Receding optimal design of constrained Sontag-type controllers

The optimal design of Sontag-type controllers was proposed for nonlinear control-affine systems subject to constraints of the state and input. Firstly, the standard Sontag formula was modified as a time-varying controller where the time-varying parameter was close to the decay rate of the closed-loop system. Secondly, two algorithms of optimal Sontag-type controller were designed by combining the principle of receding horizon control, which were guaranteed to satisfy the system constraints. The regional asymptotic stability of the closed-loop system was then achieved. Finally, the effectiveness of this control scheme was illustrated by the comparison of the controller obtained here and the standard Sontag-type controller in simulation.