Optimization design for a class of multi-input nonlinear cascade systems: backstepping approach

A novel suboptimal control design is proposed for a class of multi-input nonlinear cascade systems. Combining the backstepping recursive design with the SDARE technique, the analytic solution to suboptimal control for each subsystem can be online derived by designing state feedback control law. The resulting SDARE control law can make the original closed-loop system globally asymptotically stable (GAS). Furthermore, the designed control law is the optimal solution to the original system when the terminal time is equal to infinity. Finally, a numeric simulation example of the second-order system with two inputs is illustrated to verify the effectiveness of the backstepping based optimization design.