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

The dissertation studies the OOT problem for nonlinear systems, time-delay andnonlinear systems, nonlinear interconnected large-scale systems and a class of affinenonlinear systems, and then dicusses the optimal control law is physically realizable.The main contents are given as follows:1. Firstly, the characteristics and research methods of time-delayed systems andnonlinear systems which are relative to research objects have been summarized. Nextthe relationship and development of optimal control problem and tracking problemhave been introduced. Then based on the prepareed work, the relative studies on theOOT problem for time-delay and nonlinear systems up to now and the main methodsare given in detail.2. The OOT problem of the nonlinear systems whose reference input is generallyproduced by an exosystem is studied. With the Maximum Value Principle, thetwo-point boundary value (TPBV) problems for the OOT of the time-delay andnonlinear systems have been obtained. By introducing a sensitivity parameter, theoriginal TPBV problem for solving the OOT control with delay and advance terms istransformed into a series of TPBV problems without delay or advance terms. Then bysolving the two-point boundary value problem sequence recursively, TPBV isobtained. A reference input observer is introduced such that the optimal control law isphysically realizable. Simulation examples are employed to test the validity of thepresented sensitivity algorithm.3. The OOT for nonlinear systems is considered. The nonlinear systems ingeneral form are expanded at zero and become to a form in which the one-order linearterms separated from the high-order nonlinear terms. Using a sensitivity parameter approach, and expanding the nonlinear two-point boundary value (TPBV) problemsled by the OOT control problem with respect to the sensitivity parameter, the originalnonlinear TPBV problem is transformed into a series of linear TPBV problemscontaining known low-order nonlinear terms. Algorithm of nonlinear expanding termsis obtained and substituting them into the recursion formula of adjoint vectorequations, the OOT control law consisting of linear terms and a nonlinearcompensation term can be approximately obtained. A simulation example is employedto test the validity of the presented algorithm.4. Considering the optimal output tracking (OOT) problem for nonlinearinterconnected large-scale dynamic systems, an approach for designing suboptimalcontrol law is proposed. By introducing a sensitivity parameterε,εis expanded atzero. By using the approach, the high order, coupling, nonlinear two-point boundaryvalue (TPBV) problem is transformed into a sequence of linear decoupling TPBVproblems. By solving this sequence of linear differential equations, costate vectorsequence of nonlinear interconnected, coupling large-scale dynamic systems isobtained. Then optimal control law consists of linear feedback term and nonlinear costatevector sum. By intercepting the frontal finite terms of costate vector sum, we obtaineda suboptimal control law and its algorithm. A simulation example illustrates theefficiency of the optimal output tracking control law designed.5. This paper considers an optimal control for a class of affine nonlinear systems. Animproved successive approximation approach is proposed. By introducing the SuccessiveApproximation Approach of the nonlinear differential equation theory, a linear two-pointboundary value problem sequence is constructed to approximate the nonlinear two-point boundaryvalue problem. A technique is employed to make sure the constructed linear two-point boundaryvalue problems of the approximating sequence homogeneous, Iteratively solving thisapproximating sequence, optimal control law of linear closed-loop feedback form is designed. Analgorithm is presented to design certain approximate optimal control law by truncating thefinite iteration. An illustrative example shows the validity of the algorithm 6. Finally, the main work in this dissertation is summarized and a proposition isindicated on the research work in the future.