Co-design refers to the process of integrating the optimization of the physical design as well as the controller for a system. In this paper, a new class of co-design problems with a multi-subsystem architecture is formulated and solved, which extends earlier works on models and solution approaches from single-system to multi-subsystem co-design. In this class, the design part in each subsystem has a strictly convex objective function with linear equality constraints. The control part of each subsystem belongs to a class of finite time-horizon Linear Quadratic Regulator (LQR) feedback control. A new multi-level decentralized model and method is proposed to obtain optimal or near-optimal solutions for this class of co-design problems. Details of the model and approach are demonstrated by a numerical as well as a more complex spring-mass-damper system example. Comparison of optimal results from both centralized and decentralized methods are presented and discussed.

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