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Control theory can provide useful insights into the properties of controlled, dynamic systems. One important property of nonlinear systems is the region of attraction (ROA), a safe subset of the state space in which a given controller…
Many mainstream robust control/estimation algorithms for power networks are designed using the Lyapunov theory as it provides performance guarantees for linear/nonlinear models of uncertain power networks but comes at the expense of…
We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only…
We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for approximating the Koopman operator from data and is implemented…
Controller design for nonlinear systems with Control Lyapunov Function (CLF) based quadratic programs has recently been successfully applied to a diverse set of difficult control tasks. These existing formulations do not address the gap…
In this paper, we consider the data-driven discovery of stable dynamical models with a single equilibrium. The proposed approach uses a basis-function parameterization of the differential equations and the associated Lyapunov function. This…
Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems.…
We propose new continuous-time formulations for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance-reduced methods. We exploit these continuous-time models, together with simple Lyapunov analysis…
In this paper we provide a thorough, rigorous theoretical framework to assess optimality guarantees of sampling-based algorithms for drift control systems: systems that, loosely speaking, can not stop instantaneously due to momentum. We…
In this article, we provide a general strategy based on Lyapunov functionals to analyse global asymptotic stability of linear infinite-dimensional systems subject to nonlinear dampings under the assumption that the origin of the system is…
The development of finite/fixed-time stable optimization algorithms typically involves study of specific problem instances. The lack of a unified framework hinders understanding of more sophisticated algorithms, e.g., primal-dual gradient…
We consider a nonlinear discrete stochastic control system, and our goal is to design a feedback control policy in order to lead the system to a prespecified state. We adopt a stochastic approximation viewpoint of this problem. It is known…
We address the problem of efficient phase diagram sampling by adopting active learning techniques from machine learning, and achieve an 80% reduction in the sample size (number of sampled statepoints) needed to establish the phase boundary…
As the integration of renewable energy generation increases and as conventional generation is phased out, there is a gradual decline in the grid's strength and resilience at the connection point of wind turbines (WTs). Previous studies have…
A method for determination and two methods for approximation of the domain of attraction $D_{a}(0)$ of an asymptotically stable steady state of an autonomous, $\mathbb{R}$-analytical, discrete system is presented. The method of…
Stability analysis plays a crucial role in studying the behavior of dynamical systems with theoretical and engineering applications. Among various kinds of stability, the stability of equilibrium points is of the greatest importance which…
We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for…
We present a nonlinear dynamical approximation method for time-dependent Partial Differential Equations (PDEs). The approach makes use of parametrized decoder functions, and provides a general, and principled way of understanding and…
We present a method for synthesizing dynamic, reduced-order output-feedback polynomial control policies for control-affine nonlinear systems which guarantees runtime stability to a goal state, when using visual observations and a learned…
This study presents a sampling-based method to guarantee robust stability of general control systems with uncertainty. The method allows the system dynamics and controllers to be represented by various data-driven models, such as Gaussian…