Optimization design for a class of cascade control systems: backstepping approach

A suboptimal control design is proposed for a class of multi-input nonlinear cascade systems. Combining the backstepping recursive design with the SDARE method, the analytic solution to suboptimal control can be on-line derived by designing feedback control law. The resulting SDARE control law can make the closed-loop system asymptotically stable. A numeric simulation example of the second-order system with two inputs is provided to verify the effectiveness of the proposed optimization design.