摘要
近年来,如何设计鲁棒控制器使不确定系统满足鲁棒稳定性的同时满足一定的性能指标,已经引起了广泛的关注。解决这个问题的方法之一是Chang和Peng提出的保成本控制的方法。研究这一问题的目的是设计一个保成本控制器,使得闭环系统对于所有允许的不确定性渐近稳定,并且闭环性能指标不超过某个确定的上界。众所周知,参数不确定性和时间滞后经常是系统性能退化和系统不稳定的主要原因。因此,对于不确定时滞系统的保成本控制的研究越来越引起人们的研究兴趣,并且在线性系统中已经取得了较多有价值的成果,但由于非线性系统的特殊性和复杂性,在非线性系统中的研究成果还不多见。
海洋工程中的许多系统都是典型的不确定非线性时滞系统,例如海洋平台振动控制系统、拖曳体的轨迹和姿态控制系统以及船舶航向控制系统等。如何使这些具有不确定因素的非线性系统保持稳定性并满足一定的性能指标,是研究的热点。因此,不确定非线性时滞系统的保成本控制无论从理论上还是在实践中都是很有意义的。
本文利用Lyapunov稳定性理论和线性矩阵不等式的方法,研究具有范数有界不确定性的非线性时滞系统的保成本控制问题,主要内容如下:
1.相对于连续系统已经取得的丰硕成果,离散系统保成本控制问题的结论还不多见。本文首先研究具有状态时滞的不确定非线性离散系统的保成本控制问题。利用线性矩阵不等式方法给出保成本控制律存在的条件和保成本控制器的设计方法。通过求解一个由线性矩阵不等式表示的凸优化问题,得到系统保成本的最小上界。
2.虽然利用现有的方法得出的控制器对于系统的不确定性是鲁棒稳定的,但是没有考虑控制器的增益,当控制器参数存在摄动时,传统的鲁棒控制方法表现出高度的脆弱性。本文利用线性矩阵不等式的方法,在系统的控制器参数存在加法式摄动和乘法式摄动两种情况下,研究了具有状态时滞的不确定非线
Recently, the problem of designing robust controllers to make uncertain systems not only be stable but also guarantees an adequate level of performance has drawn considerable attention. One approach to this problem is the guaranteed cost control approach first introduced by Chang and Peng. This approach is to design a controller such that the closed-loop system is asymptotically stable for all admissible uncertainties and the closed-loop cost function value is not more than a specified upper bound. It is well known that time-delays as well as parameter uncertainties are frequently the main cause of deterioration of systems performance and instability of systems. Therefore, there has been increasing interest in the guaranteed cost control of uncertain time-delay systems, and many significant results have been presented. However, there have been few results for nonlinear systems, owing to their particularity and complexity.There are lots of uncertain nonlinear time-delay systems in the ocean engineering, for instances, offshore platform vibration control system, control systems for the tracking and positioning of towed vehicles, ship motion control systems, and so on. How to design controllers which make these systems not only be stable but also guarantee an adequate level of performance is a hot research field. Therefore, it' s of important theoretical and practical meaning to study the problems of guaranteed cost control for the uncertain nonlinear time-delay systems.
Based on Lyapunov stability theory and linear matrix inequality approach, the problems of guaranteed cost control for nonlinear time-delay systems with norm-bounded uncertainties are considered. The main contents in this paper are as follows:1. There are few results for the discrete-time guaranteed cost control problem, compared with the existed results for continuous-time systems. Firstly, the guaranteed cost control problem for uncertain nonlinear discrete-time systems with state-delay is considered. Several criteria for the existence of the guaranteed cost control law and design method of the controller are derived in terms of LM1. An upper bound on the guaranteed cost is minimized by solving a convex optimization problem with LMIs.2. Although the controllers yielded by using the existed methods are robust with regard to system uncertainties, their robustness with regard to controller uncertainties has not been considered. The controller may be very sensitive or fragile, with respect to perturbations in the controller coefficients. In this paper, using the LMI method, the nonfragile guaranteed cost control problem is discussed for uncertain nonlinear time-delay systems under two classes of controller gain perturbations, namely, additive form and multiplicative form. The existence conditions and design method of the nonfragile guaranteed cost controller are given in terms of LMI. Solving a convex optimization problem gives the optimal guaranteed cost value of the system.3. In some real plants, the system delay varies with the time going. Therefore, the guaranteed cost control problem for the systems with time-varying delay needs to be considered. In this paper, the nonfragile guaranteed cost control problem for the uncertain nonlinear systems with time-varying delay is Investigated. Using the Lyapunov functional method combined with LMI technique, some delay-dependent conditions for the existence of such controller are derived. By solving the specified LMIs,
the design method for the guaranteed cost controller is given. The solutions of the optimal problem give the minimal upper bound on the cost function.4. There are lots of real control systems with multiple time delays in the ocean engineering, and the results on guaranteed cost control for systems with multiple time-delays are seldom seen. The problem of nonfragile guaranteed cost control for a class of nonlinear systems with multiple time-delays is studied in this paper. A state feedback nonfragile guaranteed cost control law is given in terms of LMI. An upper bound on the guaranteed cost is minimized by solving a convex optimization problem.5. The problem of nonfragile guaranteed cost control is discussed for the uncertain nonlinear discrete systems with time-varying delay. By representing the time-delay system in the descriptor form and using the new bounding method on the cross term, new delay-dependent sufficient condition for the existence of the guaranteed cost controller is given in terms of LMI. A convex optimization problem is introduced to find the optimal nonfragile guaranteed cost controller which minimizes the upper bound on the cost function.The last section summarizes the main work in this paper and prospects the research of uncertain nonlinear guaranteed cost control problems in the future.
引文
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