Studies On The Approximate Design Of Optimal Controller For Nonlinear Systems With Time-Delay

Nonlinear and time-delay exist in many systems such as industry, aerospace and ocean engineering. For example, the attitude and movement trajectory control systems for towed vehicles are nonlinear time-delay systems with six degree-of-freedom. And the vibration control systems for offshore platforms are nonlinear systems with time-delay. But for the general optimal control for nonlinear systems with time-delay, the analytical solution does not exist. So the analysis of optimal control for nonlinear systems with time-delay is significant both in theory and in practice.Based on the present situation on the optimal control, this thesis studies the successive approximation approach of optimal control for nonlinear systems and time-delay systems. The major results are shown as follows.1. The history of the development in optimal control is reviewed firstly. The latest research tendency in this field and the main methods of optimal control problem for nonlinear systems with time-delay are alsointroduced.2. A successive approximation algorithm of feedforward and feedbackoptimal control is developed for finite time linear systems with state time-delay affected by persistent disturbances. The linear two-point boundary value (TPRV) problem with both time-delay terms and time-advanceterms is transformed into a sequence of nonhomogeneous linear TPBV problems without time-delay terms and time-advance terms. We prove the sequence of the solutions uniformly converges to the optimal control law for the systems. The optimal control law obtained is composed of feedforward and feedback optimal terms without time-delay in analytic forms and a compensation term with time-delay in a sequence limit form of adjoint vectors. By taking the finite-times iteration of the compensation sequence, we obtain a finite time suboptimal control law.3. The successive approximation algorithm of feedforward and feedback optimal control for finite time linear systems with state time-delay affected by persistent disturbances is applied to the optimal control for infinite time linear systems with state time-delay affected by persistent disturbances.4. Using a successive approximation algorithm of feedforward and feedback, optimal control of linear large-scale systems with state time-delay affected by persistent disturbances is solved. The TPBV problem with time-delay terms, time-advance terms and coupling terms is transformed into a sequence of nonhomogeneous linear TPBV problems without time-delay terms, time-advance terms and coupling terms. We prove the sequence of the solutions uniformly converges to the optimal control law for the systems. The optimal control law obtained is composed of feedforward and feedback optimal terms without time-delay in analytic forms and a compensation term with time-delay in a sequence limit form of adjoint vectors.5. A successive approximation approach designing optimal controllers is discussed for affine nonlinear discrete-time systems. By constructing a sequence of linear TPBV problems that uniformly convergent to the optimal solution for the system, the original optimal control problems are transformed into a sequence of nonhomogeneous linear TPBVproblems. The optimal control law consists of an accurate linear term and a nonlinear compensating series.6. The successive approximation approach designing optimal controllers for affine nonlinear discrete-time systems is investigated to the optimal control for nonlinear discrete-time systems.7. Optimal control of nonlinear discrete-time systems with persistent disturbances is considered by using a successive approximation algorithm of feedforward and feedback.8. The conclusions are given finally. And the directions for the future research work are indicated.