Designing Robust Controllers by the Mini-Max Search Method : Keynote paper

The problem of regulators (controllers) design is extremely relevant in connection with the penetration into all technological areas of the methods of precise control of objects with feedback. Such devices are being more and more used, which increases the variety of controlled objects. This list includes all new objects of robotics and technological setups, which have much more complex mathematical models. One of the most urgent problems in this area is control of non-stationary objects. Parameters of mathematical model of these objects are given with some uncertainty, but not in fixed values, i.e. by only intervals of their possible changes. If the intervals are too wide, adaptive systems have to be designed, but if they are not too wide, then one can try to find a universal regulator setting that will be sufficiently effective for all ratios of the model parameters within the acceptable intervals of their changes. The paper proposes a new method of the numerical optimization of regulator for finding such a setting for the worst object model that is for the worst combination of all variable parameters. Finding the worst model is also carried out by a numerical optimization method, in which a combination of model parameters is found where the best regulator gives the worst result. The problem is proposed to solve in several optimization cycles with alternation of objective functions. The technique has been well illustrated by a numerical example.