Minimum-Time Control of a Linear System With Input Saturation: A Practical Approach

A simple algorithm is presented to find near-minimum-time control inputs for a controllable continuous-time linear time-invariant system with any number of states and inputs. The well-known digital deadbeat control algorithm is modified to satisfy input constraints, and the design issue is the selection of sampling period to minimize the time required to reach the desired final state. During each sampling period, the input required to place all the poles at the origin of z-plane (deadbeat control) via state feedback is computed. If the infinity norm of the deadbeat input exceeds the input constraint, the input is found by placing the poles as close to the origin as possible. A sufficient condition for the system stability is developed. Numerical examples illustrate that this algorithm can lead to true time-optimal control or near time-optimal control.