On external and internal approximations for reachability sets of bilinear systems

Sinyakov, Vladimir

doi:10.1134/s1064562414060052

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λF (T X) = λA(t)x(t) + λB(t)u (T) = A(t)(λx(t)) + B(t)(λu (1

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2015

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“…For an alternative approach to the reachability problem of bilinear systems in terms of ellipsoidal approximations please see [21].…”

Section: λF (T X) = λA(t)x(t) + λB(t)u (T) = A(t)(λx(t)) + B(t)(λu (mentioning

confidence: 99%

Partial Differential Equation for Evolution of Star-Shaped Reachability Domains of Differential Inclusions

Mazurenko

2015

Set-Valued Var. Anal

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The problem of reachability for differential inclusions is an active topic in the recent control theory. Its solution provides an insight into the dynamics of an investigated system and also enables one to design synthesizing control strategies under a given optimality criterion. The primary results on reachability were mostly applicable to convex sets, whose dynamics is described through that of their support functions. Those results were further extended to the viability problem and some types of nonlinear systems. However, non-convex sets can arise even in simple bilinear systems. Hence, the issue of nonconvexity in reachability problems requires a more detailed investigation. The present article follows an alternative approach for this cause. It deals with star-shaped reachability sets, describing the evolution of these sets in terms of radial (Minkowski gauge) functions. The derived partial differential equation is then modified to cope with additional state constraints due to on-line measurement observations. Finally, the last section is on designing optimal closed-loop control strategies using radial functions.

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“…For an alternative approach to the reachability problem of bilinear systems in terms of ellipsoidal approximations please see [21].…”

Section: λF (T X) = λA(t)x(t) + λB(t)u (T) = A(t)(λx(t)) + B(t)(λu (mentioning

confidence: 99%

Partial Differential Equation for Evolution of Star-Shaped Reachability Domains of Differential Inclusions

Mazurenko

2015

Set-Valued Var. Anal

View full text Add to dashboard Cite

show abstract

On external and internal approximations for reachability sets of bilinear systems

Cited by 1 publication

References 8 publications

Partial Differential Equation for Evolution of Star-Shaped Reachability Domains of Differential Inclusions

Partial Differential Equation for Evolution of Star-Shaped Reachability Domains of Differential Inclusions

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