Paper: A solution of nonlinear TPBVP's occuring in optimal control

  • Authors:

  • Raimo P. Hämäläinen;Aarne Halme

  • Affiliations:

  • Systems Theory Lab., Helsinki University of Technology, 02150 Espoo, 15, Finland;Control Engn. Lab., Tampere University of Technology, BOX 527, 33101 Tampere, 10, Finland

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 1976

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Abstract

Abstract: A new method is presented to obtain feedback solution for nonsingular optimal control problems, which lead to polynomial type nonlinear two-point boundary-value problems. Examples of such problems treated in the paper are quadratic state regulators for nonlinear systems with an analytic generator including the special case of a bilinear problem, linear quadratic regulators with magnitude constraints on the control variables, and also linear problems with nonquadratic performance indices. The solution method is based on solving a related two-point boundary value problem by using an equivalent functional equation and the theory of the so-called polynomial operators. Considerations are made in discrete form and the resulting algorithms are readily applicable to direct computing and control. Due to computational burden the method is restricted to low dimensional problems. Demonstration of the use of the method is given by designing nonlinear regulators for two computer controlled pilot processes.