Related papers: Learning Dynamical Systems using Local Stability P…
Despite Neural Ordinary Differential Equations (Neural ODEs) exhibiting intrinsic robustness, existing methods often impose Lyapunov stability for formal guarantees. However, these methods still face a fundamental accuracy-robustness…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
This technical note studies Lyapunov-like conditions to ensure a class of dynamical systems to exhibit predefined-time stability. The origin of a dynamical system is predefined-time stable if it is fixed-time stable and an upper bound of…
Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results…
This study presents a method, along with its algorithmic and computational framework implementation, and performance verification for dynamical system identification. The approach incorporates insights from phase space structures, such as…
This work proposes a novel method for estimating the influence that unknown static objects might have over mobile agents. Since the motion of agents can be affected by the presence of fixed objects, it is possible use the information about…
We present a learning-based predictive control methodology using the differentiable programming framework with probabilistic Lyapunov-based stability guarantees. The neural Lyapunov differentiable predictive control (NLDPC) learns the…
We develop a finite-dimensional sensitivity framework for studying stability in learning systems whose states include representations, parameters, and update variables. The central object is the \emph{Learning Stability Profile}, a…
The need for rapid and reliable robot deployment is on the rise. Imitation Learning (IL) has become popular for producing motion planning policies from a set of demonstrations. However, many methods in IL are not guaranteed to produce…
The paper presents an approach to the construction of stabilizing feedback for strongly nonlinear systems. The class of systems of interest includes systems with drift which are affine in control and which cannot be stabilized by continuous…
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…
In this paper, we consider the state estimation problem for nonlinear stochastic discrete-time systems. We combine Lyapunov's method in control theory and deep reinforcement learning to design the state estimator. We theoretically prove the…
This paper presents a data-integrated framework for learning the dynamics of fractional-order nonlinear systems in both discrete-time and continuous-time settings. The proposed framework consists of two main steps. In the first step,…
Hybrid systems are prevalent in robotics. However, ensuring the stability of hybrid systems is challenging due to sophisticated continuous and discrete dynamics. A system with all its system modes stable can still be unstable. Hence special…
Traditional Lyapunov based transient stability assessment approaches focus on identifying the stability region (SR) of the equilibrium point under study. When trying to estimate this region using Lyapunov functions, the shape of the final…
This paper presents a non-linear stability analysis for dc-microgrids in both, interconnected mode and island operation with primary control. The proposed analysis is based on the fact that the dynamical model of the grid is a gradient…
Stabilizing controller design and region of attraction (RoA) estimation are essential in nonlinear control. Moreover, it is challenging to implement a control Lyapunov function (CLF) in practice when only partial knowledge of the system is…
Learning long-term dynamics models is the key to understanding physical common sense. Most existing approaches on learning dynamics from visual input sidestep long-term predictions by resorting to rapid re-planning with short-term models.…
We propose a principled method for projecting an arbitrary square matrix to the non-convex set of asymptotically stable matrices. Leveraging ideas from large deviations theory, we show that this projection is optimal in an…
We propose a technique for the design and analysis of adaptation algorithms in dynamical systems. The technique applies both to systems with conventional Lyapunov-stable target dynamics and to ones of which the desired dynamics around the…