Displaying similar documents to “On the solutions of the dissipation inequality.”

On the circle criterion for boundary control systems in factor form : Lyapunov stability and Lur’e equations

Piotr Grabowski, Frank M. Callier (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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A Lur’e feedback control system consisting of a linear, infinite-dimensional system of boundary control in factor form and a nonlinear static sector type controller is considered. A criterion of absolute strong asymptotic stability of the null equilibrium is obtained using a quadratic form Lyapunov functional. The construction of such a functional is reduced to solving a Lur’e system of equations. A sufficient strict circle criterion of solvability of the latter is found, which is based...

Receding horizon optimal control for infinite dimensional systems

Kazufumi Ito, Karl Kunisch (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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The receding horizon control strategy for dynamical systems posed in infinite dimensional spaces is analysed. Its stabilising property is verified provided control Lyapunov functionals are used as terminal penalty functions. For closed loop dissipative systems the terminal penalty can be chosen as quadratic functional. Applications to the Navier–Stokes equations, semilinear wave equations and reaction diffusion systems are given.

Output stabilization for infinite-dimensional bilinear systems

El Zerrik, Mohamed Ouzahra (2005)

International Journal of Applied Mathematics and Computer Science

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The purpose of this paper is to extend results on regional internal stabilization for infinite bilinear systems to the case where the subregion of interest is a part of the boundary of the system evolution domain. Then we characterize either stabilizing control on a boundary part, or the one minimizing a given cost of performance. The obtained results are illustrated with numerical examples.

On adaptive control for the continuous time-varying JLQG problem

Adam Czornik, Andrzej Świernik (2005)

International Journal of Applied Mathematics and Computer Science

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In this paper the adaptive control problem for a continuous infinite time-varying stochastic control system with jumps in parameters and quadratic cost is investigated. It is assumed that the unknown coefficients of the system have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Under these assumptions it is shown that the optimal value of the quadratic cost can be reached based only on the values of these limits, which, in turn, can...