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This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the…
This article presents an adaptive nonlinear delayed feedback control scheme for stabilizing the unstable periodic orbit of unknown fractional-order chaotic systems. The proposed control framework uses the Lyapunov approach and sliding mode…
The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of…
In this paper, we study the output feedback stabilization for a scalar conservation law with a nonlocal velocity, that models a highly re-entrant manufacturing system as encountered in semi-conductor production. By spectral analysis, we…
We introduce a system of equations that models a non-isothermal magnetoviscoelastic fluid. We show that the model is thermodynamically consistent, and that the critical points of the entropy functional with prescribed energy correspond…
Recent advances in learning-based control leverage deep function approximators, such as neural networks, to model the evolution of controlled dynamical systems over time. However, the problem of learning a dynamics model and a stabilizing…
We consider the problem of designing a stabilizing and optimal static controller with a pre-specified sparsity pattern. Since this problem is NP-hard in general, it is necessary to resort to approximation approaches. In this paper, we…
Some of the guiding problems in partially hyperbolic systems are the following: (1) Examples, (2) Properties of invariant foliations, (3) Accessibility, (4) Ergodicity, (5) Lyapunov exponents, (6) Integrability of central foliations, (7)…
In this work, we propose a methodology for the expression of necessary and sufficient Lyapunov-like conditions for the existence of stabilizing feedback laws. The methodology is an extension of the well-known Control Lyapunov Function (CLF)…
We study ergodic properties of partially hyperbolic systems whose central direction is mostly contracting. Earlier work of Bonatti, Viana about existence and finitude of physical measures is extended to the case of local diffeomorphisms.…
We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting…
When neural networks are used to model dynamics, properties such as stability of the dynamics are generally not guaranteed. In contrast, there is a recent method for learning the dynamics of autonomous systems that guarantees global…
This paper studies the rapid stabilization of a multidimensional heat equation in the presence of an unknown spatially localized disturbance. A novel multivalued feedback control strategy is proposed, which synthesizes the frequency…
Using a nonlocal second-order traffic flow model we present an approach to control the dynamics towards a steady state. The system is controlled by the leading vehicle driving at a prescribed velocity and also determines the steady state.…
We establish a link between stability estimates for a hyperbolic inverse problem via the Boundary Control method and the blowup of a constant appearing in the contexts of optimal unique continuation and cost of approximate controllability.
This paper studies input-to-state stability for hybrid systems with memory, which models hybrid dynamics affected by time delays. Using both Lyapunov-Razumikhin functions and Lyapunov-Krasovskii functionals, Lyapunov-based sufficient…
We consider the temporal periodic solutions to general nonhomogeneous quasilinear hyperbolic equations with a kind of weak diagonal dominant structure. Under the temporal periodic boundary conditions, the existence, stability and uniqueness…
A method of stabilizing 2-cycles in discrete dynamic systems by Delayed Feedback Control is developed by using classic Harmonic Analysis.
In this paper, we develop and analyze an integral fixed-time sliding mode control method for a scenario in which the system model is only partially known, utilizing Gaussian processes. We present two theorems on fixed-time convergence. The…
In the present article we study the stabilization of first-order linear integro-differential hyperbolic equations. For such equations we prove that the stabilization in finite time is equivalent to the exact controllability property. The…