbance. Via switched multiple Lyapunov function method, the adaptive updated laws and the admissible switching signals have been developed to guarantee that the resulting closed-loop system is asymptotically Lyapunov stable such that the joint position follows any given bounded desired output signal. Finally, we give a simulation example of a two-joint robotic manipulator to demonstrate the proposed methods and make a comparative analysis.

Jun Huang

Papers

Robust Stabilization of Discrete-Time Positive Switched Systems with Uncertainties and Average Dwell Time Switching

Further Result on Interval Observer Design for Discrete-Time Switched Systems and Application to Circuit Systems

Design of Robust Adaptive Neural Switching Controller for Robotic Manipulators with Uncertainty and Disturbances

Robust Switching Control of the Direct-Drive Servo Control Systems Based on Disturbance Observer for Switching Gain Reduction

Trajectory Switching Control of Robotic Manipulators Based on RBF Neural Networks