Feedback stabilization of the three-dimensional Navier-Stokes equations using generalized Lyapunov equations
Copyright policy )Feedback stabilization of the three-dimensional Navier-Stokes equations using generalized Lyapunov equations
The approximation of the value function associated to a stabilization problem formulated as optimal control problem for the Navier-Stokes equations in dimension three by means of solutions to generalized Lyapunov equations is proposed and analyzed. The specificity, that the value function is not differentiable on the state space must be overcome. For this purpose a new class of generalized Lyapunov equations is introduced. Existence of unique solutions to these equations is demonstrated. They provide the basis for feedback operators, which approximate the value function, the optimal states and controls, up to arbitrary order.
- MEDIZINISCHE UNIVERSITAT GRAZ Austria
- University of Graz Austria
- Austrian Academy of Sciences Austria
generalized Lyapunov equations, Taylor expansion, Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory, Existence theories for optimal control problems involving partial differential equations, PDEs in connection with fluid mechanics, stabilization, value function, feedback control, optimal control, Optimization and Control (math.OC), FOS: Mathematics, Stabilization of systems by feedback, 3-D Navier-Stokes equations, Optimal feedback synthesis, Mathematics - Optimization and Control
generalized Lyapunov equations, Taylor expansion, Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory, Existence theories for optimal control problems involving partial differential equations, PDEs in connection with fluid mechanics, stabilization, value function, feedback control, optimal control, Optimization and Control (math.OC), FOS: Mathematics, Stabilization of systems by feedback, 3-D Navier-Stokes equations, Optimal feedback synthesis, Mathematics - Optimization and Control
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