Wyniki wyszukiwania

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Robust Control of Linear Stochastic Systems with Fully Observable State

100%

Poznyak A. S., Taksar M. I.

Applicationes Mathematicae

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1996-1997

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tom 24

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nr 1

35-46

EN

We consider a multidimensional linear system with additive inputs (control) and Brownian noise. There is a cost associated with each control. The aim is to minimize the cost. However, we work with the model in which the parameters of the system may change in time and in addition the exact form of these parameters is not known, only intervals within which they vary are given. In the situation where minimization of a functional over the class of admissible controls makes no sense since the value of such a functional is different for different systems within the class, we should deal not with a single problem but with a family of problems. The objective in such a setting is twofold. First, we intend to establish existence of a state feedback linear robust control which stabilizes any system within the class. Then among all robust controls we find the one which yields the lowest bound on the cost within the class of all systems under consideration. We give the answer in terms of a solution to a matrix Riccati equation and we present necessary and sufficient conditions for such a solution to exist. We also state a criterion when the obtained bound on the cost is sharp, that is, the control we construct is actually a solution to the minimax problem.

2

Delay-dependent asymptotic stabilitzation for uncertain time-delay systems with saturating actuators

100%

Liu P.-L.

International Journal of Applied Mathematics and Computer Science

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2005

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tom 15

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nr 1

45-51

EN

This paper concerns the issue of robust asymptotic stabilization for uncertain time-delay systems with saturating actuators. Delay-dependent criteria for robust stabilization via linear memoryless state feedback have been obtained. The resulting upper bound on the delay time is given in terms of the solution to a Riccati equation subject to model transformation. Finally, examples are presented to show the effectiveness of our result.

3

J-energy preserving well-posed linear systems

51%

Staffans O. J.

International Journal of Applied Mathematics and Computer Science

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2001

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tom 11

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nr 6

1361-1378

EN

The following is a short survey of the notion of a well-posed linear system. We start by describing the most basic concepts, proceed to discuss dissipative and conservative systems, and finally introduce J-energy-preserving systems, i.e., systems that preserve energy with respect to some generalized inner products (possibly semi-definite or indefinite) in the input, state and output spaces. The class of well-posed linear systems contains most linear time-independent distributed parameter systems: internal or boundary control of PDE’s, integral equations, delay equations, etc. These systems have existed in an implicit form in the mathematics literature for a long time, and they are closely connected to the scattering theory by Lax and Phillips and to the model theory by Sz.-Nagy and Foiaş. The theory has been developed independently by many different schools, and it is only recently that these different approaches have begun to converge. One of the most interesting objects of the present study is the Riccati equation theory for this class of infinite-dimensional systems (H^2 - and H^∞ -theories).

Ograniczanie wyników

2 International Journal of Applied Mathematics and Computer Science

1 Applicationes Mathematicae

1 Liu P.-L.

1 Poznyak A. S.

1 Staffans O. J.

1 Taksar M. I.

1 2005

1 2001

1 1996

Robust Control of Linear Stochastic Systems with Fully Observable State

Delay-dependent asymptotic stabilitzation for uncertain time-delay systems with saturating actuators

J-energy preserving well-posed linear systems