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We derive a saturated feedback control, which locally stabilizes a linear reaction-diffusion equation. In contrast to most other works on this topic, we do not assume the Lyapunov stability of the uncontrolled system and consider general…
This paper proposes a reinforcement learning-based approach for optimal transient frequency control in power systems with stability and safety guarantees. Building on Lyapunov stability theory and safety-critical control, we derive…
The finite-time control problem of quantum systems is investigated in this paper. We first define finite-time stability and present a finite-time Lyapunov stability criterion for finite-dimensional quantum systems in coherence vector…
Current research suggests the use of a liner quadratic performance index for optimal control of regulators in various applications. Some examples include correcting the trajectory of rocket and air vehicles, vibration suppression of…
This article is devoted to the analysis of necessary and/or sufficient conditions for metric regularity in terms of Demyanov-Rubinov-Polyakova quasidifferentials. We obtain new necessary and sufficient conditions for the local metric…
This paper analyzes the scattering theory for periodic tight-binding Hamiltonians perturbed by a finite range impurity. The classical energy gradient flow is used to construct a conjugate (or dilation) operator to the unperturbed…
In this paper we study the quadratic regulator problem for a process governed by a Volterra integral equation in ${\mathbb R}^n$. Our main goal is the proof that it is possible to associate a Riccati differential equation to this quadratic…
We consider an optimal control problem governed by a class of boundary value problem with the spectral Dirichlet fractional Laplacian. Some sufficient condition for the existence of optimal processes is stated. The proof of the main result…
We use the version of the Lyapunov--Perron method operating on individual solutions to investigate the existence of invariant manifolds for non-autonomous dynamical systems, focusing in particular on inertial and stable manifolds. We…
This paper presents a new method for synthesizing stochastic control Lyapunov functions for a class of nonlinear stochastic control systems. The technique relies on a transformation of the classical nonlinear Hamilton-Jacobi-Bellman partial…
We study a class of optimal control problems with state constraints where the state equation is a differential equation with delays. This class includes some problems arising in economics, in particular the so-called models with time to…
This paper addresses the problem of steering the distribution of the state of a discrete-time linear system to a given target distribution while minimizing an entropy-regularized cost functional. This problem is called a maximum entropy…
We consider scalar-input control systems in the vicinity of an equilibrium, at which the linearized systems are not controllable. For finite dimensional control systems, the authors recently classified the possible quadratic behaviors.…
We study the constrained linear quadratic regulator with unknown dynamics, addressing the tension between safety and exploration in data-driven control techniques. We present a framework which allows for system identification through…
We study the possibility to stabilize unstable steady states and unstable periodic orbits in chaotic fractional-order dynamical systems by the time-delayed feedback method. By performing a linear stability analysis, we establish the…
It is a longstanding unsolved problem to characterize the optimal feedback controls for general linear quadratic optimal control problem of stochastic evolution equation with random coefficients. A solution to this problem is given in [21]…
We investigate the asymptotic properties of a finite-time horizon linear-quadratic optimal control problem driven by a multiscale stochastic process with multiplicative Brownian noise. We approach the problem by considering the associated…
A robust controller is developed for uncertain, second-order nonlinear systems subject to simultaneous unknown, time-varying state delays and known, time-varying input delays in addition to additive, sufficiently smooth disturbances. An…
Recent progress in reinforcement learning has led to remarkable performance in a range of applications, but its deployment in high-stakes settings remains quite rare. One reason is a limited understanding of the behavior of reinforcement…
Quantum metrology offers an enhanced performance in experiments such as gravitational wave-detection, magnetometry or atomic clocks frequency calibration. The enhancement, however, requires a delicate tuning of relevant quantum features…