On Stability of Perturbed Nonlinear Switched Systems with Adaptive Reinforcement Learning

In this paper, a tracking control approach is developed based on an adaptive reinforcement learning algorithm with a bounded cost function for perturbed nonlinear switched systems, which represent a useful framework for modelling these converters, such as DC–DC converter, multi-level converter, etc. An optimal control method is derived for nominal systems to solve the tracking control problem, which results in solving a Hamilton–Jacobi–Bellman (HJB) equation. It is shown that the optimal controller obtained by solving the HJB equation can stabilize the perturbed nonlinear switched systems. To develop a solution to the translated HJB equation, the proposed neural networks consider the training technique obtaining the minimization of square of Bellman residual error in critic term due to the description of Hamilton function. Theoretical analysis shows that all the closed-loop system signals are uniformly ultimately bounded (UUB) and the proposed controller converges to optimal control law. The simulation results of two situations demonstrate the effectiveness of the proposed controller.

[1]  Xiaoguang Liu,et al.  Optimized Adaptive Nonlinear Tracking Control Using Actor–Critic Reinforcement Learning Strategy , 2019, IEEE Transactions on Industrial Informatics.

[2]  Yuzhu Huang.  Optimal guaranteed cost control of uncertain non-linear systems using adaptive dynamic programming with concurrent learning , 2018 .

[3]  Shuzhi Sam Ge,et al.  Adaptive Tracking Control of Surface Vessel Using Optimized Backstepping Technique , 2019, IEEE Transactions on Cybernetics.

[4]  Yan-Jun Liu,et al.  ADP-Based Online Tracking Control of Partially Uncertain Time-Delayed Nonlinear System and Application to Wheeled Mobile Robots , 2020, IEEE Transactions on Cybernetics.

[5]  Tianping Zhang,et al.  Adaptive optimal dynamic surface control of strict‐feedback nonlinear systems with output constraints , 2020 .

[6]  Zhong-Ping Jiang,et al.  Output-feedback adaptive optimal control of interconnected systems based on robust adaptive dynamic programming , 2016, Autom..

[7]  Changyin Sun,et al.  ADP-Based Robust Tracking Control for a Class of Nonlinear Systems With Unmatched Uncertainties , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[8]  D. Vinnikov,et al.  Step-Up Series Resonant DC–DC Converter with Bidirectional-Switch-Based Boost Rectifier for Wide Input Voltage Range Photovoltaic Applications , 2020, Energies.

[9]  Min Xiao,et al.  Stabilization of discrete-time switched singular systems with state, output and switching delays , 2019, J. Frankl. Inst..

[10]  Andrei Blinov,et al.  Review of Isolated Matrix Inverters: Topologies, Modulation Methods and Applications , 2020 .

[11]  Ding Wang,et al.  Adaptive-Critic-Based Robust Trajectory Tracking of Uncertain Dynamics and Its Application to a Spring–Mass–Damper System , 2018, IEEE Transactions on Industrial Electronics.

[12]  Yu Guo,et al.  Online adaptive optimal control for continuous-time nonlinear systems with completely unknown dynamics , 2016, Int. J. Control.

[13]  Qinglai Wei,et al.  Adaptive Critic Learning for Constrained Optimal Event-Triggered Control With Discounted Cost , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[14]  Chaoxu Mu,et al.  Neural-network-based adaptive guaranteed cost control of nonlinear dynamical systems with matched uncertainties , 2017, Neurocomputing.

[15]  Jie Lian,et al.  Event-triggered control for a class of switched uncertain nonlinear systems , 2020, Syst. Control. Lett..

[16]  Frank L. Lewis,et al.  Reinforcement Learning-Based Adaptive Optimal Exponential Tracking Control of Linear Systems With Unknown Dynamics , 2019, IEEE Transactions on Automatic Control.

[17]  Ming-Li Chiang,et al.  Adaptive stabilization of a class of uncertain switched nonlinear systems with backstepping control , 2014, Autom..

[18]  Pierluigi Siano,et al.  Design and Development of Non-Isolated Modified SEPIC DC-DC Converter Topology for High-Step-Up Applications: Investigation and Hardware Implementation , 2020 .

[19]  Bart De Schutter,et al.  A novel Lyapunov function for a non-weighted L2 gain of asynchronously switched linear systems , 2018, Autom..

[20]  F. Lewis,et al.  Online adaptive algorithm for optimal control with integral reinforcement learning , 2014 .

[21]  Kyriakos G. Vamvoudakis,et al.  Model-free event-triggered control algorithm for continuous-time linear systems with optimal performance , 2018, Autom..

[22]  Hermes José Loschi,et al.  Aggregated Conducted Electromagnetic Interference Generated by DC/DC Converters with Deterministic and Random Modulation , 2020 .

[23]  Youxian Sun,et al.  Robust ADP Design for Continuous-Time Nonlinear Systems With Output Constraints , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[24]  Tieshan Li,et al.  Adaptive Reinforcement Learning Neural Network Control for Uncertain Nonlinear System With Input Saturation , 2020, IEEE Transactions on Cybernetics.

[25]  Lei Chen,et al.  Modified value-function-approximation for synchronous policy iteration with single-critic configuration for nonlinear optimal control , 2019, Int. J. Control.

[26]  Corentin Briat,et al.  Convex conditions for robust stabilization of uncertain switched systems with guaranteed minimum and mode-dependent dwell-time , 2015, Syst. Control. Lett..

[27]  Weiming Xiang,et al.  Mode-identifying time estimation and switching-delay tolerant control for switched systems: An elementary time unit approach , 2016, Autom..

[28]  Li Jin,et al.  An Improved Stability Criterion for Load Frequency Control of Power Systems with Time-Varying Delays , 2020, Energies.

[29]  Jae Young Lee,et al.  Adaptive dynamic programming for discrete-time linear quadratic regulation based on multirate generalised policy iteration , 2018, Int. J. Control.

[30]  James Lam,et al.  On stability and H∞ control of switched systems with random switching signals , 2018, Autom..