Optimal Control of Linear Singularly Perturbed Systems via Eigenvalue Assignment

Optimal control of certain singularly perturbed systems‎, ‎with slow and fast dynamics‎, ‎presents notable challenges, including ill-conditioning‎, ‎high dimensionality‎, ‎and ill-posed algebraic Riccati equations‎. ‎In this paper‎, ‎ we introduce a novel inverse optimal control method based on the eigenvalue assignment approach to address these issues‎. The proposed method optimizes the objective function while ensuring system stability through the strategic placement of eigenvalues in the singular perturbed closed-loop system‎. ‎ To facilitate analysis and support the implementation, a new theorem is proved, and a corresponding algorithm is developed‎. ‎The proposed algorithm is free of ill-conditioned numerical problems, making it more robust in terms of numerical diffusion and perturbation measurement‎. ‎Finally‎, ‎two simulation examples are presented to illustrate the advantages of the proposed method, demonstrating improvement in controller robustness, substantial reductions in cost functions, and decreased control amplitudes‎.

کلیدواژه ها:

Singularly Perturbed Systems ، Optimal Control ، Eigenvalue Placement ، Certainty Matrix