论文信息 - Singularly perturbed difference equations in optimal control problems

Singularly perturbed difference equations in optimal control problems

A linear regular problem involving singularly perturbed difference equations is considered. The basic features of singularly perturbed systems-order reduction, separation of time scales, boundary layers, etc.-are highlighted. Application to the numerical treatment of control problems involving stiff differential equations is discussed.

G. Blankenship

[1] R. Has’minskiĭ. On Stochastic Processes Defined by Differential Equations with a Small Parameter , 1966 .

[2] P. Dorato,et al. Optimal linear regulators: The discrete-time case , 1971 .

[3] P. Kokotovic,et al. Singular perturbation of linear regulators: Basic theorems , 1972 .

[4] P. Kokotovic,et al. A decomposition of near-optimum regulators for systems with slow and fast modes , 1976 .

[5] H. Kushner. Probabilistic methods for finite difference approximations to degenerate elliptic and parabolic equations with Neumann and Dirichlet boundary conditions , 1976 .

[6] C. Comstock,et al. Singular perturbatilons for difference equations , 1976 .

[7] W. Miranker,et al. Multitime Methods for Systems of Difference Equations , 1977 .

[8] H. Kushner. Convergence of recursive adaptive and identification procedures via weak convergence theory , 1977 .

[9] M. Dmitriev,et al. Singular Perturbations and Some Optimal Control Problems , 1978 .

[10] Michael Athans,et al. Survey of decentralized control methods for large scale systems , 1978 .

[11] R. Phillips. Reduced order modelling and control of two-time-scale discrete systems† , 1980 .