Related papers: Lyapunov-Net: A Deep Neural Network Architecture f…

Constraint admissible positively invariant (CAPI) sets play a pivotal role in ensuring safety in control and planning applications, such as the recursive feasibility guarantee of explicit reference governor and model predictive control.…

We provide explicit closed form expressions for strict Lyapunov functions for time-varying discrete time systems. Our Lyapunov functions are expressed in terms of known nonstrict Lyapunov functions for the dynamics and finite sums of…

In recent years, nonlinear dynamic system identification using artificial neural networks has garnered attention due to its broad potential applications across science and engineering. However, purely data-driven approaches often struggle…

In this work we show that given a nonlinear programming problem, it is possible to construct a family of dynamical systems defined on the feasible set of the given problem, so that: (a) the equilibrium points are the unknown critical points…

We explore the phase diagram of approximation rates for deep neural networks and prove several new theoretical results. In particular, we generalize the existing result on the existence of deep discontinuous phase in ReLU networks to…

This paper presents a counterexample-guided iterative algorithm to compute convex, piecewise linear (polyhedral) Lyapunov functions for uncertain continuous-time linear hybrid systems. Polyhedral Lyapunov functions provide an alternative to…

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…

The capability of recurrent neural networks to approximate trajectories of a random dynamical system, with random inputs, on non-compact domains, and over an indefinite or infinite time horizon is considered. The main result states that…

The purpose of this article is to develop a machinery to study the capacity of deep neural networks (DNNs) to approximate high-dimensional functions. In particular, we show that DNNs have the expressive power to overcome the curse of…

This paper presents a reinforcement learning-based neuroadaptive control framework for robotic manipulators operating under deferred constraints. The proposed approach improves traditional barrier Lyapunov functions by introducing a smooth…

Neural networks are known to be effective function approximators. Recently, deep neural networks have proven to be very effective in pattern recognition, classification tasks and human-level control to model highly nonlinear realworld…

This paper develops methods for proving Lyapunov stability of dynamical systems subject to disturbances with an unknown distribution. We assume only a finite set of disturbance samples is available and that the true online disturbance…

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…

Stability, reachability, and safety are crucial properties of dynamical systems. While verification and control synthesis of reach-avoid-stay objectives can be effectively handled by abstraction-based formal methods, such approaches can be…

Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…

Time bounded reachability is a fundamental problem in model checking continuous-time Markov chains (CTMCs) and Markov decision processes (CTMDPs) for specifications in continuous stochastic logics. It can be computed by numerically solving…

Deep Neural Networks (DNNs) are widely used for their ability to effectively approximate large classes of functions. This flexibility, however, makes the strict enforcement of constraints on DNNs an open problem. Here we present a framework…

Estimating the Region of Attraction (RoA) for nonlinear dynamical systems is a fundamental problem in control theory, with direct implications for stability analysis and safe controller design. Traditional approaches rely on analytically…

Let $\Omega = [0,1]^d$ be the unit cube in $\mathbb{R}^d$. We study the problem of how efficiently, in terms of the number of parameters, deep neural networks with the ReLU activation function can approximate functions in the Sobolev spaces…

Neural-network-based controllers (NNCs) can represent complex, highly nonlinear control laws, but verifying the closed-loop stability of dynamical systems using them remains challenging. This work presents contributions to a…