相关论文: On the construction of Lyapunov functions with com…

We study the convergence analysis of continuous-time dynamical systems associated with optimization methods for strongly convex functions. Recent works have proposed systematic constructions of Lyapunov functions for such analysis, while…

Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…

Complete Lyapunov functions for a dynamical system, given by an autonomous ordinary differential equation, are scalar-valued functions that are strictly decreasing along orbits outside the chain-recurrent set. In this paper we show that we…

We construct a generic, simple, and efficient scheduling policy for stochastic processing networks, and provide a general framework to establish its stability. Our policy is randomized and prioritized: with high probability it prioritizes…

We consider the first order periodic systems perturbed by a $2N\ts 2N$ matrix-valued periodic potential on the real line. The spectrum of this operator is absolutely continuous and consists of intervals separated by gaps. We define the…

We generate new hierarchy of many-parameter family of maps of the interval [0,1] with an invariant measure, by composition of the chaotic maps of reference [1]. Using the measure, we calculate Kolmogorov-Sinai entropy, or equivalently…

Stiff and chaotic differential equations are challenging for time-stepping numerical methods. For explicit methods, the required time step resolution significantly exceeds the resolution associated with the smoothness of the exact solution…

While there has been increasing interest in using neural networks to compute Lyapunov functions, verifying that these functions satisfy the Lyapunov conditions and certifying stability regions remain challenging due to the curse of…

Many modern nonlinear control methods aim to endow systems with guaranteed properties, such as stability or safety, and have been successfully applied to the domain of robotics. However, model uncertainty remains a persistent challenge,…

This paper presents a synthesis approach aiming to guarantee a minimum upper-bound for the time taken to reach a target set of non-zero measure that encompasses the origin, while taking into account uncertainties and input and state…

In contexts where data samples represent a physically stable state, it is often assumed that the data points represent the local minima of an energy landscape. In control theory, it is well-known that energy can serve as an effective…

Barrier Lyapunov functions are suitable for learning control designs, due to their feature of finite duration tracking. This paper presents fractional barrier Lyapunov functions, provided and compared with the conventional ones in the…

Deep learning methods have been widely used in robotic applications, making learning-enabled control design for complex nonlinear systems a promising direction. Although deep reinforcement learning methods have demonstrated impressive…

In this paper, we propose a Lyapunov-based reinforcement learning method for distributed control of nonlinear systems comprising interacting subsystems with guaranteed closed-loop stability. Specifically, we conduct a detailed stability…

We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check,…

We propose a sampling-based approach to learn Lyapunov functions for a class of discrete-time autonomous hybrid systems that admit a mixed-integer representation. Such systems include autonomous piecewise affine systems, closed-loop…

We construct a family of globally defined dynamical systems for a nonlinear programming problem, such that: (a) the equilibrium points are the unknown (and sought) critical points of the problem, (b) for every initial condition, the…

With the ever increasing computational power available and the development of high-performances computing, investigating the properties of realistic very large-scale nonlinear dynamical systems has been become reachable. It must be noted…

Visual inspections for identifying focusing points in inertial microfluidic flows are prone to misinterpreting stable locations and focusing shifts in the case of non-trivial focusing patterns. We develop and deploy an approach for…

Using a nonlocal macroscopic LWR-type traffic flow model, we present an approach to control the nonlocal velocity towards a given equilibrium velocity. Therefore, we present a Lyapunov function measuring the $L^2$ distance between these…