Mathematical Models and Methods in Applied Sciences Vol. No. ( ) – ❢c World Scientific Publishing Company OPTIMAL CONTROL OF A BIOREACTOR WITH MODAL SWITCHING ∗

ABSTRACT: We consider a model for bioremediation of a pollutant by bacteria in a well-stirred bioreactor. A key feature is the inclusion of dormancy for bacteria, which occurs when the critical nutrient level falls below a critical threshold. This feature gives a discrete component to the system due to the change in dynamics (governed by a system of ordinary differential equations between transitions) at switches to/from dormancy. After setting the problem in an appropriate state space, the control is the rate of injection of the critical nutrient and the functional to be minimized is the pollutant level at the final time and the amount of nutrient added. The existence of an optimal control and a discussion of the transitions between dormant and active states are given. Key Words: system. Optimal control, existence, bioremediation, modal switching, hybrid Mathematics Subject Classification: 49J15, 93A30, 93C15