An optimal sliding mode-like regulator for nonlinear polynomial systems

This article presents the optimal control problem for a nonlinear polynomial system with respect to a Bolza–Meyer criterion with non-quadratic state energy terms. A distinctive feature of the obtained result is that a part of the optimally controlled state trajectory occurs to be in a sliding mode, i.e. represents a motion along a certain manifold. The optimal solution is obtained as a sliding mode-like control, whereas the conventional linear feedback control fails to provide a causal solution. 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 favour of the designed sliding mode control.