Related papers: Contraction Theory for Nonlinear Stability Analysi…
Neural-based, data-driven analysis and control of dynamical systems have been recently investigated and have shown great promise, e.g. for safety verification or stability analysis. Indeed, not only do neural networks allow for an entirely…
Deep learning methods have demonstrated significant potential for addressing complex nonlinear control problems. For real-world safety-critical tasks, however, it is crucial to provide formal stability guarantees for the designed…
We present a method for contraction-based feedback motion planning of locally incrementally exponentially stabilizable systems with unknown dynamics that provides probabilistic safety and reachability guarantees. Given a dynamics dataset,…
Dynamic surface control (DSC) method uses high gain filters to avoid the "explosion of complexity" issue inherent in backstepping based controller designs. As a result, the closed loop system and filter dynamics possess time scale…
To predict allowable time-step size for the fully discretized nonlinear differential equations, a stability theory is developed using exact determination of an infinite perturbation series. Mathematical induction is used to determine the…
The main objective of this paper is to propose an alternative procedure to carry out one of the key steps of immersion and invariance stabilising controller design. Namely, the one that ensures attractivity of the manifold whose internal…
Control of complex turbulent dynamical systems involving strong nonlinearity and high degrees of internal instability is an important topic in practice. Different from traditional methods for controlling individual trajectories, controlling…
In this paper we present a foundational study on a constrained method that defines learning problems with Neural Networks in the context of the principle of least cognitive action, which very much resembles the principle of least action in…
This paper proposes a new adaptation methodology to find the control inputs for a class of nonlinear systems with time-varying bounded uncertainties. The proposed method does not require any prior knowledge of the uncertainties including…
Motivated by the grid search method and Bayesian optimization, we introduce the concept of contractibility and its applications in model-based optimization. First, a basic framework of contraction methods is established to construct a…
This study presents a policy optimisation framework for structured nonlinear control of continuous-time (deterministic) dynamic systems. The proposed approach prescribes a structure for the controller based on relevant scientific knowledge…
Relative temporal-difference (TD) learning was introduced to mitigate the slow convergence of TD methods when the discount factor approaches one by subtracting a baseline from the temporal-difference update. While this idea has been studied…
The growing complexity of dynamical systems and advances in data collection necessitates robust data-driven control strategies without explicit system identification and robust synthesis. Data-driven stability has been explored in linear…
In this paper we define contractive and nonexpansive properties for adapted stochastic processes $X_1, X_2, \ldots $ which can be used to deduce limiting properties. In general, nonexpansive processes possess finite limits while contractive…
This paper considers the equilibrium-free stability and performance analysis of discrete-time nonlinear systems. We consider two types of equilibrium-free notions. Namely, the universal shifted concept, which considers stability and…
In this paper, we develop and analyze an integral fixed-time sliding mode control method for a scenario in which the system model is only partially known, utilizing Gaussian processes. We present two theorems on fixed-time convergence. The…
We consider the problem of global stability of nonlinear sampled-data systems. Sampled-data systems are a form of hybrid model which arises when discrete measurements and updates are used to control continuous-time plants. In this paper, we…
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…
Critical questions in dynamical neuroscience and machine learning are related to the study of continuous-time neural networks and their stability, robustness, and computational efficiency. These properties can be simultaneously established…
A new framework is developed for control of constrained nonlinear systems with structured parametric uncertainties. Forward invariance of a safe set is achieved through online parameter adaptation and data-driven model estimation. The new…