Adaptive Dynamic Programming-based Decentralized Robust Control Via Event-triggering Mechanism

With the increasing demand for production quality and economic benefits,the existing systems gradually tend to be complex and large-scale.Limited by the calculation resource,the centralized control method can not respond to the demand.Inspired by the idea of “divide and rule”,the large-scale system(well known as the interconnected system)is decomposed into several subsystems,and then the decentralized controllers are designed for each subsystems independently.Without the global information,the decentralized control can effectively meet the real-time requirements,so it has attracted extensive attention in the control field.Simultaneously,with the increase of the scale of the system,the problems of modeling accuracy and resource utilization are serious in large-scale systems.Therefore,it is significant to study the decentralized robust control method.Adaptive dynamic programming(ADP),combining the ideas of dynamic programming,reinforcement learning and neural networks,is an excellent method with self-learning and optimization.It can effectively solve the problem of “curse of dimensionality”.Thus,it has great prospect in solving the robust optimal control problem.The main contents of this study are divided into two parts:(1)The guaranteed cost control problem of the matched interconnected systems is considered,and the ADP-based event-triggered decentralized guaranteed cost control method is proposed.Firstly,the cost function of the isolated subsystems are constructed with the upper bound function of the interconnection.The robust stabilization of the interconnected system can be transformed into the guaranteed cost control problem of the isolated subsystem.Then,a single-critic network is constructed to evaluate strategy and improve strategy,and the trigger conditions are deduced according to Lyapunov stability theory.Eventually,the effectiveness of the proposed algorithm is verified by simulation.(2)For the mismatched interconnected system,a novel ADP-based auxiliary control method is developed.To overcome the difficulty of mismatched interconnection,the auxiliary control is designed to compensate it,and the augmented control system is constructed for the isolated subsystem.The robust optimal solution is obtained by solving the Hamilton-JacobiBellman(HJB)equation.The approximate numerical solution is obtained iteratively based on the single-critic network framework.Employing Lyapunov stability theory,the trigger condition and robust control laws are derived to ensure the convergence and robust stability of the closed-loop system.Finally,the simulation result is to verify the method feasibility.In summary,this thesis mainly studies the ADP-based robust decentralized control with the limitation of communication and computational resources.It mainly involves neural networks,adaptive dynamic programming and modern control theory,aiming to develop ADP to solve the robust control problem of the interconnected systems.