Asymptotic analysis and solution of a finite-horizon \(H_{\infty}\) control problem for singularly-perturbed linear systems with small state delay

DOI10.1023/A:1023631706975zbMath1036.93013OpenAlexW67460923MaRDI QIDQ1411505

D. Massart

Publication date: 29 October 2003

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1023631706975

zbMATH Keywords

asymptotic solutionssingular perturbationsstate delay\(H_{\infty}\) controlcomposite controllerfunctional-differential equations of Riccati typereduced-order and boundary-layer \(H_{\infty}\) subproblemssimplified controllers

Mathematics Subject Classification ID

Control/observation systems governed by functional-differential equations (93C23) (H^infty)-control (93B36) Time-scale analysis and singular perturbations in control/observation systems (93C70) System structure simplification (93B11)

Related Items (44)

Robust numerical method for singularly perturbed differential equations with large delay ⋮ UNIFORMLY CONVERGENT NUMERICAL METHOD FOR SINGULARLY PERTURBED DELAY PARABOLIC DIFFERENTIAL EQUATIONS ARISING IN COMPUTATIONAL NEUROSCIENCE ⋮ Reproducing kernel Hilbert space method for nonlinear second order singularly perturbed boundary value problems with time-delay ⋮ A parameter uniform numerical method for singularly perturbed delay problems with discontinuous convection coefficient ⋮ Finite-Horizon $$H_{\infty }$$ Control Problem with Singular Control Cost ⋮ Robust numerical method for singularly perturbed differential equations having both large and small delay ⋮ An initial value technique for singularly perturbed convection-diffusion problems with a negative shift ⋮ Unnamed Item ⋮ Accelerated fitted operator finite difference method for singularly perturbed delay differential equations with non-local boundary condition ⋮ Unnamed Item ⋮ Almost second-order uniformly convergent numerical method for singularly perturbed convection–diffusion–reaction equations with delay ⋮ A second order stabilized central difference method for singularly perturbed differential equations with a large negative shift ⋮ Uniformly convergent finite difference method for reaction-diffusion type third order singularly perturbed delay differential equation ⋮ Uniformly convergent hybrid numerical scheme for singularly perturbed turning point problems with delay ⋮ An iterative numerical method for singularly perturbed reaction-diffusion equations with negative shift ⋮ Asymptotic numerical method for third-order singularly perturbed convection diffusion delay differential equations ⋮ Fitted numerical scheme for singularly perturbed convection-diffusion reaction problems involving delays ⋮ Uniform hybrid difference scheme for singularly perturbed differential-difference turning point problems exhibiting boundary layers ⋮ Analysis of a Hybrid Numerical Scheme for Singularly Perturbed Convection-Diffusion Type Delay Problems ⋮ Parametric uniform numerical method for singularly perturbed differential equations having both small and large delay ⋮ A Numerical Method for a System of Singularly Perturbed Differential Equations of Reaction-Diffusion Type with Negative Shift ⋮ A Parameter Uniform Numerical Method for an Initial Value Problem for a System of Singularly Perturbed Delay Differential Equations with Discontinuous Source Terms ⋮ A Parameter-Uniform First Order Convergent Numerical Method for a Semi-linear System of Singularly Perturbed Second Order Delay Differential Equations ⋮ Numerical integration of a class of singularly perturbed delay differential equations with small shift ⋮ Unnamed Item ⋮ Numerical solution of singularly perturbed delay differential equations with layer behavior ⋮ High-order uniformly convergent method for nonlinear singularly perturbed delay differential equations with small shifts ⋮ Unnamed Item ⋮ Numerical solution of singularly perturbed differential difference equations with mixed parameters ⋮ A uniformly almost second order convergent numerical method for singularly perturbed delay differential equations ⋮ Solution of singularly perturbed differential-difference equations with mixed shifts using Galerkin method with exponential fitting ⋮ A numerical method based on finite difference for boundary value problems for singularly perturbed delay differential equations ⋮ FITTED MESH METHOD FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL TURNING POINT PROBLEMS EXHIBITING TWIN BOUNDARY LAYERS ⋮ A parameter uniform numerical method for a singularly perturbed two-parameter delay differential equation ⋮ Exponentially fitted numerical method for singularly perturbed differential-difference equations ⋮ Higher-order uniformly convergent numerical scheme for singularly perturbed differential difference equations with mixed small shifts ⋮ A Parameter-Uniform First Order Convergent Numerical Method for a System of Singularly Perturbed Second Order Delay Differential Equations ⋮ Unnamed Item ⋮ A parameter-uniform collocation scheme for singularly perturbed delay problems with integral boundary condition ⋮ Singularly perturbed delay differential equations of convection-diffusion type with integral boundary condition ⋮ Solving linear second-order singularly perturbed differential difference equations via initial value method ⋮ Unnamed Item ⋮ Second order singularly perturbed delay differential equations with non-local boundary condition ⋮ A hybrid numerical scheme for singular perturbation delay problems with integral boundary condition

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Representation and control of infinite dimensional systems. Volume I
• Asymptotic expansions for game-theoretic Riccati equations and stabilization with disturbance attenuation for singularly perturbed systems
• Singular perturbations and time-scale methods in control theory: Survey 1976-1983
• Decomposition of linear optimal singularly perturbed systems with aftereffect
• Singular perturbations in optimal control problems
• \(H_{\infty}\)-state-feedback control of linear systems with small state delay
• \(H_\infty\) control for singularly perturbed systems
• \({\mathcal H}_{\infty{}}\) control of two-time-scale systems
• Asymptotic solution of a singularly perturbed set of functional-differential equations of Riccati type encountered in optimal control theory
• Separation of motions in multirate discontinuous systems with time delay
• \(H_ \infty\)-control for distributed parameter systems: A state-space approach
• On the Isaacs equation of differential games for descriptor systems
• Asymptotic solution of zero-sum linear-quadratic differential game with cheap control for minimizer
• \(H_\infty\) control of linear singularly perturbed systems with small state delay
• Asymptotic solution of a boundary-value problem for linear singularly-perturbed functional differential equations arising in optimal control theory
• \(H^ \infty\)-optimal control for singularly perturbed systems. I: Perfect state measurements
• Perturbations, approximations and sensitivity analysis of optimal control systems
• Stabilizability and detectability of singularly perturbed linear time-invariant systems with delays in state and control
• Optimal control of stochastic systems with aftereffect
• Differential equations: Stability, oscillations, time lags
• Finite horizon H/sub ∞/ state-feedback control of continuous-time systems with state delays
• The linear-quadratic optimal regulator for descriptor systems
• Applications of Singular Perturbation Techniques to Control Problems
• State-space solutions to standard H/sub 2/ and H/sub infinity / control problems
• Variational calculus for descriptor problems
• Stability and the Infinite-Time Quadratic Cost Problem for Linear Hereditary Differential Systems
• H/sup ∞/-optimal control for singularly perturbed systems. II. Imperfect state measurements
• Delay Sensitivity of Quadratic Controllers: A Singular Perturbation Approach
• Near-optimal H/sup ∞/ control of linear singularly perturbed systems
• On the Control of a Linear Functional-Differential Equation with Quadratic Cost

This page was built for publication: Asymptotic analysis and solution of a finite-horizon \(H_{\infty}\) control problem for singularly-perturbed linear systems with small state delay