On Computing Control Inputs to Achieve State Transition for a Class of Nearly Controllable Discrete-time Bilinear Systems

Abstract

Near-controllability is defined for those systems that are uncontrollable but have a large controllable region. It is a property of nonlinear control systems introduced recently, and it has been well demonstrated on discrete-time bilinear systems. The purpose of this paper is to propose a useful algorithm to compute the control inputs, which achieve the transition of a given pair of states, for a class of discrete-time bilinear systems that are nearly controllable. Accordingly, for such class of bilinear systems, not only near-controllability is proved, but also the computability of control inputs for near-controllability is shown. An example is provided to demonstrate the effectiveness of the proposed algorithm.