随机、不确定非线性系统的若干控制问题研究
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摘要
自从随机稳定性理论被建立和发展以来,随机非线性系统控制器设计和稳定性分析取得了丰富的理论成果.由于时滞现象广泛存在于许多的实际系统中,并且时滞的存在往往是导致系统性能恶化和不稳定的一个重要因素.因此,近些年来,随机非线性时滞系统的研究受到了广泛的关注.本文针对几类重要的随机、不确定非线性系统,研究了控制器设计和稳定性分析等问题.主要成果包括:
1、针对一类具有随机逆动态的随机高阶非线性系统,研究了状态反馈控制问题.在子系统的逆动态是随机输入状态稳定(SISS)的假设下,通过推广增加幂次积分方法,选取合适的Lyapunov函数,并使用改变供能函数的思想,构造出一个光滑的状态反馈控制器使得闭环系统的平衡点在原点是依概率全局渐近稳定的,状态几乎处处调节到零点.
2、本章首次研究了一类具有时变时滞的随机高阶非线性系统的输出反馈控制.通过在随机系统中引入增加幂次积分方法和标量变换,并且选取一个合适的Lyapunov-Krasoviskii泛函,构造出一个输出反馈控制器使得闭环系统是依概率全局渐近稳定的,输出几乎处处调节到零点.
3、本章引入了齐次占优方法,解决了一类具有时变时滞的随机高阶非线性系统的状态反馈镇定问题.在漂移和扩散项的微弱条件下,通过使用齐次占优方法,并解决设计和分析过程中的一些障碍,构造出一个状态反馈控制器使得闭环系统是依概率全局渐近稳定的.
4、本章进一步研究了具有时变时滞的随机高阶非线性系统的输出反馈镇定问题.在非线性漂移和扩散向量场的微弱条件下,通过使用齐次占优方法的思想,巧妙的选取一个合适的Lyapunov-Krasoviskii泛函,并成功的解决了设计和分析过程中的一些障碍,构造出一个输出反馈控制器使得闭环系统是依概率全局渐近稳定的.
5、本章研究了一类具有时变时滞的随机前馈非线性系统.通过将齐次占优方法引入到随机系统中,构造出一个状态反馈控制器使得闭环系统是依概率全局渐近稳定的.
6、本章通过使用MT滤波器和反推设计方法研究了一类具有动态输入、输出和非线性交互作用的关联系统的分散自适应输出反馈镇定问题.并且证明了基于MT滤波器的闭环分散系统是全局一致有界的,除了参数估计外的所有信号都渐近调节到零点,并且系统输出的L2和L∞范数可通过设计参数的函数来限定.
7、本章通过使用MT滤波器和反推设计方法研究了一类具有未知输入和输出时滞的非线性系统的自适应输出反馈镇定问题.并且证明了闭环系统的所有信号都是全局一致有界的,输出调节到零点.
Ever since the stochastic stability theory is established and improved, the controllerdesign and stability analysis for stochastic nonlinear systems have achieved remarkable the-oretical results. Due to time-delay phenomena existing in many practical systems, and theexistence of time-delay being often a significant cause of instability and deteriorative per-formance, the study on stochastic nonlinear time-delay systems has received much attentionin recent years. This paper investigated problems of controller design and stability analysisfor several classes of important stochastic、uncertain nonlinear systems. The main contri-butions include:
1. For a class of stochastic high-order nonlinear systems with stochastic inverse dynam-ics, this chapter investigates state-feedback control problem. Under the assumption thatthe inverse dynamics of the subsystem is stochastic input-to-state stable, by extending theadding a power integrator technique, choosing an appropriate Lyapunov function and usingthe idea of changing supply function, a smooth state-feedback controller is constructed toensure that the equilibrium at the origin of the closed-loop system is globally asymptoticallystable in probability and the states can be regulated to the origin almost surely.
2. This chapter investigates output-feedback control for a class of stochastic high-ordernonlinear systems with time-varying delay for the first time. By introducing the adding apower integrator technique in the stochastic systems and a rescaling transformation, andchoosing an appropriate Lyapunov-Krasoviskii functional, an output-feedback controller isconstructed to render the closed-loop system globally asymptotically stable in probability,the output can be regulated to the origin almost surely.
3. The homogeneous domination approach is introduced to solve the state feedback sta-bilization problem for a class of stochastic high-order nonlinear systems with time-varyingdelay. Under the weaker conditions on the drift and difusion terms, by using the homo-geneous domination approach and solving several troublesome obstacles in the design andanalysis procedure, a state feedback controller is constructed to render the closed-loop systemglobally asymptotically stable in probability.
4. This chapter further discusses the output feedback stabilization problem for stochas-tic high-order nonlinear systems with time-varying delay. Under the weaker conditions onnonlinearities in drift and difusion vector fields, by using the idea of homogeneous dom- ination approach, skillfully choosing an appropriate Lyapunov-Krasoviskii functional, andsuccessfully solving several troublesome obstacles in the design and analysis procedure, anoutput feedback controller is constructed to render the closed-loop system globally asymp-totically stable in probability.
5. This chapter investigates a class of stochastic feedforward nonlinear systems withtime-varying delay. By introducing the homogeneous domination approach to stochasticsystem, a state feedback controller is constructed to render the closed-loop system globallyasymptotically stable in probability.
6. This paper studies the problem of decentralized adaptive output feedback stabiliza-tion for a class of interconnected systems with dynamic input and output interactions andnonlinear interactions by using MT-filters and the backstepping design method. It is shownthat the closed-loop decentralized system based on MT-filters is globally uniformly bounded,all the signals except for the parameter estimates can be regulated to zero asymptotically,and the L2and L∞norms of the system outputs are also be bounded by functions of designparameters.
7. This chapter investigates the problem of adaptive output feedback stabilizationusing MT-filters and the backstepping design method for a class of nonlinear systems withunknown input and output time-delay. It is shown that all the signals in the closed-loopsystem are globally uniformly bounded, and the output can be regulated to zero.
1、针对一类具有随机逆动态的随机高阶非线性系统,研究了状态反馈控制问题.在子系统的逆动态是随机输入状态稳定(SISS)的假设下,通过推广增加幂次积分方法,选取合适的Lyapunov函数,并使用改变供能函数的思想,构造出一个光滑的状态反馈控制器使得闭环系统的平衡点在原点是依概率全局渐近稳定的,状态几乎处处调节到零点.
2、本章首次研究了一类具有时变时滞的随机高阶非线性系统的输出反馈控制.通过在随机系统中引入增加幂次积分方法和标量变换,并且选取一个合适的Lyapunov-Krasoviskii泛函,构造出一个输出反馈控制器使得闭环系统是依概率全局渐近稳定的,输出几乎处处调节到零点.
3、本章引入了齐次占优方法,解决了一类具有时变时滞的随机高阶非线性系统的状态反馈镇定问题.在漂移和扩散项的微弱条件下,通过使用齐次占优方法,并解决设计和分析过程中的一些障碍,构造出一个状态反馈控制器使得闭环系统是依概率全局渐近稳定的.
4、本章进一步研究了具有时变时滞的随机高阶非线性系统的输出反馈镇定问题.在非线性漂移和扩散向量场的微弱条件下,通过使用齐次占优方法的思想,巧妙的选取一个合适的Lyapunov-Krasoviskii泛函,并成功的解决了设计和分析过程中的一些障碍,构造出一个输出反馈控制器使得闭环系统是依概率全局渐近稳定的.
5、本章研究了一类具有时变时滞的随机前馈非线性系统.通过将齐次占优方法引入到随机系统中,构造出一个状态反馈控制器使得闭环系统是依概率全局渐近稳定的.
6、本章通过使用MT滤波器和反推设计方法研究了一类具有动态输入、输出和非线性交互作用的关联系统的分散自适应输出反馈镇定问题.并且证明了基于MT滤波器的闭环分散系统是全局一致有界的,除了参数估计外的所有信号都渐近调节到零点,并且系统输出的L2和L∞范数可通过设计参数的函数来限定.
7、本章通过使用MT滤波器和反推设计方法研究了一类具有未知输入和输出时滞的非线性系统的自适应输出反馈镇定问题.并且证明了闭环系统的所有信号都是全局一致有界的,输出调节到零点.
Ever since the stochastic stability theory is established and improved, the controllerdesign and stability analysis for stochastic nonlinear systems have achieved remarkable the-oretical results. Due to time-delay phenomena existing in many practical systems, and theexistence of time-delay being often a significant cause of instability and deteriorative per-formance, the study on stochastic nonlinear time-delay systems has received much attentionin recent years. This paper investigated problems of controller design and stability analysisfor several classes of important stochastic、uncertain nonlinear systems. The main contri-butions include:
1. For a class of stochastic high-order nonlinear systems with stochastic inverse dynam-ics, this chapter investigates state-feedback control problem. Under the assumption thatthe inverse dynamics of the subsystem is stochastic input-to-state stable, by extending theadding a power integrator technique, choosing an appropriate Lyapunov function and usingthe idea of changing supply function, a smooth state-feedback controller is constructed toensure that the equilibrium at the origin of the closed-loop system is globally asymptoticallystable in probability and the states can be regulated to the origin almost surely.
2. This chapter investigates output-feedback control for a class of stochastic high-ordernonlinear systems with time-varying delay for the first time. By introducing the adding apower integrator technique in the stochastic systems and a rescaling transformation, andchoosing an appropriate Lyapunov-Krasoviskii functional, an output-feedback controller isconstructed to render the closed-loop system globally asymptotically stable in probability,the output can be regulated to the origin almost surely.
3. The homogeneous domination approach is introduced to solve the state feedback sta-bilization problem for a class of stochastic high-order nonlinear systems with time-varyingdelay. Under the weaker conditions on the drift and difusion terms, by using the homo-geneous domination approach and solving several troublesome obstacles in the design andanalysis procedure, a state feedback controller is constructed to render the closed-loop systemglobally asymptotically stable in probability.
4. This chapter further discusses the output feedback stabilization problem for stochas-tic high-order nonlinear systems with time-varying delay. Under the weaker conditions onnonlinearities in drift and difusion vector fields, by using the idea of homogeneous dom- ination approach, skillfully choosing an appropriate Lyapunov-Krasoviskii functional, andsuccessfully solving several troublesome obstacles in the design and analysis procedure, anoutput feedback controller is constructed to render the closed-loop system globally asymp-totically stable in probability.
5. This chapter investigates a class of stochastic feedforward nonlinear systems withtime-varying delay. By introducing the homogeneous domination approach to stochasticsystem, a state feedback controller is constructed to render the closed-loop system globallyasymptotically stable in probability.
6. This paper studies the problem of decentralized adaptive output feedback stabiliza-tion for a class of interconnected systems with dynamic input and output interactions andnonlinear interactions by using MT-filters and the backstepping design method. It is shownthat the closed-loop decentralized system based on MT-filters is globally uniformly bounded,all the signals except for the parameter estimates can be regulated to zero asymptotically,and the L2and L∞norms of the system outputs are also be bounded by functions of designparameters.
7. This chapter investigates the problem of adaptive output feedback stabilizationusing MT-filters and the backstepping design method for a class of nonlinear systems withunknown input and output time-delay. It is shown that all the signals in the closed-loopsystem are globally uniformly bounded, and the output can be regulated to zero.
引文
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