Positively invariance and time-optimal control for distributed linear time-invariant discrete-time systems

The problem of time-optimal control for a discrete-time system with bounded disturbances is discussed. The system considered is a linear time-invariant discrete-time system whose states, inputs, and disturbances are restricted by certain inequality constraints using notations of polyhedral convex sets. The problem is to minimize the time to bring states into the specified set W. The proposed design method can be summarized as follows: given a system with its restrictions and a specified set W, (a) find a PIDIC (positively invariant with disturbance and input constraint) set S ⊆W, and (b) obtain the time-optimal control such that the states are driven to S under any disturbances which satisfy the conditions. PIDIC sets are defined precisely and a method to calculate them is proposed. Then, the authors propose a novel method for the time-optimal problem, and verify that the time-optimal control is more efficient than the conventional time-optimal control for which disturbances are not taken into account