Minimum-energy Control of Nearly-controllable Discrete-time Bilinear Systems with Nondiagonalizable Structure

In this paper, a class of discrete-time bilinear systems which are uncontrollable but can be nearly-controllable is considered. A necessary and sufficient condition for near-controllability of such systems was obtained and the corresponding control inputs to achieve the transition of the systems between any given pair of states are computable, but there are infinite groups of such control inputs. Therefore, this paper proposes a new algorithm, which attempts to find a minimum-energy control sequence to achieve the state transition and improves the previous algorithm for computing the control inputs. Analysis and examples are given to illustrate the proposed algorithm.