Constrained controllability of discrete-time bilinear systems

In real systems, control inputs are often constrained, and the constrained controllability problems are far more difficult to deal with than the unconstrained controllability ones. In this paper, we consider the constrained controllability problem of discrete-time bilinear systems. Specifically, we study the bounds of the control inputs for the systems to be controllable. Our approach is to first prove constrained near-controllability of a special class of bilinear system and then use constrained near-controllability to approximate constrained controllability of general bilinear systems. Based on this approach, we derive conditions for constrained controllability of the systems, where the upper bound of the control inputs can be easily computed. Algorithms and examples are provided to demonstrate the results of this paper.