Plenary talk


Introduction :



Franco BLANCHINI - Professor

University of Udine,
Dipartimento di Matematica e Informatica,
Via Delle Scienze,
208 - 33100 Udine,

Electronic mail : Franco BLANCHINI
Professional page

Tel. int : +39/0432/558466,    Fax. int : +39/0432/558499


Title :
Lyapunov and invariance methods in control design
(Slide of the presentation)


Abstract :
Many control problems can be naturally formulated, analyzed and solved in a set--theoretic context. Sets appear naturally when three aspects, which are crucial in control systems design, are considered: constraints, uncertainties and design specifications. Furthermore sets are the most appropriate language to specify several system performances, for instance when we are interested in determining the domain of attraction, in measuring the effect of a persistent noise in a feedback loop or in bounding the error of an estimation algorithm. Generally speaking, in the control theory context, all the techniques which are theoretically based on some properties of subsets of the state--space could be referred to as set--theoretic methods. The most popular and clear link is that with the Lyapunov theory and positive invariance. These techniques have been presented for the first time around forty years ago but it is quite important to revise them in a renewed light, especially in view of the modern computing possibilities.

The main purpose of this talk is to survey the set theoretic approach for the control and analysis of dynamic systems from both a theoretical and practical standpoint, with special regards to the connections with important areas in control theory including constrained control, robust control, disturbance rejection and robust estimation. The talk will be centered on the crucial issue of computational complexity and the conservativity of the set--theoretic techniques. In particular a critical view on the methods based on the quadratic functions and those based on the non quadratic ones will be proposed.


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