Studies On The Approximate Approac Hes Of Optimal Control For Nonlinear Discrete Systems

It is well known that the optimal control problem of nonlinear discrete-time system with a quadratic performance index under the necessary optimality conditions may lead to find a solution sequence of the nonlinear discrete TPBV problem. Generally, the analytic solution of TPBV problems does not exist but for some simplest cases, which arose us a lot of interests in finding approximate approaches to solve the optimal control problem of nonlinear systems. For decades, the studies of the approximate approaches of optimal control have received considerable attentions.In this thesis, two approximation approaches for solving the optimal control of linear discrete systems with time-delays and nonlinear discrete-time systems with a quadratic performance index are developed. The first approach is a non-delay transformation approach. A sequence of non-delay discrete systems is structured, which uniformly converges to the original discrete system with time-delay. Then the optimal control for the original discrete system is transformed into an optimal control sequence for non-delay systems. By intercepting a finite term of the optimal sequence, a suboptimal control law is obtained. Simulations show the algorithm has less workload and is easily implemented. Even there is large delay in the systems, the accuracy of the optimal solution and efficiency of the process are satisfied.The second approach is extended basing on the first approach from linear systems to nonlinear system. We develop a new successive approximation optimal control algorithm for discrete-time nonlinear systems with a quadratic performance index. An iterative process is proposed to find a solution sequence of the nonlinear TPBV problem, which is obtained from the necessary optimality conditions. We introduce a nonlinear term as an additional disturbance of the system and turn the system model into an iterative form. Using the successive approximation approachsystem and turn the system model into an iterative form. Using the successive approximation approach of differential equation theory, we transform the nonlinear two-point boundary value problem to a sequence of nonhomogeneous linear TPBV problems. By taking the finite iterative value, we obtain a suboptimal control law. Simulation examples are employed to test the validity of the optimal control algorithm.In Chapter 1, the backgrounds and knowledge of optimal control approaches are introduced. Two approximation approaches and illustrated examples are given in Chapter 2 and Chapter 3 respectively. The conclusion is given in the last Chapter.