Sliding mode regulator as solution to optimal control problem for non-linear polynomial systems

This paper presents the optimal control problem for a non-linear polynomial system with respect to a Bolza–Meyer criterion with a non-quadratic non-integral term. The optimal solution is obtained as a sliding mode control, whereas the conventional polynomial-quadratic regulator does not lead to a causal solution and, therefore, fails. Performance of the obtained optimal controller is verified in the illustrative example against the conventional polynomial-quadratic regulator that is optimal for the quadratic Bolza–Meyer criterion. The simulation results confirm an advantage in favor of the designed sliding mode control.