Related papers: Underapproximating Safe Domains of Attraction for …
This paper develops a method for obtaining guaranteed outer approximations for global attractors of continuous and discrete time nonlinear dynamical systems. The method is based on a hierarchy of semidefinite programming problems of…
Backward reachability analysis computes the set of states that reach a target set under the competing influence of control input and disturbances. Depending on their interplay, the backward reachable set either represents all states that…
To verify the correct operation of systems, engineers need to determine the set of configurations of a dynamical model that are able to safely reach a specified configuration under a control law. Unfortunately, constructing models for…
A method is proposed to compute robust inner-approximations to the backward reachable set for uncertain nonlinear systems. It also produces a robust control law that drives trajectories starting in these sets to the target set. The method…
The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent…
In this paper, we propose an iterative method for using SOS programming to estimate the region of attraction of a polynomial vector field, the conjectured convergence of which necessitates the existence of polynomial Lyapunov functions…
Reachability analysis is at the core of many applications, from neural network verification, to safe trajectory planning of uncertain systems. However, this problem is notoriously challenging, and current approaches tend to be either too…
We have recently constructed a piecewise quadratic Lyapunov function to prove the boundedness of the reachable values set of piecewise affine discrete-time systems. The method developed also provided an overapproximation of the reachable…
Timely detection of abrupt anomalies is crucial for real-time monitoring and security of modern systems producing high-dimensional data. With this goal, we propose effective and scalable algorithms. Proposed algorithms are nonparametric as…
Implicit regularization refers to the tendency of local search algorithms to converge to low-dimensional solutions, even when such structures are not explicitly enforced. Despite its ubiquity, the mechanism underlying this behavior remains…
Nonlinear underactuated systems such as two-wheeled inverted pendulums (TWIPs) exhibit a limited region of attraction (RoA), which defines the set of initial conditions from which the closed-loop system converges to the equilibrium. The RoA…
Pseudospectral analysis is fundamental for quantifying the sensitivity and transient behavior of nonnormal matrices, yet its computational cost scales cubically with dimension, rendering it prohibitive for large-scale systems. While…
This paper concerns identification of uncontrolled or closed loop nonlinear systems using a set of trajectories that are generated by the system in a domain of attraction. The objective is to ensure that the trajectories of the identified…
In this paper, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving a sequence of linear programs, resulting in a sequence of affine upper and lower hyperplanes…
This paper over-approximates the reachable sets of a continuous-time uncertain system using the sensitivity of its trajectories with respect to initial conditions and uncertain parameters. We first prove the equivalence between an existing…
Contraction metrics are crucial in control theory because they provide a powerful framework for analyzing stability, robustness, and convergence of various dynamical systems. However, identifying these metrics for complex nonlinear systems…
In this paper we propose a convex programming based method to address a long-standing problem of inner-approximating backward reachable sets of state-constrained polynomial systems subject to time-varying uncertainties. The backward…
In this paper, we analyze the behavior of stochastic approximation schemes with set-valued maps in the absence of a stability guarantee. We prove that after a large number of iterations if the stochastic approximation process enters the…
We develop an indirect-adaptive model predictive control algorithm for uncertain linear systems subject to constraints. The system is modeled as a polytopic linear parameter varying system where the convex combination vector is constant but…
Designing provably safe control is a core problem in trustworthy autonomy. However, most prior work in this regard assumes either that the system dynamics are known or deterministic, or that the state and action space are finite,…