Continuous-time optimal control for switched positive systems with application to mitigating viral escape*

The optimal control problem for a particular class of switched systems is addressed in this paper. Using a linear co–positive cost function, a necessary and sufficient condition for optimal control is derived. Optimal states and costates can lie on a sliding surface, and this corresponds to a chattering switching law. Due to the complexity of exact solution of the general optimal control problem, we introduce a suboptimal, guaranteed cost algorithm, associated with the optimal problem. These results are then applied to a simplified model of HIV viral mutation dynamics, which under simplifying assumptions can be viewed as a positive switched linear system. Simulations compare the optimal switching control law with the sub-optimal guaranteed cost approach.