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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…
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…
Recent advancements in model-free deep reinforcement learning have enabled efficient agent training. However, challenges arise when determining the region of attraction for these controllers, especially if the region does not fully cover…
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…
In this paper, we present a method to analyze local and global stability in offset-free setpoint tracking using neural network controllers and we provide ellipsoidal inner approximations of the corresponding region of attraction. We…
A novel control method is proposed to ensure compatibility of safe, stabilizing control laws, i.e., simultaneous satisfaction of asymptotic stability and constraint satisfaction for nonlinear affine systems. The results are dependent on an…
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…
Leveraging a stochastic extension of Zubov's equation, we develop a physics-informed neural network (PINN) approach for learning a neural Lyapunov function that captures the largest probabilistic region of attraction (ROA) for stochastic…
We present a learning-based predictive control methodology using the differentiable programming framework with probabilistic Lyapunov-based stability guarantees. The neural Lyapunov differentiable predictive control (NLDPC) learns the…
Deep Neural Networks (DNNs) are increasingly used in control applications due to their powerful function approximation capabilities. However, many existing formulations focus primarily on tracking error convergence, often neglecting the…
A method is presented to learn neural network (NN) controllers with stability and safety guarantees through imitation learning (IL). Convex stability and safety conditions are derived for linear time-invariant plant dynamics with NN…
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.…
This work presents several improvements to the closed-loop stability verification framework using semialgebraic sets and convex semidefinite programming to examine neural-network-based control systems regulating nonlinear dynamical 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…
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…
In this paper, we describe a lightweight Python framework that provides integrated learning and verification of neural Lyapunov functions for stability analysis. The proposed tool, named LyZNet, learns neural Lyapunov functions using…
Hybrid systems are prevalent in robotics. However, ensuring the stability of hybrid systems is challenging due to sophisticated continuous and discrete dynamics. A system with all its system modes stable can still be unstable. Hence special…
Koopman operator theory has gained significant attention in recent years for identifying discrete-time nonlinear systems by embedding them into an infinite-dimensional linear vector space. However, providing stability guarantees while…
This paper studies data-driven stabilization of a class of unknown polynomial systems using data corrupted by bounded noise. Existing work addressing this problem has focused on designing a controller and a Lyapunov function so that a…
The search for Lyapunov functions is a crucial task in the analysis of nonlinear systems. In this paper, we present a physics-informed neural network (PINN) approach to learning a Lyapunov function that is nearly maximal for a given stable…