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This paper presents the concepts of exact, null, and approximate controllability in the Stackelberg-Nash sense for abstract forward and backward stochastic evolution equations, involving two types of controls: leaders and followers. We…
A study of the linear quadratic (LQ) control problem on a finite time interval for a model equation in Hilbert spaces which comprehends the memory of the inputs was performed recently by the authors. The outcome included a closed-loop…
We study the null-controllability properties of heat-like equations posed on the whole Euclidean space $\mathbb R^n$. These evolution equations are associated with Fourier multipliers of the form $\rho(\vert D_x\vert)$, where…
In this Note, we review the main existing results, methods, and some key open problems on the controllability of nonlinear hyperbolic and parabolic equations. Especially, we describe our recent universal approach to solve the local…
We study the null-controllability properties of heat-like equations posed on the whole Euclidean space $\mathbb R^n$. These evolution equations are associated with Fourier multipliers of the form $\rho(\vert D_x\vert)$, where…
Differential balancing theory for nonlinear model reduction relies on differential controllability and observability functions. In this paper, we further investigate them from two different perspectives. First, we establish novel…
The increasing ease of obtaining and processing data together with the growth in system complexity has sparked the interest in moving from conventional model-based control design towards data-driven concepts. Since in many engineering…
We consider a class of evolution equations describing population dynamics in the presence of a carrying capacity depending on the population with delay. In an earlier work, we presented an exhaustive classification of the logistic equation…
This paper is devoted to studying null controllability for a class of stochastic fourth order semi-discrete parabolic equations, where the spatial variable is discretized with finite difference scheme and the time is kept as a continuous…
We consider a fully-discrete approximations of 1-D heat equation with dynamic boundary conditions for which we provide a controllability result. The proof of this result is based on a relaxed observability inequality for the corresponding…
We study the null-controllability of parabolic equations associated to non-autonomous Ornstein-Uhlenbeck operators. When a Kalman type condition holds for some positive time $T>0$, these parabolic equations are shown to enjoy a Gevrey…
In this paper, we accomplish two objectives: First, we provide a new mathematical characterization of the value function for impulse control problems with implementation delay and present a direct solution method that differs from its…
This paper is devoted to the controllability of a general linear hyperbolic system in one space dimension using boundary controls on one side. Under precise and generic assumptions on the boundary conditions on the other side, we previously…
Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end,…
The paper addresses the problem of optimization of a guaranteed (worst case) result for a control system driven by a controlling side in presence of a dynamical disturbance. The disturbances as functions of time are subject to functional…
This paper explores the controllability of a class of N-dimensional hyperbolic equations featuring a single interior degenerate point. Firstly, we establish the well-posedness of the equation through the application of the Hardy inequality.…
Time delays due to signal latency, computational complexity, and sensor-denied environments, pose a critical challenge in both engineered and biological control systems. In this work, we investigate biologically inspired strategies to…
This work is concerned with the obtainment of new Carleman estimates for linear parabolic equations, where the second-order differential operator brings a super strong degeneracy in a positive measure subset of the spatial domain. In order…
Time delays are ubiquitous in industry, and they must be accounted for when designing control strategies. However, numerical optimal control (NOC) of delay differential equations (DDEs) is challenging because it requires specialized…
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…