Related papers: Learning a Stable Dynamic System with a Lyapunov E…

We introduce ImitationFlow, a novel Deep generative model that allows learning complex globally stable, stochastic, nonlinear dynamics. Our approach extends the Normalizing Flows framework to learn stable Stochastic Differential Equations.…

Reinforcement learning is showing great potentials in robotics applications, including autonomous driving, robot manipulation and locomotion. However, with complex uncertainties in the real-world environment, it is difficult to guarantee…

This paper considers a wide class of smooth continuous dynamic nonlinear systems (control objects) with a measurable vector of state. The problem is to find a special function (Lyapunov function), which in the framework of the second…

Neural Ordinary Differential Equations (Neural ODEs), as a novel category of modeling big data methods, cleverly link traditional neural networks and dynamical systems. However, it is challenging to ensure the dynamics system reaches a…

We develop a versatile deep neural network architecture, called Lyapunov-Net, to approximate Lyapunov functions of dynamical systems in high dimensions. Lyapunov-Net guarantees positive definiteness, and thus it can be easily trained to…

Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end,…

Dynamical Systems (DS) are an effective and powerful means of shaping high-level policies for robotics control. They provide robust and reactive control while ensuring the stability of the driving vector field. The increasing complexity of…

Learning for control of dynamical systems with formal guarantees remains a challenging task. This paper proposes a learning framework to simultaneously stabilize an unknown nonlinear system with a neural controller and learn a neural…

We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings which incorporates prior knowledge in the form of systems of ordinary differential equations. NDS uses neural networks 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…

Dynamical system (DS)-based learning from demonstration (LfD) is a powerful tool for generating motion plans in the operation (`task') space of robotic systems. However, the realization of the generated motion plans is often compromised by…

For complex nonlinear systems, it is challenging to design algorithms that are fast, scalable, and give an accurate approximation of the stability region. This paper proposes a sampling-based approach to address these challenges. By…

In this paper, a deep reinforcement learning (DRL)-based approach to the Lyapunov optimization is considered to minimize the time-average penalty while maintaining queue stability. A proper construction of state and action spaces is…

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…

In the design and operation of complex dynamical systems, it is essential to ensure that all state trajectories of the dynamical system converge to a desired equilibrium within a guaranteed stability region. Yet, for many practical systems…

This paper addresses the problem of Neural Network (NN) based adaptive stability certification in a dynamical system. The state-of-the-art methods, such as Neural Lyapunov Functions (NLFs), use NN-based formulations to assess the stability…

We present a new approach for constructing polytope Lyapunov functions for continuous-time linear switching systems (LSS). This allows us to decide the stability of LSS and to compute the Lyapunov exponent with a good precision in…

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…

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…

Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems.…