Document Type : Research Article
Authors
Department of Mathematics and Computer Science, Lorestan University, Lorestan, Iran.
10.30473/coam.2025.73999.1294
Abstract
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.
Highlights
- A novel robust optimal control algorithm based on eigenvalue assignment within a prescribed region is developed.
- The method is free from issues related to ill-conditioned numerical problems.
- The stability of the controlled system is guaranteed, supported by a proven theorem.
- Unlike model reduction techniques that may neglect high-frequency dynamics, this approach retains the full system structure, ensuring robustness against singular perturbations, making it more reliable for real-time, high-dimensional control tasks.
- The method optimally assigns the eigenvalues of the Linear Singular Perturbed System (LSPS), effectively addressing numerical ill-conditioning within an inverse parametric optimal control framework.
- A novel algorithm, based on the inverse parametric optimal control, is introduced to ensure the robustness and stability of LSPS control.
Keywords
Main Subjects
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