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When neural networks are trained from data to simulate the dynamics of physical systems, they encounter a persistent challenge: the long-time dynamics they produce are often unphysical or unstable. We analyze the origin of such…
The goal of this work is to identify steady-state solutions to dynamical systems defined on large, random families of networks. We do so by passing to a continuum limit where the adjacency matrix is replaced by a non-local operator with…
The recent framework of performative prediction is aimed at capturing settings where predictions influence the target/outcome they want to predict. In this paper, we introduce a natural multi-agent version of this framework, where multiple…
Learning-based neural network (NN) control policies have shown impressive empirical performance. However, obtaining stability guarantees and estimates of the region of attraction of these learned neural controllers is challenging due to the…
Although deep neural network (DNN)-based controllers are popularly used to control uncertain nonlinear dynamic systems, most results use DNNs that are pretrained offline and the corresponding controller is implemented post-training. Recent…
In real-world networks the interactions between network elements are inherently time-delayed. These time-delays can not only slow the network but can have a destabilizing effect on the network's dynamics leading to poor performance. The…
Social robot navigation can be helpful in various contexts of daily life but requires safe human-robot interactions and efficient trajectory planning. While modeling pairwise relations has been widely studied in multi-agent interacting…
We study how the connectivity within a recurrent neural network determines and is determined by the multistable solutions of network activity. To gain analytic tractability we let neural activation be a non-smooth Heaviside step function.…
This work is concerned with the efficient optimization method for solving a large class of optimal mass transport problems. An inexact primal-dual algorithm is presented from the time discretization of a proper dynamical system, and by…
Understanding the role of network structure in the evolution of cooperation is a key research goal at the intersection between physics and biology. Recent studies have particularly focused on multiplex networks given that multiple social…
The behaviour of multi-agent learning in many player games has been shown to display complex dynamics outside of restrictive examples such as network zero-sum games. In addition, it has been shown that convergent behaviour is less likely to…
This paper considers the distributed robust suboptimal consensus control problem of linear multi-agent systems, with both H2 and H_infty performance requirements. A novel two-step complementary design approach is proposed. In the first…
We consider stability analysis of constrained switching linear systems in which the dynamics is unknown and whose switching signal is constrained by an automaton. We propose a data-driven Lyapunov framework for providing probabilistic…
Safety-critical autonomy in adversarial settings demands more than Lyapunov stability of tracking error signals. An agent executing a goal-directed trajectory is intrinsically legible to a passive observer running online Bayesian inference,…
A fundamental premise of statistical physics is that the particles in a physical system are interchangeable, and hence the state of each specific component is representative of the system as a whole. This assumption breaks down for complex…
Incremental input-to-state stability (delta-ISS) offers a robust framework to ensure that small input variations result in proportionally minor deviations in the state of a nonlinear system. This property is essential in practical…
Most existing neural network-based approaches for solving stochastic optimal control problems using the associated backward dynamic programming principle rely on the ability to simulate the underlying state variables. However, in some…
The paper is concerned with the development of Lyapunov methods for the analysis of equilibrium stability in a dynamical system on the space of probability measures driven by a non-local continuity equation. We derive sufficient conditions…
The planning domain has experienced increased interest in the formal synthesis of decision-making policies. This formal synthesis typically entails finding a policy which satisfies formal specifications in the form of some well-defined…
Dynamic processes of interacting units on a network are out of equilibrium in general. In the case of a directed tree, the dynamic cavity method provides an efficient tool that characterises the dynamic trajectory of the process for the…