Co-Optimization of Control and Actuator Selection for Cyber-Physical Systems

Abstract This paper considers actuator selection problems which aim to maintain control performance of dynamical systems, and minimize operational costs or wear-and-tear of the actuators. The logical controls of actuators make the problem combinatorial, which make exhaustive search impractical. An actuator selection problem can be cast as a binary-integer programming with bilinear matrix inequalities (BIBMIs). In this paper, we first show that such non-convex optimization can be equivalently reformulated as an optimization problem with non-convexities restricted to binary decision variables. We next consider a continuous optimization which is equivalent to the BIBMIs, and leverage the continuous reformulation to derive a branch-and-bound method employing bound refinement. Numerical simulations demonstrate the effectiveness of the proposed approach.