A gradient algorithm for optimal control problems with modelreality differences
Access Status
Authors
Date
2015Type
Metadata
Show full item recordCitation
Source Title
ISSN
School
Collection
Abstract
In this paper, we propose a computational approach to solve a modelbased optimal control problem. Our aim is to obtain the optimal solution of the nonlinear optimal control problem. Since the structures of both problems are dierent, only solving the modelbased optimal control problem will not give the optimal solution of the nonlinear optimal control problem. In our approach, the adjusted parameters are added into the model used so as the dierences between the real plant and the model can be measured. On this basis, an expanded optimal control problem is introduced, where system optimization and parameter estimation are integrated interactively. The Hamiltonian function, which adjoins the cost function, the state equation and the additional constraints, is dened. By applying the calculus of variation, a set of the necessary optimality conditions, which denes modied modelbased optimal control problem, parameter estimation problem and computation of modiers, is then derived. To obtain the optimal solution, the modied modelbased optimal control problem is converted in a nonlinear programming problem through the canonical formulation, where the gradient formulation can be made. During the iterative procedure, the control sequences are generated as the admissible control law of the model used, together with the corresponding state sequences. Consequently, the optimal solution is updated repeatedly by the adjusted parameters. At the end of iteration, the converged solution approaches to the correct optimal solution of the original optimal control problem in spite of modelreality dierences. For illustration, two examples are studied and the results show the eciency of the approach proposed.
Related items
Showing items related by title, author, creator and subject.

Kek, S.L.; Teo, Kok Lay; Aziz, M. (2015)A computational approach is proposed for solving the discrete time nonlinear stochastic optimal control problem. Our aim is to obtain the optimal output solution of the original optimal control problem through solving the ...

Lee, Wei R. (1999)In this thesis we shall investigate the numerical solutions to several important practical static and dynamic optimization problems in engineering and physics. The thesis is organized as follows.In Chapter 1 a general ...

Loxton, Ryan Christopher (2010)In this thesis, we develop numerical methods for solving five nonstandard optimal control problems. The main idea of each method is to reformulate the optimal control problem as, or approximate it by, a nonlinear programming ...