Time domain performance based nonlinear state feedback control of constrained linear systems

This paper describes a method to design a nonlinear state feedback controller that meets a set of time-domain specifications not attainable by linear state feedback. Using a constrained polynomial interpolation technique, an input signal is computed that satisfies the desired time-domain constraints on the input and state-trajectories. The computed input is constructed by nonlinear combinations of the states, such that a nonlinear state feedback law is obtained. Stability of the resulting closed-loop polynomial system is analyzed using sum-of-squares techniques. An illustrative example is presented, showing that the proposed nonlinear controller outperforms its linear counterpart. To validate the proposed method, experiments on a fourth-order motion system have been carried out.