On optimal control problems with bounded state variables and control appearing linearly

  • H. Maurer
Optimal Control Deterministic
Part of the Lecture Notes in Computer Science book series (LNCS, volume 41)


Necessary conditions for the junction of interior arcs and boundary arcs of an optimal control are given. These conditions are based on necessary conditions for the switching function holding at junction points or contact points with the state boundary. The junction theorems obtained are similar to junction theorems in singular control problems.


  1. [1]
    Jacobson, D.H., Lele, M.M., Speyer, J.L.: New Necessary Conditions of Optimality for Control Problems with State-Variable Inequality Constraints. J. of Math. Analysis and Appl. 35 (1971), 255–284.Google Scholar
  2. [2]
    Norris, D.O.: Nonlinear Programming Applied to State-Constrained Optimization Problems. J. of Math. Analysis and Appl. 43 (1973), 261–272.Google Scholar
  3. [3]
    McDanell, J.P., Powers, W.F.: Necessary Conditions for Joining Singular and Nonsingular Subarcs. SIAM J. on Control 9 (1971), 161–173Google Scholar
  4. [4]
    Maurer, H.: On Optimal Control Problems with Bounded State Variables and Control Appearing Linearly. Submitted to SIAM J. on Control.Google Scholar
  5. [5]
    Maurer, H., Gillessen, W.: Application of Multiple Shooting to the Numerical Solution of Optimal Control Problems with Bounded State Variables. To appear in COMPUTING.Google Scholar
  6. [6]
    Maurer, H.: Numerical Solution of Singular Control Problems Using Multiple Shooting Techniques. To appear in JOTA 18, No.2 (1976).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  • H. Maurer
    • 1
  1. 1.Mathematisches Institut der Universität Würzburg87 WürzburgW.-Germany

Personalised recommendations