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Pyragas time delayed feedback control has proven itself as an effective tool to non-invasively stabilize periodic solutions. In a number of publications, this method was adapted to equivariant settings and applied to stabilize branches of…
We analyze a classification of two main families of controllers that are of interest when the feedback loop is subject to switching propagation delays due to routing via a wireless multi-hop communication network. We show that we can cast…
We suggest a spatially local feedback mechanism for stabilizing periodic orbits in spatially extended systems. Our method, which is based on a comparison between present and past states of the system, does not require the external…
This note proposes a data-driven output-feedback stabilizing policy iteration for unknown linear discrete-time systems with unmeasurable states. Existing policy iteration methods for optimal control must start from a stabilizing control…
In this article, we derive a new, fast, and robust preconditioned iterative solution strategy for the all-at-once solution of optimal control problems with time-dependent PDEs as constraints, including the heat equation and the non-steady…
Solving evolutionary equations in a parallel-in-time manner is an attractive topic and many algorithms are proposed in recent two decades. The algorithm based on the block $\alpha$-circulant preconditioning technique has shown promising…
A fully analytical controller design is proposed to tackle a periodic control problem for stable linear systems with an input delay. Applying the internal model control scheme, the controller design reduces to designing a filter, which is…
We study the stability of the fixed-point solution of an array of mutually coupled logistic maps, focusing on the influence of the delay times, $\tau_{ij}$, of the interaction between the $i$th and $j$th maps. Two of us recently reported…
A review of the authors's results is given. Several methods are discussed for solving nonlinear equations $F(u)=f$, where $F$ is a monotone operator in a Hilbert space, and noisy data are given in place of the exact data. A discrepancy…
Stability and reproducibility are essential considerations in various applications of statistical methods. False Discovery Rate (FDR) control methods are able to control false signals in scientific discoveries. However, many FDR control…
This paper provides global exponential stabilization results by means of boundary feedback control for 1-D nonlinear unstable reaction-diffusion Partial Differential Equations (PDEs) with nonlinearities of superlinear growth. The class of…
We consider application of the multiple time delayed feedback for control of anharmonic (nonlinear) oscillators subject to noise. In contrast to the case of a single delay feedback, the multiple one exhibits resonances between feedback and…
We consider nonlinear delay differential and renewal equations with infinite delay. We extend the work of Gyllenberg et al, Appl. Math. Comput. (2018) by introducing a unifying abstract framework, and derive a finite-dimensional…
Optimal Control Problems consist on the optimisation of an objective functional subjected to a set of Ordinary Differential Equations. In this work, we consider the effects on the stability of the numerical solution when this optimisation…
In this paper, we study a numerical method for the solution of partial differential equations on evolving surfaces. The numerical method is built on the stabilized trace finite element method (TraceFEM) for the spatial discretization and…
We propose a novel feedback controller for a class of uncertain higher-order nonlinear systems, subject to delays in both state measurement and control input signals. Building on the prescribed performance control framework, a…
For self-sustained oscillators subject to noise the coherence, understood as a constancy of the instantaneous oscillation frequency, is one of the primary characteristics. The delayed feedback has been previously revealed to be an efficient…
This paper addresses the problem of stabilization of $1$-D parabolic equations with destabilizing terms and Dirichlet boundary disturbances. By using the method of backstepping and the technique of splitting, a boundary feedback controller…
The task of inducing, via continuous static state-feedback control, an asymptotically stable heteroclinic orbit in a nonlinear control system is considered in this paper. The main motivation comes from the problem of ensuring convergence to…
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…