Related papers: On equilibrium in control problems with applicatio…
We review the theory of one-sided coupled operator matrices with a focus on evolution equations with inhomogeneous boundary conditions. (The original article had no abstract.)
We introduce the notion of equilibrium index for statically isolated invariant sets of the system $u_t+A u=f_\lambda(u)$ on Banach space $X$ (where $A$ is a sectorial operator with compact resolvent) and present a reduction theorem and an…
In this paper, we deal with the equilibrium selection problem, which amounts to steering a population of individuals engaged in strategic game-theoretic interactions to a desired collective behavior. In the literature, this problem has been…
The Variation Evolving Method (VEM), which seeks the optimal solutions with the variation evolution principle, is further developed to be more flexible in solving the Optimal Control Problems (OCPs) with terminal constraint. With the…
One of the main aspects of switched affine systems that makes their stabilizability study intricate is the existence of (generally) infinitely many equilibrium points in the state space. Thus, prior to designing the switched control, the…
This article studies Volterra evolution equations from the point of view of control theory, in the case that the generator of the underlying semigroup has a Riesz basis of eigenvectors. Conditions for admissibility of the system's control…
We examine the approach to equilibrium of the micromaser. Analytic methods are first used to show that for large times (i.e. many atoms) the convergence is governed by the next to leading eigenvalue of the corresponding discrete evolution…
Lotka-Volterra (LV) equations play a key role in the mathematical modeling of various ecological, biological and chemical systems. When the number of species (or, depending on the viewpoint, chemical components) becomes large, basic but…
This paper studies the problem of steering a linear time-invariant system subject to state and input constraints towards a goal location that may be inferred only through partial observations. We assume mixed-observable settings, where the…
The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show…
Ensemble control offers rich and diverse opportunities in mathematical systems theory. In this paper, we present a new paradigm of ensemble control, referred to as distributional control, for ensemble systems. We shift the focus from…
We consider funnel control for linear infinite-dimensional systems that are impedance passive, meaning that they satisfy an energy balance in which the stored energy equals the squared norm of the state and the supplied power is the inner…
In this paper we study the vanishing inertia and viscosity limit of a second order system set in an Euclidean space, driven by a possibly nonconvex time-dependent potential satisfying very general assumptions. By means of a variational…
We consider applications of the Boundary Control (BC) method to generalized spectral estimation problems and to inverse source problems. We derive the equations of the BC method for this problems and show that solvability of this equations…
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…
We study the controllability of the multidimensional wave equation in a bounded domain with Dirichlet boundary condition, in which the support of the control is allowed to change over time. The exact controllability is reduced to the proof…
The control of bilinear systems has attracted considerable attention in the field of systems and control for decades, owing to their prevalence in diverse applications across science and engineering disciplines. Although much work has been…
Enlightened from the inverse consideration of the stable continuous-time dynamics evolution, the Variation Evolving Method (VEM) analogizes the optimal solution to the equilibrium point of an infinite-dimensional dynamic system and solves…
The present paper represents a continuation of our previous one. There, a continuous dependence result for the solution of an elliptic variational-hemivariational inequality was obtained and then used to prove the existence of optimal pairs…
A method for constructing evolution equations admitting a master symmetry is proposed. Several examples illustrating the method are presented. It is also noted that for certain evolution equations master symmetries can be useful for…