非线性系统控制器综合的一种新方法(英文)

基于正切线性化控制技术和状态依赖Riccati微分方程方法,提出了一种新的非线性控制器综合策略.受正切线性化控制的启发,首先,将一类非线性系统的非线性反馈镇定问题转化为状态依赖线性时变系统的反馈镇定器设计问题.然后,给出了求解导出线性时变系统反馈镇定器设计问题的一种基于状态依赖Riccati微分方程方法.为实现该控制器的求解,仅需实时求解给定正定初始条件下的状态依赖Riccati微分方程.此外,本文所得到的解析结果还能保证非线性闭环反馈系统的指数渐近稳定性.最后,用一个数值算例验证了本文给出方法的有效性.

A new approach to controller synthesis for nonlinear systems

A new approach to nonlinear controller synthesis is proposed using tangent linearization control and state-dependent Riccati differential equation.Motivated by tangent linearization control,the nonlinear feedback stabilization problem for nonlinear systems is first reduced to that of a feedback stabilizing controller design for linear time-varying state-dependent systems.Then,a state-dependent Riccati differential equation based approach is presented to design of state-feedback controller of the deduced linear time-varying system.To implement such a controller,only a state-dependent Riccati differential equation with given positive definite initial condition need to be solved online.Moreover,it is shown analytically that the closed-loop system under the proposed nonlinear feedback is exponentially asymptotically stable.Finally,a numerical example shows the effectiveness of the proposed approach.