A new formulation for co-design of linear systems with system matrices having affine design variables

Co-design is a process of simultaneous optimization of design and control of an engineering system. Previous studies in the co-design literature have primarily focused on sequential or nested approaches with rare guarantees of even local optimality. In this paper, a new approach to co-design for a class of linear time invariant systems with Linear Quadratic Regulator (LQR) control is presented. The dynamic co-design problem is first reformulated as a static nonlinear optimization problem whose solution is independent of the initial conditions of the state variables. A heuristic solution procedure is then presented to solve the non-convex optimization problem. Numerical simulations using two simple spring-mass-damper examples indicate the potential of the proposed procedure in obtaining global optimal solutions for the co-design problem.