基于观测器的受扰多项式系统H∞输出跟踪控制

考虑一类受到外部扰动影响的多项式系统在状态不完全可测情况下的H_∞输出跟踪控制问题.首先,综合前馈-反馈复合控制思想,设计基于观测器的输出跟踪控制器,其中反馈镇定控制器用于保证闭环系统稳定,前馈补偿控制器用以实现对参考模型输出信号的跟踪;然后,提出具有输出反馈结构的跟踪控制方法,其优势在于实现了分离原则,可单独设计观测器和控制器,降低计算复杂度;接着,利用依赖全状态的齐次多项式Lyapunov函数导出使得闭环系统渐近稳定且满足H_∞跟踪性能的充分条件,借助多项式平方和凸优化技术可直接求得相应的观测器和控制器;最后,通过数值仿真实例验证所提出设计方法的有效性和优越性.

Observer-based $H_infty$ output tracking control for a class of polynomial systems with external disturbances

An $H_\infty$ output tracking control problem is considered for a class of polynomial systems with partially unknown states under external disturbances. Firstly, an observer-based output tracking controller is presented from the perspective of the feedforward and feedback composite control method. The feedback stabilization controller is employed to ensure the stability of the closed-loop system, and the feedforward compensation controller is used to track the output signal of the reference model. Furthermore, a tracking controller is proposed with an output feedback structure, its advantage is that the observer and controller can be given separately, satisfying the separation principle and reducing the computational complexity. Then using a homogeneous polynomial Lyapunov function dependent on whole state variables, the sufficient condition of the asymptotic stability with $H_\infty$ tracking performance is derived for the closed-loop system. The corresponding observer and controller can be obtained directly by the polynomial sum of squares convex optimization technique. Finally, numerical simulation examples are given to verify the validity and superiority of the proposed method.