All optimal controls for the singular linear-quadratic problem without stability; a new interpretation of the optimal cost

DOI10.1016/0024-3795(89)90403-5zbMath0674.49001OpenAlexW2142648659MaRDI QIDQ1121511

Ton Geerts

Publication date: 1989

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(89)90403-5

zbMATH Keywords

dissipation inequalitydual structure algorithmsingular linear-quadratic control problem

Mathematics Subject Classification ID

Existence theories for optimal control problems involving ordinary differential equations (49J15)

Related Items (5)

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 ⋮ Constrained minimum variance control for discrete-time stochastic linear systems ⋮ Minimal representations of continuous-time processes having spectral density with zeros in the extended imaginary axis ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

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• The role of the dissipation matrix in singular optimal control
• System structure and singular control
• A necessary and sufficient condition for solvability of the linear- quadratic control problem without stability
• Cheap control of the time-invariant regulator
• The time-invariant linear-quadratic optimal control problem
• Geometric state-space theory in linear multivariable control: A status report
• Generalizations of singular optimal control theory
• A nine-fold canonical decomposition for linear systems
• Singular Optimal Control: A Geometric Approach
• Almost invariant subspaces: An approach to high gain feedback design--Part I: Almost controlled invariant subspaces
• On the existence of a negative semidefinite, antistabilizing solution to the discrete-time algebraic Riccati equation
• On the discrete time algebraic Riccati equation
• Singular perturbations and singular arcs--Part I
• The stabilizing solution of the discrete algebraic riccati equation
• A strong controllability and observability in linear multivariable control
• External solutions of Riemann-Stieltjes inequalities of linear optimal control
• Singular perturbations and singular arcs--Part II
• Spectral theory of the linear-quadratic optimal control problem: Discrete-time single-input case
• Correspondence : Correction to ‘The zeros of a system’
• Nonnegativity of a Quadratic Functional
• Optimal state estimation in high noise
• Input–Output Structure of Linear Systems with Application to the Decoupling Problem
• The zeros of a system†
• A contribution to matrix quadratic equations

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