Algebraic Riccati equations with non-smoothing observation arising in hyperbolic and Euler-Bernoulli boundary control problems

DOI10.1007/BF01762397zbMath0674.49004MaRDI QIDQ1121513

Franco Flandoli, Irena Lasiecka, Roberto Triggiani

Publication date: 1988

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

zbMATH Keywords

unbounded operatorsabstract differential equationsoptimal quadratic cost problemsecond order hyperbolic scalar equations

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items

Rapid exponential stabilization of a Boussinesq system of KdV–KdV Type, High level interior and boundary regularity results of the euler-bernoulli equation with application to differential riccati equations in optimal control¹, On the direct solution of Riccati equations arising in boundary control theory, From PDEs with boundary control to the abstract state equation with an unbounded input operator: a tutorial. With discussion by Laurent Lefèvre and Didier Georges and comments by the authors., Infinite-horizon boundary control of distributed systems, On the discrete and continuous time infinite-dimensional algebraic Riccati equations, Optimal boundary control with critical penalization for a PDE model of fluid-solid interactions, FREQUENCY DOMAIN CONDITIONS FOR THE EXISTENCE OF ALMOST PERIODIC SOLUTIONS IN EVOLUTIONARY VARIATIONAL INEQUALITIES, Min-max game theory and algebraic Riccati equations for boundary control problems with analytic semigroups—II. The general case, Periodic optimal control in Hilbert space, Exact controllability of the wave equation with Neumann boundary control, Exponential stabilization of hyperbolic systems with nonlinear, unbounded perturbations—riccati operator approach, Differential Riccati equations with unbounded coefficients: applications to boundary control/boundary observation hyperbolic problems, Optimal control of stable weakly regular linear systems, Frequency domain conditions for finite-dimensional projectors and determining observations for the set of amenable solutions, Maximal controllability for boundary control problems, An example in linear quadratic optimal control, Characterizations of Complete Stabilizability, Feedback law to stabilize linear infinite-dimensional systems, Boundary controllability and stabilizability of a coupled first-order hyperbolic-elliptic system, Unnamed Item, Exact controllability of the Euler-Bernoulli equation with boundary controls for displacement and moment, Dynamical reconstruction of inputs for contraction semigroup systems: Boundary input case, Min-max game theory and nonstandard differential Riccati equations for abstract hyperbolic-like equations, Exact controllability and uniform stabilization of Kirchhoff plates with boundary control only on \(\Delta{} w{} _ \Sigma\) and homogeneous boundary displacement, Estimation du taux de décroissance pour la solution de problèmes de stabilisation, application à la stabilisation de l'équation des ondes, The regulator problem with indefinite quadratic cost for boundary control systems: the finite horizon case, Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions, The fluid-structure interaction model with both control and disturbance at the interface: a game theory problem via an abstract approach, Conservative Control Systems Described by the Schrödinger Equation, Feedback stabilization of a boundary layer equation, Exact controllability of the Euler-Bernoulli plate via bending moments only on the space of optimal regularity, Galerkin approximations of infinite-dimensional compensators for flexible structures with unbounded control action, Regularity with interior point control of Schrödinger equations, Approximations of solutions to infinite–dimensional algebraic riccati equations with unbounded input operators, Abstract settings for tangential boundary stabilization of Navier--Stokes equations by high- and low-gain feedback controllers., A Lifting Theorem for the Time Regularity of Solutions to Abstract Equations with Unbounded Operators and Applications to Hyperbolic Equations, Boundary control of a class of hyperbolic systems, Discussion on: ``Boundary control of a class of hyperbolic systems, Linear Hyperbolic and Petrowski Type PDEs with Continuous Boundary Control → Boundary Observation Open Loop Map: Implication on Nonlinear Boundary Stabilization with Optimal Decay Rates, Algebraic Riccati equations arising from systems with unbounded input-solution operator: applications to boundary control problems for wave and plate equations, Characterization by observability inequalities of controllability and stabilization properties, Open-loop stabilizability of infinite-dimensional systems, Exponential stabilization on infinite dimensional system with impulse controls, Extended algebraic Riccati equations in the abstract hyperbolic case, Equivalent conditions for the solvability of nonstandard and singular LQ-problems with application to parabolic equations, Differential Riccati equation for the active control of a problem in structural acoustics, A trace regularity result for thermoelastic equations with application to optimal boundary control, Acoustic wave guides as infinite-dimensional dynamical systems, The Kalman-Yakubovich-Popov theorem for stabilizable hyperbolic boundary control systems, Quadratic optimal control through spectral and coprime factorisation, Synthesis of finite-dimensional Riccati-based feedback controls for problems arising in structural acoustics, Min-max game theory and algebraic Riccati equations for boundary control problems with continuous input-solution map. II: The general case, Stabilization of the semilinear wave equation with viscous damping, Numerical approximations and regularizations of Riccati equations arising in hyperbolic dynamics with unbounded control operators, Exact controllability of semilinear abstract systems with application to waves and plates boundary control problems, The dual algebraic Riccati equations: additional results under isomorphism of the Riccati operator, Feedback exact null controllability for unbounded control problems in Hilbert space, Feedback approximation of the minimum energy control for linear infinite- dimensional systems with zero terminal state, Optimal Neumann control for the 1D wave equation: finite horizon, infinite horizon, boundary tracking terms and the turnpike property

Cites Work

• Regularity of hyperbolic equations under \(L^ 2(0,T;L_ 2(\Gamma))\)- Dirichlet boundary terms
• Energie decay estimates and exact boundary value controllability for the wave equation in a bounded domain
• Decay of solutions of wave equations in a bounded region with boundary dissipation
• Riccati equations for nonsymmetric and nondissipative hyperbolic systems with \(L_ 2\)-boundary controls
• A direct study of the Riccati equation arising in hyperbolic boundary control problems
• Invertibility of Riccati operators and controllability of related systems
• Uniform exponential energy decay of wave equations in a bounded region with \(L_ 2(0,\infty;L_ 2(\Gamma))\)-feedback control in the Dirichlet boundary conditions
• Non homogeneous boundary value problems for second order hyperbolic operators
• The regulator problem for parabolic equations with Dirichlet boundary control. I: Riccati's feedback synthesis and regularity of optimal solution
• Exact boundary controllability on \(L_ 2(\Omega)\times H^{-1}(\Omega)\) of the wave equation with Dirichlet boundary control acting on a portion of the boundary \(\partial \Omega\), and related problems
• Exact controllability of the wave equation with Neumann boundary control
• A cosine operator approach to modeling \(L_ 2(\)0,T;\(L_ 2(\)Gammma))- boundary input hyperbolic equations
• Quelques résultats d'existence, unicité et régularité pour un problème de la théorie du contrôle
• Extending a theorem of A. M. Liapunov to Hilbert space
• A linear control problem in an abstract Hilbert space
• Riccati Equation Arising in a Boundary Control Problem with Distributed Parameters
• A Lifting Theorem for the Time Regularity of Solutions to Abstract Equations with Unbounded Operators and Applications to Hyperbolic Equations
• Infinite Dimensional Linear Systems With Unbounded Control and Observation: A Functional Analytic Approach
• Exact Controllability, Stabilization and Perturbations for Distributed Systems
• Exact Controllability of the Euler–Bernoulli Equation with Controls in the Dirichlet and Neumann Boundary Conditions: A Nonconservative Case
• A Note on the Boundary Stabilization of the Wave Equation
• The Infinite-Dimensional Riccati Equation for Systems Defined by Evolution Operators
• The Riccati Integral Equations for Optimal Control Problems on Hilbert Spaces
• Riccati Equations for Hyperbolic Partial Differential Equations with $L_2 (0,T;L_2 (\Gamma ))$—Dirichlet Boundary Terms
• The Linear Quadratic Control Problem for Infinite Dimensional Systems with Unbounded Input and Output Operators
• Dirichlet Boundary Control Problem for Parabolic Equations with Quadratic Cost: Analyticity and Riccati’s Feedback Synthesis
• Initial boundary value problems for hyperbolic systems
• L₂ is a continuable initial condition for kreiss' mixed problems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item