Sliding mode controller design for polynomial systems with unmeasured states

This paper addresses the optimal controller problem for a polynomial system over linear observations with respect to a Bolza-Meyer criterion, where the integral control and state energy terms are quadratic and the non-integral term is of the first degree. The optimal solution is obtained as a sliding mode controller consisting of a sliding mode filter and a sliding mode regulator, whereas the conventional feedback polynomial-quadratic controller fails to provide a causal solution. Performance of the obtained optimal controller is verified in the illustrative example against the conventional LQG controller that is optimal for the quadratic Bolza-Meyer criterion. The simulation results confirm an advantage in favor of the designed sliding mode controller.