饱和切换非线性系统的控制及其在忆阻系统中的应用

In many practical dynamic systems, physical input saturation on hardware dictates that the magnitude of the control signal is always constrained. Saturation is a potential problem for actuators of control systems and it often severely limits system performance, giving rise to undesirable inaccuracy or leading instability. Therefore research on the control of switched systems composed of nonlinear subsystems subject to actuator saturation has been an interesting task with both practical and theoretical significances. Nevertheless it is a challenging problem mainly due to the difficulties caused by simultaneous existence of non-smooth saturation, subsystem nonlinearity and switching characteristics and their coupling. It is not possible to directly apply the existing approaches of dealing with switched nonlinear systems or nonlinear systems with saturation to solve the problem. In this proposal, sliding mode control method and invariance principle will be considered to address the problem. By thoroughly exploring and rigorously establishing the interdependent relationships between the sliding surface design and the controller design, it is possible to transform the actuator saturation problem to the design problem of the sliding surface which in turn gives rise to a saturation-dependent sliding mode control strategy. By extending invariance principle, it is feasible to establish conditions on stabilizing switched nonlinear systems subject to saturation and thus satisfactorily solve the stabilization problem. Furthermore, the obtained results are to be applied to design amplitude constraint controllers and switching laws for memristive systems. Experimental implementation will also be carried out to verify the effectiveness of the designed controllers. In conclusion, the proposal aims to provide an effective analysis and design approach for switched nonlinear systems subject to saturation and further develop switched system theories. In addition, the application of the obtained results to memristive systems also illustrates the feasibility of applying switched system theories to real systems.

饱和切换非线性系统的研究是具有广泛实际应用前景的难点问题。由于饱和非光滑特性、子系统非线性和切换特性并存并且相互耦合，导致现有切换非线性系统和饱和非线性系统的研究方法很难直接应用于饱和切换非线性系统。本项目利用滑模控制方法和不变集原理，研究饱和切换非线性系统的控制问题。深入分析滑模控制中滑模面设计和控制器设计的依赖关系，提出饱和依赖滑模控制策略，将执行器饱和问题转化为滑模面设计问题；扩展切换系统不变集原理，寻找饱和非线性子系统不稳定情况下切换系统的镇定条件，解决饱和切换非线性系统的控制问题。进而，将研究结果应用于忆阻系统，完成饱和控制设计和切换控制设计，并进行试验验证。本项目的研究为饱和切换非线性系统提供有效的分析和设计方法，发展和完善切换系统理论，其结果在忆阻中的应用为切换理论解决实际问题提供可行方案。

切换系统是一类具有连续和离散动态的混杂系统。由于实际系统的动态行为常常需要使用多个模态来刻画，切换系统在电力系统、智能交通等方面得到了广泛应用。同时，实际系统在运行过程中常受到物理器件、传输条件等多方面的限制。然而对于切换非线性系统的饱和控制问题尚缺乏有效方法，其主要原因是饱和非线性、系统非线性和切换特性相互耦合，导致一般的切换系统理论和饱和控制方法很难直接应用于饱和切换系统。为此，项目针对具有饱和、受限的线性和非线性切换系统的控制问题进行研究。通过深入分析饱和非线性和切换特性相互作用机理，扩展切换系统多Lyapunov函数方法，获得控制受限切换系统饱和可镇定条件。进一步研究具有状态正性受限和传输受限时的切换系统的控制问题，获得受限切换系统的稳定条件。最后，将切换系统的研究结果应用于忆阻神经网络。将具有记忆和切换特性的记忆电阻作为神经突触，建立切换忆阻神经网络，基于切换系统理论分析切换忆阻神经网络的性能。项目的研究丰富了切换系统理论，研究结果在忆阻神经网络上的应用为切换系统理论在工程中解决实际问题提供可行方案。围绕上述工作，申请者及其团队成员发表学术论文40篇，其中SCI检索期刊论文18篇，培养博士研究生5名，硕士研究生15名。