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Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
This paper deals with the output feedback stabilization problem of nonlinear multi-input multi-output systems having an uncertain input gain matrix. It is assumed that the system has a well-defined vector relative degree and that the zero…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
Maintaining numerical stability in machine learning models is crucial for their reliability and performance. One approach to maintain stability of a network layer is to integrate the condition number of the weight matrix as a regularizing…
Robust finite-time feedback controller introduced for the second-order systems in [1] can be seen as a non-overshooting quasi-continuous sliding mode control. The paper proposes a regularization scheme to suppress inherent chattering due to…
A periodic perturbation generates a complicated dynamics close to separatrices and saddle points. We construct an asymptotic solution which is close to the separatrix for the unperturbed Duffing's oscillator over a long time. This solution…
Over the last two decades, several methods have been proposed for stabilizing the dynamics of biological populations. However, these methods have typically been evaluated using different population dynamics models and in the context of very…
A novel delayed feedback control based on full state is proposed. The designed scheme combines the difference between two delayed states and a periodic control gain. System stabilization is achieved in any hyperbolic unstable equilibrium…
We propose a new risk-constrained formulation of the classical Linear Quadratic (LQ) stochastic control problem for general partially-observed systems. Our framework is motivated by the fact that the risk-neutral LQ controllers, although…
If one wants to explore the properties of a dynamical system systematically one has to be able to track equilibria and periodic orbits regardless of their stability. If the dynamical system is a controllable experiment then one approach is…
Reaction-diffusion equations are ubiquitous in various scientific domains and their patterns represent a fascinating area of investigation. However, many of these patterns are unstable and therefore challenging to observe. To overcome this…
The stationary distribution of a fully chaotic system typically exhibits a fractal structure, which dramatically changes if the dynamical equations are even slightly modified. Perturbative techniques are not expected to work in this…
We study finite horizon linear quadratic control with additive noise in a perturbancewise framework that unifies the classical model, a constraint embedded affine policy class, and a distributionally robust formulation with a Wasserstein…
A novel adaptive control approach is proposed to solve the globally asymptotic state stabilization problem for uncertain pure-feedback nonlinear systems which can be transformed into the pseudo-affine form. The pseudo-affine pure-feedback…
This paper is concerned with the problem of regularization by noise of systems of reaction-diffusion equations with mass control. It is known that $\textit{strong}$ solutions to such systems of PDEs may blow-up in finite time. Moreover, for…
In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…
This paper addresses the problem of stabilization of switched affine systems under dwell-time constraint, giving guarantees on the bound of the quadratic cost associated with the proposed state switching control law. Specifically, two…
Constrained model predictive control (MPC) is a widely used control strategy, which employs moving horizon-based on-line optimisation to compute the optimum path of the manipulated variables. Nonlinear MPC can utilize detailed models but it…
Reinforcement learning methods often produce brittle policies -- policies that perform well during training, but generalize poorly beyond their direct training experience, thus becoming unstable under small disturbances. To address this…