Recursive designs of robust and adaptive controllers for extensions of existing canonical forms and for their interconnections

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Nonlinear systems appear in many modern engineering problems. Stability is one of the fundamental properties of such systems needed for their performance. Another challenging aspect is the robustness with respect to disturbances that can destabilize them. Furthermore, some parameters of a system can be unknown that leads to various adaptive control problems. During the last two decades such recursive designs as backstepping and forwarding became classical and found many applications in various industrial and engineering problems. However all this classical theory is applicable to some special canonical forms only: strict-feedback or purefeedback in the regular case (feedback linearizable systems), or to their very special polynomial extensions. The goals of the project are: 1) To extend as wide as possible the existing classes of systems the backstepping framework is applicable to and to extend the methods for solving robust and adaptive control problems for these new classes. First, this will be done for ODE systems, then for a wider classes such as delay systems, switched systems (and other types of hybrid systems). 2) To provide constructive algorithms that solve the above-mentioned problems numerically and which suit for the singular case (for systems that do not have a controllable linearization and are not feedback linearizable). 3) As we will work with time-varying systems and use the ISS framework to cope with disturbances, another goal is to extend the ISS theory that exists for time-varying systems to the case of time-varying ones and to use it for the achievement of the first two goals.