Nearest Neighbor Control for Practical Stabilization of Passive Nonlinear Systems

Overview & Synopsis

This paper studies static output feedback stabilization of continuous-time (incrementally) passive nonlinear systems where the control actions can only be chosen from a discrete (and possibly finite) set of points. For this purpose, we are working under the assumption that the system under consideration is large-time norm observable and the convex hull of the realizable control actions contains the target constant input (which corresponds to the equilibrium point) in its interior. We propose a nearest-neighbor based static feedback mapping from the output space to the finite set of control actions, that is able to practically stabilize the closed-loop systems. Consequently, we show that for such systems with m-dimensional input space, it is sufficient to have $m + 1$ elements (other than the zero element for general passive systems or the target constant input for incrementally passive systems). Furthermore, we present constructive algorithms to design such $m + 1$ input points that satisfy the conditions for practical stability using our proposed nearest-neighbor control.