A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy / In this thesis we used the following four types of optimal control problems:
(i) Problems governed by systems of ordinary differential equations;
(ii) Problems governed by systems of ordinary differential equations with
time-delayed arguments appearing in both the state and the control
variables;
(iii) Problems governed by linear systems subject to sudden jumps in parameter
values;
(iv) A chemical reactor problem governed by a couple of nonlinear diffusion
equations.
• The aim of this thesis is to devise computational algorithms for solving the optimal control
problems under consideration. However, our main emphasis are on the mathematical
theory underlying the techniques, the convergence properties of the algorithms and the
efficiency of the algorithms.
Chapters II and III deal with problems of the first type, Chapters IV and V deal with
problems of the second type, and Chapters VI and VII deal with problems of the third and
fourth type respectively. A few numerical problems have been included in each of these
Chapters to demonstrate the efficiency of the algorithms involved.
The class of optimal control problems considered in Chapter II consists of a nonlinear
system, a nonlinear cost functional, initial equality constraints, and terminal equality
constraints. A Sequential Gradient-Restoration Algorithm is used to devise an iterative
algorithm for solving this class of problems. 'I'he convergence properties of the algorithm
are investigated.
The class of optimal control problems considered in Chapter III consists of a nonlinear
system, a nonlinear cost functional, and terminal as well as interior points equality
constraints. The technique of control parameterization and Liapunov concepts are used to
solve this class of problems,
A computational algorithm for solving a class of optimal control problems involving
terminal and continuous state constraints or inequality type was developed by Rei. 103 in
1989. In Chapter IV, we extend the results of Ref. 103 to a more general class of
constrained time-delayed optimal control problems, which involves terminal state equality
constraints, as well as terminal state inequality constraints and continuous state inequality
constraints.
In Ref. 104, a computational scheme using the technique of control parameterization was
developed for solving a class of optimal control problems in which the cost functional includes the full variation of control. Chapter V is a straightforward extension of Ref. 104
to the time-delayed case. However the main contribution of this chapter is that many
numerical examples have been solved.
In Chapter VI, a class of linear systems subject to sudden jumps in parameter values is
considered. To solve this class of stochastic control problem, we try to seek for the best
feedback control law depending only on the measurable output. Based on this idea, we
convert the original problem into an approximate constrained deterministic optimization
problem, which can be easily solved by any existing nonlinear programming technique.
In Chapter VII, a chemical reactor problem and its control to achieve a desired output
temperature is considered. A finite element Galerkin method is used to convert the
original distributed optimal control problem into a quadratic programming problem with
linear constraints, which can he solved by any standard quadratic programming software . / Andrew Chakane 2018
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/25911 |
| Date | January 1992 |
| Creators | Kaji, Keiichi |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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