随机非线性系统镇定、跟踪及采样控制

Random phenomena exist in realistic systems, which usually affect the performance of the systems, and therefore, it is of great significance to investigate the control problem for stochastic systems from both theoretical and practical point of view. Combining the adding one power integrator technique, domination approach, and the emulation method by discretizing continuous time controllers, with stochastic Lyapunov stability theory, this project aims to study a variety of control problems for stochastic nonlinear systems. By using the adding one power integrator technique and stochastic finite-time Lyapunov stability theorem, an output feedback controller is designed for stochastic nonlinear systems, under which the trajectories of the closed-loop system converge to the equilibrium point in a finite time in probability. Then, according to Dynkin formula and Lyapunov-Krasovskii stability theorem, we consider the problems of stabilization and tracking for stochastic high-order Markov jump nonlinear systems and the corresponding time-delay systems. Output feedback controller design schemes are presented under assumptions that the transition rates of Markov chain is known and unknown, respectively. On the basis of aforementioned works, we further investigate the sampled-data control problem for stochastic nonlinear systems by using the emulation method. By choosing appropriate maximum allowable sampling period (MASP), a sampled-data controller is constructed to guarantee that the system is globally stable in probability. Finally, the effectiveness of the control design schemes will be demonstrated by computer simulation results. In summary, the results of this project will not only enrich and improve stochastic systems control theory, but also provide theoretical basis for implementation on digital computers.

随机现象普遍存在于实际系统中，它会对系统的性能产生影响，因此对随机系统的研究具有重要理论价值和实际意义。本项目将利用增加幂积分方法、压制法、连续域-离散化方法和Lyapunov稳定性理论，研究随机非线性系统若干控制问题。利用增加幂积分方法，根据随机有限时间Lyapunov稳定性定理，设计输出反馈控制器，使得系统的轨迹在有限时间内依概率收敛到平衡点。根据Dynkin公式和Lyapunov-Krasovskii稳定性定理，设计在Markov链转移率已知和未知两种情形下的输出反馈控制器，实现随机高阶Markov跳变非线性系统及其相应时滞系统的镇定和跟踪。在此基础上，利用连续域-离散化方法研究随机非线性系统采样控制问题，给出系统全局稳定的离散控制器设计方法和相应的最大允许采样周期。综上所述，本项目研究成果将不仅丰富和完善随机系统控制理论，而且也将为随机系统控制理论在数字计算机上的实现提供理论依据。

实际系统中存在测量漂移、参数不确定性、时滞及随机干扰等因素，不可避免地对系统的控制性能产生影响。本项目将上述因素融入到随机非线性系统控制框架内，建立以系统的稳定性和抑制干扰能力提高为目的的控制器设计方法。将Lyapunov稳定性理论、增加幂积分方法和自适应控制技术相结合，研究了一类随机非线性系统的全局输出反馈控制、有限时间控制和实际跟踪等问题。将齐次压制法、动态增益技术和随机Barbalat引理相结合，研究了一类随机非线性时滞系统的全局输出反馈调节、镇定和自适应控制等问题。将非光滑控制理论、Gronwall不等式和自适应控制技术相结合，研究了一类随机非线性系统的采样及量化控制问题。将齐次系统理论、增加幂积分方法和自适应控制技术相结合，研究了一类随机非线性切换系统的全局状态反馈、输出反馈控制、有限时间镇定及跟踪控制等问题。上述研究成果丰富了随机非线性系统控制理论。