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While ensuring stability for linear systems is well understood, it remains a major challenge for nonlinear systems. A general approach in such cases is to compute a combination of a Lyapunov function and an associated control policy.…
We propose new methods for learning control policies and neural network Lyapunov functions for nonlinear control problems, with provable guarantee of stability. The framework consists of a learner that attempts to find the control and…
In this paper, we focus on the problem about direct way to design a stable controller for nonlinear system. A framework of learning controller with Lyapunov-based constraint is proposed, which is intended to transform designing and analyis…
Neural-based, data-driven analysis and control of dynamical systems have been recently investigated and have shown great promise, e.g. for safety verification or stability analysis. Indeed, not only do neural networks allow for an entirely…
We propose a method for training ordinary differential equations by using a control-theoretic Lyapunov condition for stability. Our approach, called LyaNet, is based on a novel Lyapunov loss formulation that encourages the inference…
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…
Deep learning has had a far reaching impact in robotics. Specifically, deep reinforcement learning algorithms have been highly effective in synthesizing neural-network controllers for a wide range of tasks. However, despite this empirical…
Safety and stability are common requirements for robotic control systems; however, designing safe, stable controllers remains difficult for nonlinear and uncertain models. We develop a model-based learning approach to synthesize robust…
Learning controllers merely based on a performance metric has been proven effective in many physical and non-physical tasks in both control theory and reinforcement learning. However, in practice, the controller must guarantee some notion…
This article presents novel methods for synthesizing distributionally robust stabilizing neural controllers and certificates for control systems under model uncertainty. A key challenge in designing controllers with stability guarantees for…
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…
With a growing interest in data-driven control techniques, Model Predictive Control (MPC) provides an opportunity to exploit the surplus of data reliably, particularly while taking safety and stability into account. In many real-world and…
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…
We present a technique for learning control Lyapunov-like functions, which are used in turn to synthesize controllers for nonlinear dynamical systems that can stabilize the system, or satisfy specifications such as remaining inside a safe…
Transient stability of power systems is becoming increasingly important because of the growing integration of renewable resources. These resources lead to a reduction in mechanical inertia but also provide increased flexibility in frequency…
The lack of stability guarantee restricts the practical use of learning-based methods in core control problems in robotics. We develop new methods for learning neural control policies and neural Lyapunov critic functions in the model-free…
This paper proposes a novel transient stability assessment tool for networked microgrids based on neural Lyapunov methods. Assessing transient stability is formulated as a problem of estimating the dynamic security region of networked…
We propose an automatic and formally sound method for synthesising Lyapunov functions for the asymptotic stability of autonomous non-linear systems. Traditional methods are either analytical and require manual effort or are numerical but…
Finding a control Lyapunov function (CLF) in a dynamical system with a controller is an effective way to guarantee stability, which is a crucial issue in safety-concerned applications. Recently, deep learning models representing CLFs have…
Stability certification and identifying a safe and stabilizing initial set are two important concerns in ensuring operational safety, stability, and robustness of dynamical systems. With the advent of machine-learning tools, these issues…