Optimization design for a class of cascade control systems: Backstepping approach
一类串联控制系统的优化设计:Backstepping方法

A suboptimal control design is proposed based on Backstepping method for a class of multi-input nonlinear cascade systems.First,the cascade control system is decomposed into several subsystems.Then,the auxiliary subsystem and corresponding auxiliary control variables for each actual subsystem are devised,respectively.Third,a suboptimal control law for each auxiliary subsystem is designed with State-Dependent Algebraic Riccati Equation (SDARE) technique.The original state variables and the auxiliary control variables (i.e. auxiliary feedback variables) have an asymptotical characteristic by imposing the proposed control law,thus the analytic solution to suboptimal control can be achieved on-line and the global asymptotical stability (GAS) of the original closed-loop system can be guaranteed.Finally,the numeric simulation results of the second-order system with two inputs are provided to verify the effectiveness of the proposed optimization design.