A Matrix Inequality Approach to Guaranteed Cost Control of a Nonlinear Bioreactor

This paper considers design of a state-feedback controller to solve a guaranteed cost control problem for a nonlinear continuous bioreactor. The control input in the controller design problem must be within a certain range to prevent the system from exhibiting undesirable traits such as bifurcation. To address this practical challenge, we present a new condition for state feedback design for nonlinear systems that includes guaranteed constraints on the cost functions as well as bounds on the input magnitudes in this study. The nonlinear bioreactor system is transformed into a polynomial system by the Taylor’s series expansion. By exploiting polynomial structure of the systems, the proposed design condition is convex in the decision variables, and hence can be cast as a specific convex optimization so called a sum-of-squares programming which can be efficiently solved via the existing software tools. In addition, the proposed approach allow extension to robust state-feedback design of the bioreactor system affected by parametric uncertainty. Numerical experiments evaluate the applicability and effectiveness of the proposed approach.