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Optimal control of hybrid systems


M. Morari

Savoy Place, London, Tustin Lecture, IEE

Over the last few years we have focused on the development of controller synthesis techniques for discrete time linear systems with constraints, logic and switches (linear hybrid systems). At present, there is a wealth of practical problems of this type which can only be handled by trial and error, thus requiring excessive development time. Our ultimate goal is to provide tools which automatically generate controllers guaranteed to satisfy the designers' specifications for such complex situations in much less time. In this seminar I will first summarize our theoretical efforts, starting with the solution of the famous Linear Quadratic Regulator problem for systems with constraints. Then I will show how these results can be extended to hybrid systems. I will conclude with a number of application studies from areas as diverse as automotive systems, power systems and biomedical engineering.

Professor Arnold Tustin 1899 - 1994 Tustin is perhaps best known for the bilinear transformations that bear his name, but his achievements were far greater. Apprenticed to the Parsons Company of Newcastle-upon-Tyne at the age of 16, he was awarded a North East Coast Scholarship, which enabled him to attend Armstrong College (later incorporated into Newcastle University). Just young enough to miss active military service in the First World War, he was able to complete his degree studies before joining Metropolitan Vickers as a graduate trainee. His involvement in feedback control came about through the use of the 'Metadyne' constant-current DC generator for gun control - work which began in 1937/38 and continued during the Second World War. During the early part of the war, his group at Metropolitan Vickers also developed a British approach to frequency-response servo design independently of workers in North America. At around the same time he was responsible, along with the mathematician P.J. Daniell, for a version of the describing function approach to non-linearities. Furthermore, he invented a 'signal flow graph' representation of feedback loops, and developed a 'time series' description of signals much closer to the modern view of discrete processing than the contemporary ‘pulsed-servo' approach of Stibitz, MacColl and Hurewicz in the US. In addition to all this, he made significant contributions to mainstream electrical engineering and was the author of many published papers on electrical machines. Tustin's massive achievements in classical control are perhaps illustrated most clearly in a series of four papers published in 1947 in the Journal of the Institution of Electrical Engineers. In addition to contributions on describing functions and operator response, these include 'Analysing the behaviour of linear systems in terms of time series', which sets out clearly a whole calculus of discrete signals. In this paper, Tustin showed how discrete convolution corresponded to multiplication in the frequency domain; proposed the trapezoidal discrete differentiator with which his name is now associated; and applied his new techniques to analyse a number of simple feedback systems. Conscious of the need to develop an industrial base in control engineering in the immediate post-war years, Tustin was an active participant in the activities of all the relevant British professional bodies. A glance through the proceedings of the IMechE, the IEE and the Society of Instrument Technology (later the Institute of Measurement and Control) reveals, in addition to his own papers, his regular and perceptive comments on the work of others. He chaired the organising committee of one of the first major international conferences on control, held at Cranfield in 1951, and chaired the IEE's Measurement & Control Section in 1959/60. He was Professor of Engineering at Birmingham University from 1947 to 1955 and Imperial College from 1955 to 1964, and Visiting Professor at MIT in 1953/54. Like a number of his contemporaries, Tustin became interested in later life in the application of systems thinking to social and biological systems. As early as 1953 he had published his Mechanism of Economic Systems, which applied feedback ideas to economic models, and he continued to take an interest in psychology and artificial intelligence up until his death. Even in his nineties, blind and almost deaf, he continued to work with the aid of an amanuensis.


Type of Publication:

(05)Plenary/Invited/Honorary Lecture

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