Study And Application Of Optimal Output Tracking Control For Discrete Time-delay And Nonlinear Systems

As one of the important application aspects of the optimal control theory, the optimal output tracking (OOT) problem has achieved great advancement and applications in variety areas including modern industries, national defenses and scientific researches in recently. The dissertation studies the OOT problem about controller designing and realizing for discrete time-delay systems, discrete time-delay systems with persistent disturbances and nonlinear systems whose reference input to be tracked is produced by a general exosystem, and then gives the results with application. The main contents are given as follows:1. Firstly, the characteristics and research methods of discrete systems, time-delayed systems and nonlinear systems which are relative to research objects have been summarized. Next the relationship and development of optimal control problem and tracking problem have been introduced. Then based on the prepare work, the relative studies on the OOT problem for time-delay and nonlinear systems up to now and the main methods are given in detail.2. The OOT problem of the discrete time-delay systems whose reference input is generally produced by an exosystem is studied. For the finite-time and infinite-time horizon quadratic performance indexes, the two-point boundary value (TPBV) problems for the OOT of the discrete time-delay systems have been obtained respectively. By introducing a sensitivity parameter, the original TPBV problem for solving the OOT control with delay and advance terms is transformed into a series of TPBV problems without delay or advance terms. Then by solving the two-point boundary value problem sequence recursively, the optimal output tracking control law consisting of linear analytic functions and a compensation term is obtained. The analytic functions can be solved by a Riccati equation and matrix equation. The compensation term can be obtained by a recursion formula of adjoint vector equations. A reference input observer is constructed such that the optimal control law is physically realizable. Simulation examples are employed to test the validity of the presented sensitivity algorithm.3. The OOT for discrete time-delay systems affected by persistent disturbances with infinite and finite horizon quadratic performance indexes is considered. For the OOT problem of the discrete time-delay systems whose reference input is generally produced by an exosystem, the state of the exosystem is used as the information of feedforward control action, instead of constructing an dimension expanded system. Because a feedforward control action is added, the tracking error can be reduced. By designing two external disturbances observers, the physically realizable problem of the OOT control law is solved. In this case we compared simulation results by the method proposed in this paper and that based on classical optimal control theory with expanding the system's dimension.4. The OOT problem for a class of discrete nonlinear systems in which the linear terms can be separated is considered. The nonlinear systems in general form are expanded at zero and become to a form in which the one-order linear terms separated from the high-order nonlinear terms. Using a sensitivity parameter approach, and expanding the nonlinear two-point boundary value (TPBV) problems led by the OOT control problem with respect to the sensitivity parameter, the original nonlinear TPBV problem is transformed into a series of linear TPBV problems containing known low-order nonlinear terms. Algorithm of nonlinear expanding terms is obtained and substituting them into the recursion formula of adjoint vector equations, the OOT control law consisting of linear terms and a nonlinear compensation term can be approximately obtained. A simulation example from continuously stirred tank reactor (CSTR) is employed to test the validity of the presented algorithm.5. The obtained theories of the OOT problem for discrete nonlinear systems are used into the studies of the control problem for autonomous underwater vehicles (AUV). The AUV using for ocean observation or deep water photography is considered. For this kind of AUV usually moving at a low speed, the general 6-dof model of underwater vehicles is simplified to a 4-dof one according to AUV's purpose. The linear part is departed from the nonlinear part of the systems, and the theories of the OOT problem for discrete nonlinear systems are applied to design the OOT controller of AUV. A simulation example from AUV is given to show the effectiveness of the presented algorithm.6. Finally, the main work in this dissertation is summarized and a proposition is indicated on the research work in the future.