The study of discrete singularly perturbed linear-quadratic control systems

Zoran Gajic, Myotaeg Lim, Xuemin Shen

Research output: Chapter in Book/Report/Conference proceedingChapter

7 Citations (Scopus)

Abstract

This chapter studies the reduced-order parallel algorithms for solving the algebraic Lyapunov and Riccati equations of discrete-time singularly perturbed systems. The algebraic Riccati equation is solved efficiently by using a bilinear transformation. The obtained results are extended to the discrete-time linear regulator problem. An F-8 aircraft model is used to demonstrate the presented technique. The chapter discusses studies the discrete-time Kalman filtering and the corresponding linear optimal stochastic control problem. It examines that the algebraic regulator and filter Riccati equations of singularly perturbed discrete-time control systems are completely and exactly decomposed into reduced-order continuous-time algebraic Riccati equations corresponding to the slow and fast time scales. The exact solution of the global discrete algebraic Riccati equation is obtained in terms of the reduced-order pure-slow and pure-fast non-symmetric continuous-time algebraic Riccati equations. The optimal global Kalman filter is decomposed into pure-slow and pure-fast local optimal filters both driven by the system measurements and the system optimal control input. It is shown that these two filters are implemented independently in the different time scales. As a result, the optimal linear-quadratic Gaussian control problem for singularly perturbed linear discrete systems takes the complete decomposition and parallelism between pure-slow and pure-fast filters and controllers.

Original languageEnglish
Title of host publicationControl and Dynamic Systems
Pages199-242
Number of pages44
EditionC
DOIs
Publication statusPublished - 1995 Jan 1

Publication series

NameControl and Dynamic Systems
NumberC
Volume70
ISSN (Print)0090-5267

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Information Systems

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  • Cite this

    Gajic, Z., Lim, M., & Shen, X. (1995). The study of discrete singularly perturbed linear-quadratic control systems. In Control and Dynamic Systems (C ed., pp. 199-242). (Control and Dynamic Systems; Vol. 70, No. C). https://doi.org/10.1016/S0090-5267(06)80030-7