An iterative approach to the optimal co-design of linear control systems

Abstract

Keywords: Co-design; optimal control; non-convex optimization; iterative scheme. This paper investigates the optimal co-design of both physical plants and control policies for a class of continuoustime linear control systems. The optimal co-design of a specific linear control system is commonly formulated as a nonlinear non-convex optimization problem (NNOP), and solved by using iterative techniques, where the plant parameters and the control policy are updated iteratively and alternately. This paper proposes a novel iterative approach to solve the NNOP, where the plant parameters are updated by solving a standard semi-definite programming problem, with non-convexity no longer involved. The proposed system design is generally less conservative in terms of the system performance compared to the conventional system-equivalence-based design, albeit the range of applicability is slightly reduced. A practical optimization algorithm is proposed to compute a sub-optimal solution ensuring the system stability, and the convergence of the algorithm is established. The effectiveness of the proposed algorithm is illustrated by its application to the optimal co-design of a physical load positioning system.

Optimal Codesign of Nonlinear Control Systems Based on a Modified Policy Iteration Method

“…The resultant optimization problem for linear control systems is challenging due to the nonconvexity [8]. When nonlinear system dynamics and nonquadratic cost functions are taken into consideration, there is Manuscript less hope of solving the problem analytically.…”

Optimal codesign of controller and linear plants with input saturation: The sensitivity Lyapunov approach

“…Naraghi and Moradi modified the method proposed by Salama et al using LEs so that the direct solution of Riccati equation is not required since there is no need for optimized controller in a nonoptimal plant. However, many of the previous studies are not applicable to the input‐saturated cases …”

“…Jiang et al extended the conventional solution to PCCD without consideration to the additional LEs for updating the plant. Similarly, Wang and Bortoff and Jiang et al developed an algorithm for solving the problem of HJB without using sensitivity function, which is appropriated for full actuated systems.…”

“…However, many of the previous studies 1,24 are not applicable to the input-saturated cases. 32 Some considerations for input saturation are known in the literature. The weight matrix tuning method results in a low gain control that avoids saturation and decreases control performance.…”

“…The method used in the previous work is based on a well‐known Riccati equation that is not devoted for a saturated input case. In contrast to the work of Jiang et al, the sensitivity equations are derived directly from the direct differentiation of HJB. Finally, the proposed method is implemented on an active suspension control system and an underactuated pendulum positioner system.…”