Related papers: Almost Surely Stable Deep Dynamics
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…
Forecasting physical signals in long time range is among the most challenging tasks in Partial Differential Equations (PDEs) research. To circumvent limitations of traditional solvers, many different Deep Learning methods have been…
Imitation learning presents an effective approach to alleviate the resource-intensive and time-consuming nature of policy learning from scratch in the solution space. Even though the resulting policy can mimic expert demonstrations…
In this paper, we study the stability problem of a stochastic, nonlinear, discrete-time system. We introduce a linear transfer operator-based Lyapunov measure as a new tool for stability verification of stochastic systems. Weaker…
We consider the problem of formally verifying almost-sure (a.s.) asymptotic stability in discrete-time nonlinear stochastic control systems. While verifying stability in deterministic control systems is extensively studied in the…
Learning stable dynamics from observed time-series data is an essential problem in robotics, physical modeling, and systems biology. Many of these dynamics are represented as an inputs-output system to communicate with the external…
We address the problem of safely learning controlled stochastic dynamics from discrete-time trajectory observations, ensuring system trajectories remain within predefined safe regions during both training and deployment. Safety-critical…
This work presents an approach to synthesize a Lyapunov-like function to ensure incrementally input-to-state stability ($\delta$-ISS) property for an unknown discrete-time system. To deal with challenges posed by unknown system dynamics, we…
This work makes several contributions on stability and performance verification of nonlinear dynamical systems controlled by neural networks. First, we show that the stability and performance of a polynomial dynamical system controlled by a…
This work provides a framework for nonlinear model-free control of systems with unknown input-output dynamics, but outputs that can be controlled by the inputs. This framework leads to real-time control of the system such that a feasible…
As autonomous systems become more complex and integral in our society, the need to accurately model and safely control these systems has increased significantly. In the past decade, there has been tremendous success in using deep learning…
We present a new method for learning control law that stabilizes an unknown nonlinear dynamical system at an equilibrium point. We formulate a system identification task in a self-supervised learning setting that jointly learns a controller…
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…
Reinforcement learning is a powerful paradigm for learning optimal policies from experimental data. However, to find optimal policies, most reinforcement learning algorithms explore all possible actions, which may be harmful for real-world…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
This paper considers the problem of characterizing the stability region of a large-scale networked system comprised of dissipative nonlinear subsystems, in a distributed and computationally tractable way. One standard approach to estimate…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…
Since batch algorithms suffer from lack of proficiency in confronting model mismatches and disturbances, this contribution proposes an adaptive scheme based on continuous Lyapunov function for online robot dynamic identification. This paper…
Stability is a fundamental property of dynamical systems, yet to this date it has had little bearing on the practice of recurrent neural networks. In this work, we conduct a thorough investigation of stable recurrent models. Theoretically,…
Modelling real world systems involving humans such as biological processes for disease treatment or human behavior for robotic rehabilitation is a challenging problem because labeled training data is sparse and expensive, while high…