Related papers: A Converse Control Lyapunov Theorem for Joint Safe…
We develop a direct Lyapunov method for the almost sure open-loop stabilizability and asymptotic stabilizability of controlled degenerate diffusion processes. The infinitesimal decrease condition for a Lyapunov function is a new form of…
The safety and security of robotic systems are paramount when navigating around a hostile target. This paper addresses the problem of circumnavigating an unknown target by a unicycle robot while ensuring it maintains a desired safe distance…
This paper considers safe control synthesis for dynamical systems with either probabilistic or worst-case uncertainty in both the dynamics model and the safety constraints. We formulate novel probabilistic and robust (worst-case) control…
This paper establishes relationships between continuous-time, receding horizon, nonlinear model predictive control (MPC) and control Lyapunov and control barrier functions (CLF/CBF). We show that, if the cost function "behaves well" for…
Mathematical proofs are a cornerstone of control theory, and it is important to get them right. Deduction systems can help with this by mechanically checking the proofs. However, the structure and level of detail at which a proof is…
We investigate an example of noise-induced stabilization in the plane that was also considered in (Gawedzki, Herzog, Wehr 2010) and (Birrell, Herzog, Wehr 2011). We show that despite the deterministic system not being globally stable, the…
Safety-critical whole-body robot control demands reactive methods that ensure collision avoidance in real-time. Complementarity constraints and control barrier functions (CBF) have emerged as core tools for ensuring such safety constraints,…
We present a technique for learning control Lyapunov (potential) functions, which are used in turn to synthesize controllers for nonlinear dynamical systems. The learning framework uses a demonstrator that implements a black-box, untrusted…
Safety is one of the fundamental problems in robotics. Recently, one-step or multi-step optimal control problems for discrete-time nonlinear dynamical system were formulated to offer tracking stability using control Lyapunov functions…
Robust stabilization conditions for uncertain switched affine systems subject to a unitary input delay are presented. They are obtained through the Lyapunov framework and a min-switching state-feedback predictive control law. The result…
We show that the existence of a non-coercive Lyapunov function is sufficient for uniform global asymptotic stability (UGAS) of infinite-dimensional systems with external disturbances provided the speed of decay is measured in terms of the…
The present work extends recent results by second author concerning sampled-data feedback stabilization for affine in the control of nonlinear systems with nonzero drift term, under the presence of a generalized control Lyapunov function…
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…
We present the stability analysis for the new regulation-triggered approach to adaptive control introduced in a companion paper. Due to the fact that the closed-loop system is hybrid, our proofs have essential differences from the…
A combination of control Lyapunov functions (CLFs) and control barrier functions (CBFs) forms an efficient framework for addressing control challenges in safe stabilization. In our previous research, we developed an analytical control…
In this paper quotients of control systems which are generalizations of system reductions are used to study the stabilizability property of non-linear systems. Given a control system and its quotient we study under what conditions…
We present detailed analysis of the convergence properties and effectiveness of Lyapunov control design for bilinear Hamiltonian quantum systems based on the application of LaSalle's invariance principle and stability analysis from…
In the context of mechanical Lagrangian dynamics, we prove a new Lyapunov instability criterion for a non strict local minimum equilibrium point of a smooth potential where the sufficient condition for instability is the existence of a…
This paper proposes a method for certifying the local asymptotic stability of a given nonlinear Ordinary Differential Equation (ODE) by using Sum-of-Squares (SOS) programming to search for a partially quadratic Lyapunov Function (LF). The…
We study the problem of robust global stabilization in control-affine systems, focusing on dynamic uncertainties in the control directions \emph{and} the presence of topological obstructions that prevent the existence of smooth global…