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Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
In this paper, a quasi-linear parabolic equation with a diffusion term dependent on the gradient to the state with Dirichlet boundary conditions is considered. The goal of this paper is to prove the existence of control that insensitizes…
The development of a metric for structural data is a long-term problem in pattern recognition and machine learning. In this paper, we develop a general metric for comparing nonlinear dynamical systems that is defined with Perron-Frobenius…
A new systematic approach to the construction of approximate solutions to a class of nonlinear singularly perturbed feedback control systems using the boundary layer functions especially with regard to the possible occurrence of the…
The paper deals with local robust feedback synthesis for systems with multidimensional control and unknown bounded perturbations. Using V.~I.~Korobov's controllability function method, we construct a bounded control which steers an…
We consider the problem of stabilization of a linear system, under state and control constraints, and subject to bounded disturbances and unknown parameters in the state matrix. First, using a simple least square solution and available…
Robust control is a core approach for controlling systems with performance guarantees that are robust to modeling error, and is widely used in real-world systems. However, current robust control approaches can only handle small system…
Robust control of quantum systems is an increasingly relevant field of study amidst the second quantum revolution, but there remains a gap between taming quantum physics and robust control in its modern analytical form that culminated in…
This article investigates the exact controllability of three-dimensional stochastic Maxwell equations, a coupled system comprising two stochastic partial differential equations. The research establishes the observability inequality for the…
We present a new approach to parametric robust controller design, where we compute controllers of arbitrary order and structure which minimize the worst-case $H_\infty$ norm over a pre-specified set of uncertain parameters. At the core of…
In this paper, we obtain a quantitative estimate of unique continuation and an observability inequality from an equidistributed set for solutions of the diffusion equation in the whole space RN. This kind of observability indicates that the…
We propose two bounded comparison metrics that may be implemented to arbitrary dimensions in regression tasks. One quantifies the structure of uncertainty and the other quantifies the distribution of uncertainty. The structure metric…
Stabilization of a class of time-varying parabolic equations with uncertain input data using Receding Horizon Control (RHC) is investigated. The diffusion coefficient and the initial function are prescribed as random fields. We consider…
This article aims to consider a new univariate nonparametric cumulative sum (CUSUM) control chart for small shift of location based on both change-point model and Mann-Whitney statistic. Some comparisons on the performances of the proposed…
In this paper the theory of robust output regulation of distributed parameter systems with infinite-dimensional exosystems is extended for plants with unbounded control and observation. As the main result, we present the internal model…
In this paper, we study the control of the linear heat equation with a space and time dependent coefficient function by the Dirichlet and Neumann boundary control laws. This equation models the heat diffusion and space, time dependent heat…
Many mathematical models utilize limit processes. Continuous functions and the calculus, differential equations and topology, all are based on limits and continuity. However, when we perform measurements and computations, we can achieve…
We study the robust output regulation of linear boundary control systems by constructing extended systems. The extended systems are established based on solving static differential equations under two new conditions. We first consider the…
We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $$ \partial_t u-\mathfrak{L}^{\sigma,\mu}[\varphi(u)]=f \quad\quad\text{in}\quad\quad…
The paper investigates dynamical systems for which the derivative of some positive-definite function along the solutions of this system depends on so-called density function. In turn, such dynamical systems are called density systems. The…