SOME EXAMPLES OF REACHABLE SETS AND OPTIMAL COST FUNCTIONS THAT FAIL TO BE SUBANALYTIC.

S. Lojasiewicz; H. J. Sussmann

doi:10.1137/0323037

SOME EXAMPLES OF REACHABLE SETS AND OPTIMAL COST FUNCTIONS THAT FAIL TO BE SUBANALYTIC.

S. Lojasiewicz, H. J. Sussmann

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

The authors give examples of: (a) a control system dx/dt equals f(x) plus Bu, with f a vector field whose components are quadratic polynomials, and with the controls taking values in the unit cube, such that the time T reachable sets from the origin are not subanalytic; (b) a system dx/dt equals g(x) plus Bu, with the components of g cubic polynomials, such that the system is completely controllable but the optimal time function is not subanalytic; (c) a linear system with a compact, convex, semialgebraic control constraint for which the time T reachable sets are not subanalytic.

Original language	English (US)
Pages (from-to)	584-598
Number of pages	15
Journal	SIAM Journal on Control and Optimization
Volume	23
Issue number	4
DOIs	https://doi.org/10.1137/0323037
State	Published - 1984
Externally published	Yes

All Science Journal Classification (ASJC) codes

Control and Optimization
Applied Mathematics

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10.1137/0323037

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abstract = "The authors give examples of: (a) a control system dx/dt equals f(x) plus Bu, with f a vector field whose components are quadratic polynomials, and with the controls taking values in the unit cube, such that the time T reachable sets from the origin are not subanalytic; (b) a system dx/dt equals g(x) plus Bu, with the components of g cubic polynomials, such that the system is completely controllable but the optimal time function is not subanalytic; (c) a linear system with a compact, convex, semialgebraic control constraint for which the time T reachable sets are not subanalytic.",

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N2 - The authors give examples of: (a) a control system dx/dt equals f(x) plus Bu, with f a vector field whose components are quadratic polynomials, and with the controls taking values in the unit cube, such that the time T reachable sets from the origin are not subanalytic; (b) a system dx/dt equals g(x) plus Bu, with the components of g cubic polynomials, such that the system is completely controllable but the optimal time function is not subanalytic; (c) a linear system with a compact, convex, semialgebraic control constraint for which the time T reachable sets are not subanalytic.

AB - The authors give examples of: (a) a control system dx/dt equals f(x) plus Bu, with f a vector field whose components are quadratic polynomials, and with the controls taking values in the unit cube, such that the time T reachable sets from the origin are not subanalytic; (b) a system dx/dt equals g(x) plus Bu, with the components of g cubic polynomials, such that the system is completely controllable but the optimal time function is not subanalytic; (c) a linear system with a compact, convex, semialgebraic control constraint for which the time T reachable sets are not subanalytic.

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SOME EXAMPLES OF REACHABLE SETS AND OPTIMAL COST FUNCTIONS THAT FAIL TO BE SUBANALYTIC.

Abstract

All Science Journal Classification (ASJC) codes

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