Constrained controllability of discrete-time systems†

The constrained controllability of the discrete-time system xk+1=A(k)xk+B(k)u,k is considered where the control uk is termed admissible if it satisfies specified magnitude constraints. Constrained controllability is concerned with the existence of an admissible control which steers the state x to a given target set from a specified initial state Conditions for checking constrained controllability to a given target set from a specified initial state are presented. These conditions involve solving finite-dimensional optimization problems and can be checked via numerical computation. In addition, conditions for checking global constrained controllability to a given target set are presented. A system is globally constrained controllable if for every initial state, there exists an admissible control that steers the system to the target. If a given discrete-time system is constrained controllable, it may be desirable to obtain an admissible control that steers the system to the target from a specified initial s...