Stabilization for distributed semilinear systems governed by optimal feedback control
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This paper focuses on the problem of polynomial and weak stabilization of abstract distributed semilinear systems in a real Hilbert space governed by an optimal multiplicative feedback control. A new proposed feedback control is constructed to achieves the two kinds of stabilization. Necessary and sufficient conditions for stabilization problems are investigated as well. Furthermore, the used feedback control is the unique solution of an appropriate minimization problem. Some examples of hyperbolic and parabolic partial differential equations are provided. Finally, simulations are given.
KeywordsSemilinear systems Weak stabilization Polynomial stabilization Optimal feedback control
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