Optimal Control of Switched Positive Linear Systems

The optimal control of switched positive linear systems is addressed under two strategies. The first one is to resort the dwell time method, which can avoid the problem of large state transients at the switching points. The proper performance index is introduced to study such a problem. Optimal conditions are designed to guarantee the performance criterion for switched positive systems with a dwell time constraint. The second one is to adopt the state-dependent switching law. The minimum time between successive switchings is required to avoid chattering. So, the state-dependent switching law obeying a dwell time constraints is applied. The upper bound of the guaranteed performance is calculated for the switched positive systems. Finally, numerical examples are given to demonstrate the effectiveness of the proposed methods.