Existence of Solutions for the Continuous Algebraic Riccati Equation via Polynomial Optimization

Juan Zhang; Wenjie Zhao

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arXiv · 2408.13780

Existence of Solutions for the Continuous Algebraic Riccati Equation via Polynomial Optimization

Juan Zhang·Wenjie Zhao

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Abstract

This paper studies the solution existence of the continuous-time algebraic Riccati equation (CARE). We formulate the CARE as two constrained polynomial optimization problems, and then use Lasserre's hierarchy of semi-definite relaxations to solve them. Compared to the existing work, our approaches can obtain the exact positive semi-definite solution of the CARE when the coefficient matrices are symmetric. Moreover, our methods can detect the nonexistence of the positive semi-definite solution for the CARE. Numerical examples show that our approaches are effective compared to the existing methods.

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Juan Zhang, Wenjie Zhao. 2024-08-25. Existence of Solutions for the Continuous Algebraic Riccati Equation via Polynomial Optimization. https://arxiv.org/abs/2408.13780

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