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An Invariance Problem for Control Systems with Deterministic Uncertainty

100%

Górniewicz L., Nistri P.

Banach Center Publications

1996

tom 35

nr 1

193-205

This paper deals with a class of nonlinear control systems in $R^n$ in presence of deterministic uncertainty. The uncertainty is modelled by a multivalued map F with nonempty, closed, convex values. Given a nonempty closed set $K ⊂ R^n$ from a suitable class, which includes the convex sets, we solve the problem of finding a state feedback ū(t,x) in such a way that K is invariant under any system dynamics f. As a system dynamics we consider any continuous selection of the uncertain controlled dynamics F.

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A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces

81%

Gudovich A., Kamenski M., Nistri P.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2001

tom 21

nr 2

207-234

We consider a class of singularly perturbed systems of semilinear parabolic differential inclusions in infinite dimensional spaces. For such a class we prove a Tikhonov-type theorem for a suitably defined subset of the set of all solutions for ε ≥ 0, where ε is the perturbation parameter. Specifically, assuming the existence of a Lipschitz selector of the involved multivalued maps we can define a nonempty subset $Z_L(ε)$ of the solution set of the singularly perturbed system. This subset is the set of the Hölder continuous solutions defined in [0,d], d > 0 with prescribed exponent and constant L. We show that $Z_L(ε)$ is uppersemicontinuous at ε = 0 in the C[0,d]×C[δ,d] topology for any δ ∈ (0,d].

Ograniczanie wyników

1 Banach Center Publications

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2 Nistri P.

1 Gudovich A.

1 Górniewicz L.

1 Kamenski M.

1 2001

1 1996

Wyniki wyszukiwania

An Invariance Problem for Control Systems with Deterministic Uncertainty

A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces