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Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…
Two different controlling methods are proposed to stabilize unstable continuous-sliding states of a dry-friction oscillator. Both methods are based on a delayed-feedback mechanism well-known for stabilizing periodic orbits in deterministic…
This work studies robustness to system disturbance and measurement noise of some popular general practical stabilization techniques, namely, Dini aiming, optimization-based stabilization and inf-convolution stabilization. Common to all…
Recent development of contraction theory based analysis of singularly perturbed system has opened the door for inspecting differential behavior of multi time-scale systems. In this paper a contraction theory based framework is proposed for…
For a wide class of second order nonlinear non-autonomous models, we illustrate that combining proportional state control with the feedback that is proportional to the derivative of the chaotic signal, allows to stabilize unstable motions…
Non-stationary signals are ubiquitous in real life. Many techniques have been proposed in the last decades which allow decomposing multi-component signals into simple oscillatory mono-components, like the groundbreaking Empirical Mode…
Many low-Mach or all-Mach number codes are based on space discretizations which in combination with the first order explicit Euler method as time integration would lead to an unstable scheme. In this paper, we investigate how the choice of…
We propose a method to stabilise a solution to equations describing the interface of thin liquid films falling under gravity with a finite number of actuators and restricted observations. As for many complex systems, full observation of the…
In this note we propose and analyze novel implicit-explicit methods based on second order strong stability preserving multistep time discretizations. Several schemes are developed, and a linear stability analysis is performed to study their…
In this paper, we study the inverse problem for a class of abstract ultraparabolic equations which is well-known to be ill-posed. We employ some elementary results of semi-group theory to present the formula of solution, then show the…
A novel adaptive control approach is proposed to solve the globally asymptotic state stabilization problem for uncertain pure-feedback nonlinear systems which can be transformed into the pseudo-affine form. The pseudo-affine pure-feedback…
Stabilization is a key dependability property for dealing with unanticipated transient faults, as it guarantees that even in the presence of such faults, the system will recover to states where it satisfies its specification. One of the…
This paper concerns the small-time stabilization of some classes of mechanical systems which are not stabilizable by means of at least continuous state feedback laws. This is the case of nonholonomic mechanical systems, an example being the…
We propose an algorithm to restrict the switching signals of a constrained switched system in order to guarantee its stability, while at the same time attempting to keep the largest possible set of allowed switching signals. Our work is…
Numerical solutions for the optimal feedback stabilization of discrete time dynamical systems is the focus of this paper. Set-theoretic notion of almost everywhere stability introduced by the Lyapunov measure, weaker than conventional…
We investigate modified steepest descent methods coupled with a loping Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization…
In this article we consider the possibility of controlling the dynamics of nonlinear discrete systems. A new method of control is by mixing states of the system (or the functions of these states) calculated on previous steps. This approach…
The equivalence of the chain method and Hamilton-Jacobi formalism is demonstrated. The stabilization algorithm of Hamilton-Jacobi formalism is clariffied and two examples are presented in details.
This work concerns the internal stabilization of underactuated linear systems of $m$ heat equations in cascade, where the control is placed internally in the first equation only and the diffusion coefficients are distinct. Combining the…
Learning stabilizing controllers from data is an important task in engineering applications; however, collecting informative data is challenging because unstable systems often lead to rapidly growing or erratic trajectories. In this work,…