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Reference: Stanley Michael Langdon, (1970). The application of optimal control theory to a class of extremum control systems. DPhil. University of Oxford.Citable link to this page:


The application of optimal control theory to a class of extremum control systems

Abstract: This thesis constitutes a contribution to the theory ofextremal control systems which come within the automatic controlfield of learning in engineering science.An extremal control system comprises an extremal process(which is to be controlled) and an extremal controller. Theclass of extremal control systems referred to in the title ofthe thesis refers to those systems in which the extremal processconcerned can represented by a particular form of mathematicalmodel.Investigation of the application of optimal control theoryto this class of extremal control system is motivated by twobasic requirements. The first of these originates in the controlof complex industrial processes, particularly in the direct digitalcontrol situation. Here there are a number of possible applicationsfor extremal control, and since costs involved are generally high,the requirement is generally for extremal controllers maintainingas low a system operating cost as possible, rather then forcontrollers with a simple structure. Hence there is a need foroptimal extremal controllers.The second requirement for establishing optimal extremalcontrollers lies in the design of simpler extremal controllers.The performance of the optical extremal controller is required asa basic on which to judge the simpler controllers and decidewhether any more significant improvement can be made.The major part of this investigation of the application ofoptimal control theory to extremal control systems is concernedwith the simplest possible case, where no account is taken ofinput or output lags or noise, or of multiple inputs. Since noprevious optical extremal controllers known this is thenatural starting point.A rigorous analysis of state variables, probabilitynu sufficient statistics for this simplified caseis presented, and this leads on to a new approach to the applicationof dynamic programming which in turn results in an originalfunctional recurrence equation. Analysis of this functionalrecurrence equation leads to s numerical solution procedureincluding many checks. This eventually establishes the opticalextremal controller.Simulation techniques are used to confirm the performance ofthe optimal extremal controller, and hybrid computing facilitiesused to show that it can be implemented on a small on-line computerand used in a direct digital control situation without sufferingfrom interfacing effects. Thus for the first time there is nowavailable an optimal extremal controller, and moreover it can beconfidently expected to perform optimally in a practical situation.Comparison of the performance of the optimal extremalcontroller with the performance of simpler controllers shows that,in the simplified case, there is still room for considerableimprovement on the simple controllers, and a quantitative measureof just how much improvement might be possible is now available.An initial investigation of the application of optimal controltheory to more complex processes, involving noise, lags andmultiple inputs, is presented and this shows that theoreticaldifficulties are likely to prevent further optimal extremalcontrollers from being established. In these cases there istherefore a requirement to establish closely optimal controllers.One approach would be just to use the optimal controller from thesimplified case in these more complex situations. Simulationsare presented establishing the performance of the optimalextremal controller, and a suboptimal extremal controller, controllingnot the process for which they were designed but a similar processinvolving output noise. These simulations show that thesecontrollers are certainly not optimal in the more complex situation.A different approach must therefore be taken to establishingclosely optimal controllers in the more complex situation. Thethesis finishes with a discussion of how this might be achieved.

Type of Award:DPhil Level of Award:Doctoral Awarding Institution: University of Oxford Notes:This thesis was digitised thanks to the generosity of Dr Leonard Polonsky

Bibliographic Details

Issue Date: 1970Identifiers

Urn: uuid:21bbdaeb-60a4-45ae-8500-ee79dfeb54a5

Source identifier: 601870676 Item Description

Type: Thesis;

Language: eng Tiny URL: td:601870676


Author: Stanley Michael Langdon - institutionUniversity of Oxford - - - - Bibliographic Details Issue Date: 1970 - Identifiers Urn: uuid:



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