离散非线性系统的输入状态稳定与镇定
发布时间：2018-08-11 09:27
【摘要】：近年来,随着计算机技术的高速发展,非线性离散系统的研究变得尤为重要,而输入状态稳定作为鲁棒控制研究的一个重要分支,对于分析带有外部扰动输入的非线性系统具有较好的效果,因此输入状态稳定性已经成为一种较为普遍的非线性系统的分析方法。输入状态稳定分析已经涉及众多理论研究领域并具有较强的工程背景,例如机器人控制系统、某些工程系统、生物系统、智能高速公路系统等。本文主要研究了几类非线性系统在一定条件下的输入状态稳定性以及一类非线性系统的输入状态镇定问题。(1)针对一类离散时间非线性级联系统,运用Lyapunov函数方法分析了由两个积分输入状态稳定(Integral input-to-state stability,iISS)的子系统组成的级联系统仍然是ilSS的,给出该级联系统达到iISS的充分条件,并将结果应用于线性级联的情况下,通过数值仿真证明了推导结果的正确性。(2)针对一类离散时间切换非线性系统的输入状态稳定性研究问题,首先研究了非切换情况下,系统的全局渐近稳定(Global asymptotic stability,GAS)和输入状态稳定(Input-to-state stability,ISS),然后通过多Lyapunov函数方法并结合比较定理将结果推广到离散切换非线性系统上,给出了切换系统GAS和ISS的充分条件。运用切换信号的平均停留时间方法研究了切换系统的ISS。最后,通过数值实例证明了研究结果的正确性。(3)针对一类带有外部扰动的离散时间非线性严反馈系统,利用Backstepping设计方法,设计了带有外部扰动的离散时间严反馈控制系统的输入状态镇定控制器,并利用Lyapunov函数理论对闭环系统进行了 ISS分析,最后通过数值仿真验证了所研究控制算法的正确性。
[Abstract]:In recent years, with the rapid development of computer technology, the study of nonlinear discrete systems becomes more and more important, and input state stability is an important branch of robust control. The analysis of nonlinear systems with external disturbances has a good effect, so the stability of input states has become a general analysis method for nonlinear systems. Input state stability analysis has been involved in many theoretical fields and has a strong engineering background, such as robot control systems, some engineering systems, biological systems, intelligent highway systems and so on. In this paper, the input state stability of some nonlinear systems under certain conditions and the input state stabilization of a class of nonlinear systems are studied. (1) for a class of discrete-time nonlinear cascaded systems, In this paper, the Lyapunov function method is used to analyze that the cascade system composed of two Integral input-to-state input state stability subsystems is still ilSS. The sufficient conditions for the cascade system to reach iISS are given, and the results are applied to the linear cascade. Numerical simulations show that the derivation is correct. (2) for a class of discrete-time switched nonlinear systems, the input state stability is studied. The globally asymptotically stable (Global asymptotic stability gas) and the input state stability of the system are given. Then the results are extended to discrete-time switched nonlinear systems by the method of multiple Lyapunov functions and the comparison theorem. The sufficient conditions of GAS and ISS for switched systems are given. The ISSs of switched systems are studied by means of the average residence time (RTD) method of switched signals. Finally, a numerical example is given to prove the correctness of the research results. (3) for a class of discrete-time nonlinear strict feedback systems with external disturbances, the Backstepping design method is used. The input state stabilization controller of discrete-time strict feedback control system with external disturbance is designed. The ISS analysis of the closed-loop system is carried out by using Lyapunov function theory. Finally, the correctness of the proposed control algorithm is verified by numerical simulation.
【学位授予单位】：济南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP13
本文编号：2176591
[Abstract]:In recent years, with the rapid development of computer technology, the study of nonlinear discrete systems becomes more and more important, and input state stability is an important branch of robust control. The analysis of nonlinear systems with external disturbances has a good effect, so the stability of input states has become a general analysis method for nonlinear systems. Input state stability analysis has been involved in many theoretical fields and has a strong engineering background, such as robot control systems, some engineering systems, biological systems, intelligent highway systems and so on. In this paper, the input state stability of some nonlinear systems under certain conditions and the input state stabilization of a class of nonlinear systems are studied. (1) for a class of discrete-time nonlinear cascaded systems, In this paper, the Lyapunov function method is used to analyze that the cascade system composed of two Integral input-to-state input state stability subsystems is still ilSS. The sufficient conditions for the cascade system to reach iISS are given, and the results are applied to the linear cascade. Numerical simulations show that the derivation is correct. (2) for a class of discrete-time switched nonlinear systems, the input state stability is studied. The globally asymptotically stable (Global asymptotic stability gas) and the input state stability of the system are given. Then the results are extended to discrete-time switched nonlinear systems by the method of multiple Lyapunov functions and the comparison theorem. The sufficient conditions of GAS and ISS for switched systems are given. The ISSs of switched systems are studied by means of the average residence time (RTD) method of switched signals. Finally, a numerical example is given to prove the correctness of the research results. (3) for a class of discrete-time nonlinear strict feedback systems with external disturbances, the Backstepping design method is used. The input state stabilization controller of discrete-time strict feedback control system with external disturbance is designed. The ISS analysis of the closed-loop system is carried out by using Lyapunov function theory. Finally, the correctness of the proposed control algorithm is verified by numerical simulation.
【学位授予单位】：济南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP13
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