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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…
A methodology is presented for the numerical solution of nonlinear elliptic systems in unbounded domains, consisting of three elements. First, the problem is posed on a finite domain by means of a proper nonlinear change of variables. The…
This paper proposes new quadratic constraints (QCs) to bound a quadratic polynomial. Such QCs can be used in dissipation ineqaulities to analyze the stability and performance of nonlinear systems with quadratic vector fields. The proposed…
Discrete-time stochastic systems are an essential modelling tool for many engineering systems. We consider stochastic control systems that are evolving over continuous spaces. For this class of models, methods for the formal verification…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
The celebrated sparse representation model has led to remarkable results in various signal processing tasks in the last decade. However, despite its initial purpose of serving as a global prior for entire signals, it has been commonly used…
Dynamical systems, that are used to model power grids, the brain, and other physical systems, can exhibit coexisting stable states known as attractors. A powerful tool to understand such systems, as well as to better predict when they may…
Stabilization of linear systems with unknown dynamics is a canonical problem in adaptive control. Since the lack of knowledge of system parameters can cause it to become destabilized, an adaptive stabilization procedure is needed prior to…
In this work, we study the problem of learning a nonlinear dynamical system by parameterizing its dynamics using basis functions. We assume that disturbances occur at each time step with an arbitrary probability $p$, which models the…
In this paper, we develop a provably correct optimal control strategy for a finite deterministic transition system. By assuming that penalties with known probabilities of occurrence and dynamics can be sensed locally at the states of the…
We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently…
This paper presents a new algorithm based on interval methods for rigorously constructing inner estimates of feasible parameter regions together with enclosures of the solution set for parameter-dependent systems of nonlinear equations in…
An exceedance region is the set of locations in a spatial domain where a process exceeds some threshold. Examples of exceedance regions include areas where ozone concentrations exceed safety standards, there is high risk for tornadoes or…
We introduce a framework to model the evolution of a class of open quantum systems whose environments periodically undergo an instantaneous non-unitary evolution stage. For the special case of quadratic models, we show how this approach can…
We propose a general theory for studying the \xl{landscape} of nonconvex \xl{optimization} with underlying symmetric structures \tz{for a class of machine learning problems (e.g., low-rank matrix factorization, phase retrieval, and deep…
We investigate linear-quadratic dynamical systems with energy preserving quadratic terms. These systems arise for instance as Galerkin systems of incompressible flows. A criterion is presented to ensure long-term boundedness of the system…
This paper focuses on developing a method to obtain an uncertain linear fractional transformation (LFT) system that adequately captures the dynamics of a nonlinear time-invariant system over some desired envelope. First, the nonlinear…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
The goal of this paper is to assess the robustness of an uncertain linear time-varying (LTV) system on a finite time horizon. The uncertain system is modeled as a connection of a known LTV system and a perturbation. The input/output…
This paper describes new results linking constrained optimization theory and nonlinear contraction analysis. Generalizations of Lagrange parameters are derived based on projecting system dynamics on the tangent space of possibly…