Ritz–Galerkin Approximation of the Time Optimal Boundary Control Problem for Parabolic Systems with Dirichlet Boundary Conditions
Copyright policy )Ritz–Galerkin Approximation of the Time Optimal Boundary Control Problem for Parabolic Systems with Dirichlet Boundary Conditions
The paper deals with a semidiscrete Galerkin approximation scheme of the time-optimal control problem associated with periodic systems with control acting on the boundary. As a preliminary step, an approximation scheme for parabolic equations with Dirichlet boundary conditions is given and an estimate of the rate of convergence of the approximating solutions in the \(L_{\infty}\)-norm for boundary data in \(L_{\infty}\), are derived. The approach is based on a semigroup representation of the solution given by an effective input-output formula.
Control/observation systems governed by partial differential equations, Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Existence theories for optimal control problems involving partial differential equations, Newton-type methods, semidiscrete Galerkin approximation, Groups and semigroups of linear operators, control acting on the boundary, Linear systems in control theory, Initial-boundary value problems for second-order parabolic equations, PDE in connection with control problems, time-optimal control, rate of convergence
Control/observation systems governed by partial differential equations, Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Existence theories for optimal control problems involving partial differential equations, Newton-type methods, semidiscrete Galerkin approximation, Groups and semigroups of linear operators, control acting on the boundary, Linear systems in control theory, Initial-boundary value problems for second-order parabolic equations, PDE in connection with control problems, time-optimal control, rate of convergence
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