Related papers: A Sum-of-Squares approach to the Stability and Con…
Recently sum-of-squares (SOS) based methods have been used for the stability analysis and control synthesis of polynomial dynamical systems. This analysis framework was also extended to non-polynomial dynamical systems, including power…
Sum-of-squares (SOS) methods have been shown to be very useful in computing polynomial Lyapunov functions for systems of reasonably small size. However for large scale systems it is necessary to use a scalable alternative using vector…
This work estimates safe invariant subsets of the Region of Attraction (ROA) for a seven-state vehicle-with-driver system, capturing both asymptotic stability and the influence of state-safety bounds along the system trajectory. Safe sets…
Reliable quasi-static object manuipulation and robotic locomotion require verification of the stability of equilibria under rigid contacts and friction. In a recent paper, M. Posa, M. Tobenkin, and R. Tedrake demonstrated that…
This paper presents an approach to systematically design sliding mode control and manifold to stabilize nonlinear uncertain systems. The objective is also accomplished to enlarge the inner bound of region of attraction for closed-loop…
The dynamics of many systems from physics, economics, chemistry, and biology can be modelled through polynomial functions. In this paper, we provide a computational means to find positively invariant sets of polynomial dynamical systems by…
Traditional Lyapunov based transient stability assessment approaches focus on identifying the stability region (SR) of the equilibrium point under study. When trying to estimate this region using Lyapunov functions, the shape of the final…
Lyapunov functions provide a tool to analyze the stability of nonlinear systems without extensively solving the dynamics. Recent advances in sum-of-squares methods have enabled the algorithmic computation of Lyapunov functions for…
This paper introduces a new method for proving global stability of fluid flows through the construction of Lyapunov functionals. For finite dimensional approximations of fluid systems, we show how one can exploit recently developed…
In this paper, we present a novel approach to determine the stability of switched linear and nonlinear systems using Sum of Squares optimisation. Particularly, we use Sum of Squares optimisation to search for a Lyapunov function that…
We provide a computer-assisted approach to ensure that a given continuous or discrete-time polynomial system is (asymptotically) stable. Our framework relies on constructive analysis together with formally certified sums of squares Lyapunov…
Sum of Squares programming has been used extensively over the past decade for the stability analysis of nonlinear systems but several questions remain unanswered. In this paper, we show that exponential stability of a polynomial vector…
For the class of nonlinear input-affine systems with polynomial dynamics, we consider the problem of designing an input-to-state stabilizing controller with respect to typical exogenous signals in a feedback control system, such as actuator…
Contraction analysis is a stability theory for nonlinear systems where stability is defined incrementally between two arbitrary trajectories. It provides an alternative framework in which to study uncertain interconnections or systems with…
We present a method for synthesizing dynamic, reduced-order output-feedback polynomial control policies for control-affine nonlinear systems which guarantees runtime stability to a goal state, when using visual observations and a learned…
This work presents a sum-of-squares (SOS) based framework to perform data-driven stabilization and robust control tasks on discrete-time linear systems where the full-state observations are corrupted by L-infinity bounded input,…
Neural network controllers have the potential to improve the performance of feedback systems compared to traditional controllers, due to their ability to act as general function approximators. However, quantifying their safety and…
Many dynamical systems described by nonlinear ODEs are unstable. Their associated solutions do not converge towards an equilibrium point, but rather converge towards some invariant subset of the state space called an attractor set. For a…
This paper develops methods for proving Lyapunov stability of dynamical systems subject to disturbances with an unknown distribution. We assume only a finite set of disturbance samples is available and that the true online disturbance…
We consider the problem of ensuring the safety of nonlinear control systems under adversarial signals. Using Lyapunov based reachability analysis, we first give sufficient conditions to assess safety, i.e., to guarantee that the states of…