ABSTRACT
In order to predict or control the behaviour of a system in the ‘real’ world, be it physical, biological or socio-economic, the system analyst seeks to capture its salient features in an abstraction, a mathematical model. Such a model always contains elements which are uncertain. These uncertain elements may be parameters, constant or time-varying, which are unknown or imperfectly known, or they may be unknown or imperfectly known inputs into the system. Despite such imperfect knowledge about the chosen mathematical model, one often seeks to devise controllers which will steer the system response in a desired fashion, for example so as to obtain stable behaviour. Here, two main avenues are open to the system analyst. He may choose a stochastic approach in which information about the uncertain elements as well as about the system behaviour is in statistical terms; loosely speaking, he is content with desirable behaviour on the average. For stochastic treatments in this category, see Kushner (1966) and Äström (1970). On the other hand, he may opt for a deterministic approach and attempt to construct controllers which assure the desired behaviour; loosely speaking, he wishes to guarantee that every possible response of the mathematical model possesses the desired features. Here we shall eschew the stochastic approach and discuss briefly some deterministic ones.
