【作者】 张城明；

【导师】 唐功友；

【作者基本信息】 中国海洋大学 ， 计算机应用技术， 2010， 博士

【摘要】 本文研究控制时滞和状态时滞系统及非线性系统最优问题。对于控制时滞项,采用泛函变换方法使系统简化。对于状态时滞项与非线性的最优控制问题导致的两点边值问题,本文应用逐次逼近算法,从而得到最优控制律。并且把本文对时滞与非线性的最优控制的方法应用到海洋平台的减振控制中。本文的研究内容概括如下：1.研究含有多状态时滞的时变系统的二次型最优控制控制问题。首先将含有多状态时滞的时变系统转化为无时滞系统,性能指标也相应的转化。从而,将时滞系统最优控制问题转化成等价无时滞系统的最优控制问题。然后,通过求解Riccati方程,设计最优控制律。利用实例验证了所设计的最优控制律的有效性。其算法简便,有效。2.针对一类含有状态时滞非线性系统,研究其最优控制问题。首先,通过一种模型转换方法把含有时滞的非线性系统转换成为形式上无时滞的非线性系统。接下来的问题转换成为怎样解决不含有时滞的非线性基于二次性能指标的最优控制问题。根据最有控制理论,这个问题导致求解一个两点边值问题。基于逐次逼近算法构造了两个线性非齐次向量微分方程迭代序列,并且证明了其解序列的一致收敛性从而将原最优控制问题转化为一族伴随向量微分方程序列的迭代求解问题。进而通过其解序列的有限次迭代,得到了一个由解析的状态前馈反馈项和伴随向量序列极限形式的时滞补偿项组成的近似最优控制律。仿真实例,证明该算法的有效性。3.针对含有控制与状态时滞系统的最优跟踪控制问题,设计了一种基于向量迭代的近似算法。首先把含有双时滞的原系统进行一个泛函变换,把问题转化成为形式上只有状态时滞系统的最优跟踪问题。通过设计一个逐次逼近方法来解决此状态时滞问题导致的两点边值问题中含有滞后项与超前项方程。通过构造降维状态观测器解决了参考模型中状态的物理实现。仿真实例证明了该最优跟踪控制律的有效性,并且易于实现,计算简便。4.研究波浪力作用下的含有控制时滞的海洋平台系统振动控制。首先,研究含有控制时滞的海洋平台的模型及其模型的无时滞转化。其次波浪力的模型,基于波浪理论和工程力学,获得了产生不规则波浪力的外系统。最后,根据最优扰动抑制的理论,我们设计了前馈反馈最优控制律。在控制律的设计中,考虑了波浪力的信息,因此,既能够有效降低海洋平台的振动,又能够保持小功耗。理论结果通过海洋平台的数值例子进行了验证。5.研究一类含有控制时滞和非线性项海洋平台系统的振动控制。其中非线性项是由于桩土相互作用的非线性力引起的。根据Morison方程我们得到了初值未知的不规则海浪力外系统。通过无时滞转换我们把原来海洋平台系统转换形式上不含时滞的系统。采用逐次逼近方法,我们对非线性海洋平台系统设计了近似最优振动控制律。数值仿真证明该方法的有效性。更多还原

【Abstract】 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.更多还原