Optimal Control For Time-delaye Or Nonlinear Systems And Its Application In Offshore Platform Structure With Time-delay

This dissertation investigates the problem of optimal control problem for a class of time-delay and nonlinear systems. For control delay, based on the transformations, the system with time delays is transformed to a non-delayed system. For state delay and nonlinear systems, the two-point boundary value (TPBV) problem is constructed. By solution TPBV an approximate optimal control law is obtained. We use this optimal control law to the vibration control problem of offshore jacket platforms. The contents of this dissertation are as follows:1. The optimal control problem for time-varying systems with multiple state delays is considered. Based on the transformations, the system with time delays is transformed to a non-delayed system and the optimal control problem with time-delays is transformed to equivalent optimal problem without time-delays. The optimal control law is derived from a Riccati equation. Simulation results demonstrate the effectiveness of the optimal tracking control law.2. The optimal control problem for nonlinear systems with time-delay is considered. A model transformation is first presented, which transforms the nonlinear system with time-delay into a system without delay formally. To solve the optimal control problem for nonlinear systems with time-delay is transformed into optimal control problem for non-delay nonlinear systems. Based on the optimal control theory, the two-point boundary value problem is constructed. Hence, the original problem is transformed into a problem of iterating a sequence of adjoint vector differential equations. Furthermore, by finite iterations of the solution sequence, an approximate optimal control law is obtained, which consists of an analytical state feedforward and feedback term and a time-delay compensation term in the limit of adjoint vector sequence. Simulation results demonstrate the effectiveness of the optimal control law.3. Successive approximate design of the optimal tracking controller for linear systems with time-delay is considered. A functional-based transformation is introduced, which transforms the system with control delay into a system without control delay formally. By applying the successive approximation approach of differential equations, the two-point boundary value problem with both time-delay and time-advance terms derived from the original optimal tracking control (OTC) problem is transformed into a sequence of linear TPBV problems without delay and advance terms. By finite iterations of the solution sequence, a suboptimal tracking control law is obtained. The reduced-order reference input observer is constructed to guarantee the feedforward compensator physically realizable. Simulation results demonstrate the effectiveness of the optimal tracking control law.4. Vibration control for the offshore platforms with delayed control under irregular wave forces is investigated. By a transformation, the original system with time delay is reduced into a delay free system. The unknown external wave load disturbances are supposed to be generated by an exosystem which is estimated by using the Morison equation and ocean wave theory. The feedforward and feedback optimal active control law includes the delay memory term and can guarantee the performance and stability of the system with time delay. The effectiveness and feasibility of the presented control law is demonstrated by a numerical example of jacket-type offshore platform.5. The vibration control problem of offshore jacket platforms is studied. The model of offshore platforms with nonlinear interactions of the pile-soil affected by the wave load disturbances and controlled time-delay is established. The wave loads are determined by using the Morison equation and are considered as disturbances with known dynamic characteristics but unknown initial conditions. By a transformation, the original system with time-delay is reduced into a delay free system. Based on the successive approximation approach, we propose an approximate optimal vibration control scheme for the nonlinear systems of the offshore jacket platforms. Numerical simulations illustrate the effectiveness of the proposed approach.