Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 66, Issue 10, Pages 4812-4819Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2020.3037041
Keywords
Symmetric matrices; Estimation; Time-varying systems; Tools; Thermal stability; Technological innovation; Switches; Bernstein polynomial; periodic piecewise polynomial systems (PPPSs); reachable set estimation; time-varying systems
Funding
- National Natural Science Foundation of China [61973259]
- Innovation and Technology Commission of Hong Kong [UIM/353]
- Research Grants Council of Hong Kong [17200918, 17206818, 17202317]
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In this article, a Bernstein polynomial approach is proposed for estimating reachable sets for a class of periodic piecewise polynomial systems, showing its advantages in handling time-varying parameter products. By integrating a lemma and the theory of matrix polynomials, tractable sufficient conditions are developed, leading to lower conservatism in reachable set estimation.
In this article, a Bernstein polynomial approach is first applied to the estimation of reachable set for a class of periodic piecewise polynomial systems, whose subsystems are time-varying and can be expanded to Bernstein polynomial forms. A lemma on the negativity/positivity for a class of Bernstein polynomial matrix functions is presented, which can provide a feasible set larger than that by the existing method. Based on the integration of the presented lemma and the theory of matrix polynomials, two tractable sufficient conditions are developed. For comparison of conservatism, the reachable set estimation is achieved through optimizing the ellipsoidal bounding region. Four sets of constraints with different conservatism are derived and compared. The effectiveness and superiority of the Bernstein polynomial approach in reachable set estimation are demonstrated via an illustrative example. The results show that the proposed approach enables lower conservatism in reachable set estimation, providing an intuitive route to tackle time-varying parameter products with high powers.
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