Related papers: Controllability, Observability, Realizability, and…
The paper examines questions of local asymptotic stability of random dynamical systems. Results concerning stochastic dynamics in general metric spaces, as well as in Banach spaces, are obtained. The results pertaining to Banach spaces are…
We consider the notion of herdability, a set-based reachability condition, which asks whether the state of a system can be controlled to be element-wise larger than a non-negative threshold. First a number of foundational results on…
We introduce the concept of $\epsilon$-uncontrollability for random linear systems, i.e. linear system in which the usual matrices have been replaced by random matrices. We also estimate the $\epsilon$-uncontrollability in the case where…
We propose a method to establish the rapid stabilization of the bilinear Schr\"odinger control system and its linearized system, and the finite time stabilization of the linearized system using the Grammian operators. The analysis of the…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
Results on the problem of stabilizing a nonlinear continuous-time system by a finite number of control or measurement values are presented. The basic tool is a discontinuous version of the so-called semi-global backstepping lemma. We derive…
In this paper, we consider the problem of computing robust controlled invariants for discrete-time monotone dynamical systems. We consider different classes of monotone systems depending on whether the sets of states, control inputs and…
Converse optimality theory addresses an optimal control problem conversely where the system is unknown and the value function is chosen. Previous work treated this problem both in continuous and discrete time and non-extensively considered…
This paper presents novel controllers that yield finite-time stability for linear systems. We first present a sufficient condition for the origin of a scalar system to be finite-time stable. Then we present novel finite-time controllers…
This paper is devoted to the controllability analysis of a class of linear control systems in a Hilbert space. It is proposed to use the minimum energy controls of a reduced lumped parameter system for solving the infinite dimensional…
In this paper, we analyze timed systems with data structures, using a rich interplay of logic and properties of graphs. We start by describing behaviors of timed systems using graphs with timing constraints. Such a graph is called…
In this paper, we study some controllability and observability problems for stochastic systems coupling fourth- and second-order parabolic equations. The main goal is to control both equations with only one controller localized on the drift…
The Koopman operator allows for handling nonlinear systems through a (globally) linear representation. In general, the operator is infinite-dimensional - necessitating finite approximations - for which there is no overarching framework.…
Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…
We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key idea is to develop a new control-theoretic regularizer for dynamics fitting rooted in the notion of…
Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
This paper extends our previous controllability results for a class of coupled linear parabolic systems with nonlocal interactions, motivated by applications in finance such as generalized Black--Scholes models. We establish local null…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
This paper introduces new model parameterizations for learning discrete-time dynamical systems from data via the Koopman operator and studies their properties. Whereas most existing works on Koopman learning do not take into account the…