Studies On Theory And Methods For Time-delay Switched Systems Optimal Control Problem

Optimal control is an important branch of modern control theory.The main idea for a controlled dynamic system,an optimal scheme can be found out from a class of allowable control strategies,so that the system can be transferred from an initial state to a target state,and its cost function can be optimized at the same time.Optimal control has important applications in many engineering practices,especially in industrial process control.Dynamic systems in process control problems are composed of multiple subsystems.In each subsystem,is related to not only the state functions and/or control functions at present but also the time instant in the past,and such systems are called time-delay switched systems.The time-delay switched systems optimal control problems exist widely in the metallurgy?chemical industry?machine design and so on.In the past few decades,it has gradually become a hot topic in the subject of optimization and control.This paper mainly studies the theory and numerical algorithm of time-delay switched systems optimal control problem.The chapters are arranged as follows:The first chapter gives a brief introduction to the mathematical model,theoretical analysis and solving method of general optimal control problems.In Chapter 2,we consider a time-delay switched systems with fixed time-delay.In order to overcome the computational difficulties caused by variable switching time,the new hybrid time-scaling transformation method is used to map the original dynamic system to a hybrid dynamic system which is defined on both the original time axis and the new time axis.However,this method increases the computational complexity of solving time-delay switched systems.Therefore,in this master's thesis,the analytic expression of the time-delay in the new time axis is given,and a complete form of time-scaling transformation method is obtained,which makes the new dynamic system completely defined on the new time axis with fixed switched times.Subsequently,the gradients of the cost and constraint functions with respect to time variables and system parameters are given.Finally,the gradient-based optimization method is used to solve the new problem,which improves the efficiency of solving the time-delay switched systems optimal control problem.In Chapter 3,we consider a class of time-delay switched systems with timedelay variables which are the control functions.When the time delay becomes a controllable variable,the whole dynamic system model will change with the value of the control variable,which is essentially different from the traditional time-delay switched systems.In fact,this particular dynamic system is highly uniform,and different control schemes correspond to different types of time-delay switched systems.For this particular dynamic system,firstly,we establish the optimality condition and analyze the existence and uniqueness of the system solution.Secondly,due to the particularity of the system,the numerical result cannot be calculated directly.Hence,we combine control parameterization method,time-scaling transformation technique and the gradient-based optimization method to solve this problem.In the last chapter,some concluding remarks and suggestions for future research directions are made.