Applied Mathematics and Mechanics

, Volume 15, Issue 8, pp 713–719 | Cite as

Singularly perturbed methods in the theory of optimal control of systems governed by partial differential equations

  • Tian Gen-bao
  • Lin Zong-chi


In this paper, the various problems associated with the optimal control of systems governed by partial differential equations are introduced by using singularly perturbed methods for analysis based on state equations, or the cost function and also state equations defined in perturbed domains.

Key words

optimal control perturbation techniques partial differential equations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Kokotovic, P. V., R. E. O'Malley, Jr. and P. Sannuti, Singular perturbations and order reduction in control theory—An overview,Automatica,12 (1976), 123–129.zbMATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    Kokotovic, P. V. and R. A. Vackel, Singular perturbation theory of linear state regulaters,IEEE Trans. Aut. Contr., AC-17 (1972), 29–37.zbMATHCrossRefGoogle Scholar
  3. [3]
    Lions, J. L.,Controte Optimal de Systems Gouvernes Par des Equations aux Derivees Partielles, Dunod, Paris (1968); (English trans. by S. K. Mitter. Springer) (1971).Google Scholar
  4. [4]
    Visik, M. I. and L. A. Lyusternik, Regular degeneration and boundary layer for linear differential equations with small parameter,Usp. Mat. Nauk,12, 5 (77), 3–122 (in Russian),AMS Transl., ser.2, 20, (1962), 239–364.MathSciNetGoogle Scholar
  5. [5]
    Lin Zong-chi, Perturbations of solution and characteristic value and characteristic function of elliptic differential equations of order 2 in the case of boundary perturbation,Report Acad. SSSR,157, 4 (1964), 784–787. (in Russian)Google Scholar
  6. [6]
    Lions, J. L., Perturbations singulières dans les problèms aux limites et en contrôle optimal,Lecture Notes in Mathematics, Springer-Verlag (1973).Google Scholar

Copyright information

© SUT 1994

Authors and Affiliations

  • Tian Gen-bao
    • 1
  • Lin Zong-chi
    • 2
  1. 1.Mathematical SectionShanghai Railway CollegeShanghai
  2. 2.Department of MathematicsFujian Normal UniversityFuzhou

Personalised recommendations