On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems

DOI10.3934/mcrf.2020032zbMath1462.49058OpenAlexW2991649084MaRDI QIDQ829013

Lars Grüne, Roberto Guglielmi

Publication date: 5 May 2021

Published in: Mathematical Control and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/mcrf.2020032

zbMATH Keywords

linear-quadratic optimal controldissipativitylong time behaviourdetectabilityturnpike propertyLyapunov matrix inequality

Mathematics Subject Classification ID

Asymptotic stability in control theory (93D20) Linear-quadratic optimal control problems (49N10) Existence theories for optimal control problems involving ordinary differential equations (49J15) Control/observation systems governed by ordinary differential equations (93C15) Optimality conditions for problems involving ordinary differential equations (49K15)

Related Items (10)

Turnpike in optimal control of PDEs, ResNets, and beyond ⋮ Optimal Control of Port-Hamiltonian Descriptor Systems with Minimal Energy Supply ⋮ Turnpike properties for partially uncontrollable systems ⋮ Turnpike properties of optimal boundary control problems with random linear hyperbolic systems ⋮ Turnpike Properties for Mean-Field Linear-Quadratic Optimal Control Problems ⋮ Classical System Theory Revisited for Turnpike in Standard State Space Systems and Impulse Controllable Descriptor Systems ⋮ Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs ⋮ When does stabilizability imply the existence of infinite horizon optimal control in nonlinear systems? ⋮ The turnpike property and the longtime behavior of the Hamilton-Jacobi-Bellman equation for finite-dimensional LQ control problems ⋮ Turnpike properties for stochastic linear-quadratic optimal control problems

Cites Work

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• On the relation between strict dissipativity and turnpike properties
• Optimal Neumann control for the 1D wave equation: finite horizon, infinite horizon, boundary tracking terms and the turnpike property
• Approximation properties of receding horizon optimal control
• Economic receding horizon control without terminal constraints
• The turnpike property in finite-dimensional nonlinear optimal control
• Optimal control problems over large time intervals
• Rational matrix equations in stochastic control.
• Integral and measure-turnpike properties for infinite-dimensional optimal control systems
• Nonlinear model predictive control. Theory and algorithms
• On turnpike and dissipativity properties of continuous-time optimal control problems
• Turnpike phenomenon and infinite horizon optimal control
• Dissipative dynamical systems. I: General theory
• Dissipative dynamical systems. II: Linear systems with quadratic supply rates
• Turnpike properties in the calculus of variations and optimal control
• An Exponential Turnpike Theorem for Dissipative Discrete Time Optimal Control Problems
• Optimal control of the Lotka–Volterra system: turnpike property and numerical simulations
• Optimizing Process Economic Performance Using Model Predictive Control
• Turnpike Properties and Strict Dissipativity for Discrete Time Linear Quadratic Optimal Control Problems
• Localizations of $$ U_{q}(\mathfrak{s}\mathfrak{l}(2))$$ and $$ U_{q}(\mathfrak{o}\mathfrak{s}\mathfrak{p}(1\vert 2))$$ Associated with Euclidean and Super Euclidean Algebras
• Long Time versus Steady State Optimal Control

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