基于压制法的非线性时滞系统的镇定控制与自适应控制研究

This project investigates the stabilization problem for several classes of nonlinear systems subject to time-delay. Most systems are nonlinear by nature, and time-delay is actually very common in practice, so nonlinear time-delay systems can be constructed for most industrial control procedures. In the fruitful results achieved for nonlinear time-delay systems, the methods of backstepping and LMI are exploited frequently. Most restrictions imposed on perturbations are still conservative, and most stabilization results are based on state feedback controllers. In this proposal, for several classes of nonlinear time-delay systems, the approach of domination is employed to dominate the effect of perturbations. For different nonlinear time-delay systems, the procedures for stability analysis are employed respectively. With the help of appropriate functionals, output feedback controllers can be used to globally stabilize the system, and the conditions imposed on perturbations can also be relaxed. The problems of global, local, and semi-global stabilization respect to finite-time will be solved. This proposal also include the problem of adaptive stabilization for the systems with unknown time-delays and other uncertain parameters, and the stabilization problem via output feedback controllers based on reduced-order observer. These results will be expanded to discrete-time and hybrid nonlinear time-delay systems. With the help of the method of domination, Lyapunov-Krasovskii functionals and stabilization conditions can be obtained more conveniently. Besides, compared to the state feedback case, the problem of global stabilization by output feedback is more challenging for those systems whose dynamics are highly nonlinear in the unmeasured states. Therefore the results proposed by this project are easy to be implemented in practice.

实际中系统都是非线性的，而建模误差和时滞影响等因素也不容忽视，非线性时滞系统既包含不确定项又考虑了时滞的影响，对该类系统的研究日益成为控制理论界的研究热点。目前国内外对于非线性时滞系统的研究，大都使用backstepping方法或LMI方法，不确定时滞条件限制较强，且普遍采用状态反馈控制器。本项目结合国内外的研究成果，基于压制的思想(domination)，主要研究内容如下：1通过输出反馈控制器，对不同类型的非线性时滞系统使用不同的分析模型，研究限制不确定时滞条件较为宽泛的全局镇定控制问题；2全局、局部、半全局的有限时间镇定控制问题；3不确定时滞条件包含未知时滞参数及其他不确定参数的自适应镇定控制问题；4基于降维观测器的镇定控制问题；5将上述结论推广到离散与混合域的非线性时滞系统。本项目充分考虑了实践需要，经过压制处理的不确定时滞条件有利于泛函的制定和镇定条件的确定，系统无需满足完全可观。

本项目针对非线性时滞系统，主要基于压制法的思想，对于非线性部分满足线性、齐次性、高阶非线性等增长条件下的系统设计线性、齐次、动态增益控制器，使系统实现全局镇定、半全局镇定等控制问题。在系统结构上，除了以上的较为常见的非线性增长环节，还有未知参数，非线性增长部分的高阶项也较以往结论更高，使得研究对象较以往结论更加复杂、覆盖范围更广；在控制器设计方法上，基于压制法的控制器不再像以往针对时滞系统的LMI方法需要满足一充分条件，而是只需要获得控制器增益的范围，且多基于输出反馈控制器实现，使得控制器更加实用。而动态增益的控制器设计，虽然控制增益为一动态函数，却可以在推导过程中确定其形式，即使含有未知参数，也可以在压制法的推导过程中，逐步确定未知参数自适应律及控制器增益的形式，而无需像以往方法一样去寻找满足LMI不等式的参数（实验中需要尝试不同参数），从而更符合实践的需要，对于理论研究与工程实践都具有一定的指导意义。