The time-invariant linear-quadratic optimal control problem

DOI10.1016/0005-1098(77)90017-6zbMath0359.49001OpenAlexW1993595567MaRDI QIDQ1238979

Publication date: 1977

Published in: Automatica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0005-1098(77)90017-6

Mathematics Subject Classification ID

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 (52)

Acausal models and balanced realizations of stationary processes ⋮ A Galois correspondence between sets of semidefinite solutions of continuous-time algebraic Riccati equations ⋮ Linear-quadratic control with and without stability subject to general implicit continuous-time systems: Coordinate-free interpretations of the optimal costs in terms of dissipation inequality and linear matrix inequality; existence and uniqueness of optimal controls and state trajectories ⋮ A linear quadratic optimal control problem with disturbances -- an algebraic Riccati equation and differential games approach ⋮ A note on lattices of Euclidean subspaces ⋮ Multirate LQG control of continuous-time stochastic systems ⋮ Parallel algorithms for algebraic Riccati equations ⋮ On the relation between additive and multiplicative decompositions of rational matrix functions ⋮ Partial stabilizability and hidden convexity of indefinite LQ problem ⋮ A parametrization of the solutions of the Hamiltonian system for stabilizable pairs ⋮ Existence theorem for the difference Riccati equations ⋮ Linear quadratic regulators with eigenvalue placement in a specified region ⋮ Key‐nodes selection problem for minimum cost control of directed networks ⋮ Determining quadratic weighting matrices to locate poles in a specified region ⋮ Convergence of the time-invariant Riccati differential equation and LQ-problem: mechanisms of attraction ⋮ Canonical correlation analysis, approximate covariance extension, and identification of stationary time series ⋮ All optimal controls for the singular linear-quadratic problem without stability; a new interpretation of the optimal cost ⋮ Finite-time stabilization of linear systems by bounded linear time-varying feedback ⋮ \textit{Turnpike} features in optimal selection of species represented by quota models ⋮ A unified approach to the finite-horizon linear quadratic optimal control problem* ⋮ On the mathematical theory of ensemble (linear-Gaussian) Kalman-Bucy filtering ⋮ Decentralized strategies for finite population linear-quadratic-Gaussian games and teams ⋮ Frequency theorem and the Lure equation ⋮ The Regular Indefinite Linear Quadratic Optimal Control Problem: Stabilizable Case ⋮ A separation theorem for guaranteed \(H_2\) performance through matrix inequalities ⋮ Inherent robustness properties of quasi-infinite horizon nonlinear model predictive control ⋮ Structured optimal feedback in multi-agent systems: a static output feedback perspective ⋮ Indefinite stochastic linear-quadratic optimal control problems with random coefficients: closed-loop representation of open-loop optimal controls ⋮ A result on output feedback linear quadratic control ⋮ On the solution of the Riccati differential equation arising from the LQ optimal control problem ⋮ Mean field linear-quadratic control: uniform stabilization and social optimality ⋮ The Algebraic Riccati Equation without Complete Controllability ⋮ An infinite horizon linear quadratic problem with unbounded controls in Hilbert space ⋮ Optimal pole shifting for continuous multivariable linear systems ⋮ On the stability of matrix-valued Riccati diffusions ⋮ Employing the algebraic Riccati equation for a parametrization of the solutions of the finite-horizon LQ problem: the discrete-time case ⋮ Spectral factorization with imaginary-axis zeros ⋮ The regular convex cooperative linear quadratic control problem ⋮ A parametric Lyapunov equation approach to low gain feedback design for discrete-time systems ⋮ On the robustness of Riccati flows to complete model misspecification ⋮ Mean‐field games for multiagent systems with multiplicative noises ⋮ A numerical algorithm for inner-outer factorizations of real-rational matrices ⋮ Unnamed Item ⋮ Continuity properties of the cheap-control problem without stability ⋮ Linear quadratic regulators with eigenvalue placement in a horizontal strip ⋮ Pole placement in a specified region based on a linear quadratic regulator ⋮ Square indefinite LQ-problem: Existence of a unique solution ⋮ An explicit Floquet-type representation of Riccati aperiodic exponential semigroups ⋮ A parametrization of the solutions of the finite-horizon LQ problem with general cost and boundary conditions ⋮ On the existence of solutions of the general algebraic Riccati equation ⋮ An equivalence result in linear-quadratic theory ⋮ On positive definite solutions to the algebraic Riccati equation

Cites Work

This page was built for publication: The time-invariant linear-quadratic optimal control problem