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Analyzing nonlinear systems with attracting robust invariant sets (RISs) requires estimating their domains of attraction (DOAs). Despite extensive research, accurately characterizing DOAs for general nonlinear systems remains challenging…
We study cooperative control dynamics with gradient based forcing terms. As a specific example, we focus on source-seeking dynamics with vehicles embedded in an unknown scalar field with a subset of agents having gradient information. As…
This paper addresses the problem of stabilizing a part of variables for control systems described by stochastic differential equations of the Ito type. The considered problem is related to the asymptotic stability property of invariant sets…
We investigate the important problem of certifying stability of reinforcement learning policies when interconnected with nonlinear dynamical systems. We show that by regulating the input-output gradients of policies, strong guarantees of…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
This paper presents a robust control synthesis and analysis framework for nonlinear systems with uncertain initial conditions. First, a deep learning-based lifting approach is proposed to approximate nonlinear dynamical systems with linear…
This paper develops a neural network based control framework that ensures system safety and input-to-state stability (ISS) for general nonlinear switched systems with unknown dynamics. Leveraging the concept of dwell time, we derive…
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…
We study the asymptotic stability properties of nonlinear switched systems under the assumption of the existence of a common weak Lyapunov function. We consider the class of nonchaotic inputs, which generalize the different notions of…
We study the stability of coupled impedance passive regular linear systems under power-preserving interconnections. We present new conditions for strong, exponential, and non-uniform stability of the closed-loop system. We apply the…
Deep learning methods have been widely used in robotic applications, making learning-enabled control design for complex nonlinear systems a promising direction. Although deep reinforcement learning methods have demonstrated impressive…
Control design for general nonlinear robotic systems with guaranteed stability and/or safety in the presence of model uncertainties is a challenging problem. Recent efforts attempt to learn a controller and a certificate (e.g., a Lyapunov…
This paper is concerned with robust instability analysis of linear feedback systems subject to a dynamic uncertainty. The work is motivated by, and provides a basic foundation for, a more challenging problem of analyzing persistence of…
This paper studies exponential stability properties of a class of two-dimensional (2D) systems called differential repetitive processes (DRPs). Since a distinguishing feature of DRPs is that the problem domain is bounded in the "time"…
Designing a stabilizing controller for nonlinear systems is a challenging task, especially for high-dimensional problems with unknown dynamics. Traditional reinforcement learning algorithms applied to stabilization tasks tend to drive the…
The estimation for the region of attraction (ROA) of an asymptotically stable equilibrium point is crucial in the analysis of nonlinear systems. There has been a recent surge of interest in estimating the solution to Zubov's equation, whose…
Model Predictive Control (MPC) is a powerful framework for constrained control, but its performance and safety can be severely degraded when the prediction model is learned online and thus remains uncertain. In this work, we develop a…
Envisioned applications for humanoid robots call for the design of balancing and walking controllers. While promising results have been recently achieved, robust and reliable controllers are still a challenge for the control community…
In this paper we provide a set of stability conditions for linear time-invariant networked control systems with arbitrary topology, using a Lyapunov direct approach. We then use these stability conditions to provide a novel low-complexity…
The paper proposes the stable motion control law design method for non-honomic differential-drive mobile robot with system and measurement noise in discrete time domain. This method is performed basing on dividing operating configuration of…