Finite‐time adaptive robust control of nonlinear time‐delay uncertain systems with disturbance

Abstract

This paper investigates finite-time adaptive robust control problem for a general class of nonlinear time-delay systems with uncertain and external disturbance via the Lyapunov-Krasovskii (L-K) method and presents some delay-independent and delay-dependent results on the issue. First, by applying the orthogonal decomposition method, this paper presents an equivalent form.Based on which, we study the finite-time adaptive robust control problem for the systems by constructing a specific L-K functional and designing a suitable controller. Different from existing works, this paper studies finite-time adaptive robust control problem for general nonlinear delay system and presents a delay-dependent sufficient condition on the problem. Finally, an illustrative example is given to show the effectiveness of the result in this paper. KEYWORDS finite-time adaptive robust control, L-K functional method, nonlinear time-delay uncertain system Int J Robust Nonlinear Control. 2019;29:919-934.wileyonlinelibrary.com/journal/rnc

Decentralized uniform finite‐time stabilization of large‐scale nonlinear networks by small‐gain theorems

“…All the works cited above deal with the classical asymptotic or more general input‐to‐state stability and stabilization. To our best knowledge the problem of finite‐time stabilization was originally raised and solved for linear systems as early as in Reference 10 and the solution was based on consideration of a certain Lyapunov function defined by the implicit function theorem and called “controllability function.” This topic was revived later 11 and has become very popular since 2000, 12‐24 but backstepping algorithms redesigned for finite‐time stabilization problem were especially successful 13‐17 . In some recent works design of implicit Lyapunov functions is enjoying a renaissance as well 20,21 .…”

“…Although the above‐mentioned works 12‐27 address not only the case of ordinary differential equations, but also finite‐time stabilization for switched and stochastic processes, 16,17 discrete‐time stochastic systems, 19 time‐delay and Hamiltonian systems, 23,24 and sometimes not lower‐triangular form systems, 18 it should be noted that almost all of them deal with a single (isolated) agent with nonlinear dynamics without consideration of multiagent networks of such agents and without any decentralized control of such networks. As the exception among the papers cited above, one can mention, 13,14 but these two papers deal with single strict‐feedback form systems of ordinary differential equations interconnected with some fixed uncertain (finite‐time) input‐to‐state stable system.…”

Robust model predictive control of uncertain nonlinear time‐delay systems via control contraction metric technique

“…In most cases, such phenomena might deteriorate the dynamic performance of systems, or even lead to instability. Regarding this problem, extensive research has been devoted to the robust control of uncertain time‐delay systems 1‐11 …”

Finite-Time Simultaneous Stabilization of a Set of Nonlinear Singular Systems

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