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 opti

DOI10.1016/0024-3795(94)90216-XzbMath0814.49031MaRDI QIDQ1329990

Ton Geerts

Publication date: 15 August 1994

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

zbMATH Keywords

optimal controldissipation inequalitysolvabilitymatrix inequalitytime-invariantcontinuous-timelinear quadratic control

Mathematics Subject Classification ID

Linear systems in control theory (93C05) Linear-quadratic optimal control problems (49N10) Optimality conditions for problems involving ordinary differential equations (49K15)

Related Items (5)

Higher-order continuous-time implicit systems: Consistency and weak consistency, impulse controllability, geometric concepts, and invertibility properties ⋮ Linear-Quadratic Optimal Control of Differential-Algebraic Systems: The Infinite Time Horizon Problem with Zero Terminal State ⋮ The Kalman-Yakubovich-Popov inequality for differential-algebraic systems ⋮ Use of semidefinite programming for solving the LQR problem subject to rectangular descriptor systems ⋮ Discounted cost linear quadratic Gaussian control for descriptor systems

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
• All optimal controls for the singular linear-quadratic problem without stability; a new interpretation of the optimal cost
• The autonomous linear quadratic control problem. Theory and numerical solution
• Solvability conditions, consistency, and weak consistency for linear differential-algebraic equations and time-invariant singular systems: The general case
• The time-invariant linear-quadratic optimal control problem
• Regularity and singularity in linear-quadratic control subject to implicit continuous-time systems
• Generalized linear systems: Geometric and structural approaches
• Invariant subspaces and invertibility properties for singular systems: The general case
• Dissipative dynamical systems. I: General theory
• The linear-quadratic optimal regulator for descriptor systems
• A generalized state-space for singular systems
• Descriptor variable systems and optimal state regulation
• Singular Optimal Control: A Geometric Approach
• Singular systems: A new approach in the time domain
• Geometric structure and feedback in singular systems
• Feedback and pole placement in descriptor variable Systems†
• Poles and zeros of linear multivariable systems : a survey of the algebraic, geometric and complex-variable theory
• Structural properties of linear dynamical systems
• Nonnegativity of a Quadratic Functional

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