Presentation

Laboratory of Adaptive and Robust Control Systems of Institute of Control Sciences RAS was founded by Academician Ya. Z. Tsypkin in 1956. By that time, main research interests lied in the theory of relay, impulse, and digital automatic control. Since mid-sixties, efforts were shifted to adaptive systems, and this area is still of interest in the lab. Later, in 70-s and 80-s, most efforts were concentrated on the design of robust and optimal algorithms in adaptive control and identification. Such algorithms possess high rate of convergence, and available information about the system can be exploited in full.

During the last decade, the following three research directions are worth emphasizing.

• The first one deals with robust control theory. Within the classical approach, the theory is developed under assumptions that our knowledge about the system is precise. However, in real-life applications, the presence of various uncertainties is unavoidable, and the system description is only known to a certain accuracy. Robust control theory is aimed at accounting for such uncertainties and offers effective tools for analysis and design of control systems which are "insensitive", or robust, against this imprecise description. At present, this research area is considered highly important in the control community.

• The second, newly developed research activity is directed to fixed-order controller design. All modern approaches to optimal control (such as H^¥ - theory, µ - synthesis, LMI - based design, l₁ - optimization) quite often yield regulators of very high orders, which even exceed the order of the plant. Hence, various modifications of the existing techniques are desired, leading to low-order controller design.

• The third line of research lies in a more classical framework of identification and adaptive control. Here, two topics are of most interest. The first one relates to the information approach to adaptive control of stochastic systems. Within this approach, it is possible to determine limiting (optimal) rates of convergence for the methods, and algorithms can be advised which implement this optimal behavior under various assumptions on the uncertainty. The second sub-direction, the so-called frequency theory of identification and adaptive control, is developed under assumption that exogenous disturbances are unknown-but-bounded. The basis for this research is identification of systems using harmonic test inputs followed by controller design with the methods of optimal control theory.