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

非线性系统出现在许多现代工程问题中。稳定性是这类系统性能所需的基本特性之一。另一个具有挑战性的方面是相对于可能使它们不稳定的干扰的鲁棒性。此外，系统的某些参数可能是未知的，从而导致各种自适应控制问题。在过去的二十年中，后退和正演等递归设计成为经典，并在各种工业和工程问题中得到了许多应用。然而，所有这些经典理论只适用于一些特殊的规范形式：严格反馈或纯反馈在常规情况下（反馈线性化系统），或它们非常特殊的多项式扩展。该项目的目标是：1)尽可能广泛地扩展回溯框架适用的现有系统类，并扩展解决这些新类的鲁棒和自适应控制问题的方法。首先，这将用于ODE系统，然后用于更广泛的类别，例如延迟系统、交换系统（以及其他类型的混合系统）。2)提供建设性的算法，解决上述问题的数值和适用于奇异情况（系统不具有可控线性化和不反馈线性化）。3)由于我们将处理时变系统并使用ISS框架来处理干扰，另一个目标是将存在于时变系统的ISS理论扩展到时变系统的情况，并将其用于实现前两个目标。

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.