Related papers: Reachability Analysis Using Dissipation Inequaliti…
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…
In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast…
A method is presented to obtain an inner-approximation of the backward reachable set (BRS) of a given target tube, along with an admissible controller that maintains trajectories inside this tube. The proposed optimization algorithms are…
A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of…
Determining the reachable set for a given nonlinear control system is crucial for system control and planning. However, computing such a set is impossible if the system's dynamics are not fully known. This paper is motivated by a scenario…
This paper presents a framework for abstracting uncertain or non-polynomial components of dynamical systems using polynomial constraints. This enables the application of polynomial-based analysis tools, such as sum-of-squares programming,…
In this work, we perform safety analysis of linear dynamical systems with uncertainties. Instead of computing a conservative overapproximation of the reachable set, our approach involves computing a statistical approximate reachable set. As…
We present an approach to approximate reachable sets for linear systems with bounded L-infinity controls in finite time. Our first approach investigates the boundaries of these sets and reveals an exact characterization for single-input,…
We propose a scalable method for forward stochastic reachability analysis for uncontrolled linear systems with affine disturbance. Our method uses Fourier transforms to efficiently compute the forward stochastic reach probability measure…
The problem of computing the reachable set for a given system is a quintessential question in nonlinear control theory. While previous work has yielded a plethora of approximate and analytical methods for determining such a set, these…
We present a method to overapproximate forward stochastic reach sets of discrete-time, stochastic nonlinear systems with interval geometry. This is made possible by extending the theory of mixed-monotone systems to incorporate stochastic…
This work provides a framework to compute an upper bound on the robust peak-to-peak gain of discrete-time uncertain linear systems using integral quadratic constraints (IQCs). Such bounds are of particular interest in the computation of…
We present a new approach to verifying contraction and $L_2$-gain of uncertain nonlinear systems, extending the well-known method of integral quadratic constraints. The uncertain system consists of a feedback interconnection of a nonlinear…
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…
This paper presents a novel algorithm for reachability analysis of nonlinear discrete-time systems. The proposed method combines constrained zonotopes (CZs) with polyhedral relaxations of factorable representations of nonlinear functions to…
Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the…
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…
Transient stability assessment of power systems needs to account for increased risk from uncertainties due to the integration of renewables and distributed generators. The uncertain operating condition of the power grid hinders reliable…
One often wishes for the ability to formally analyze large-scale systems---typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This work tries to further close this…
Reachability analysis is an important method in providing safety guarantees for systems with unknown or uncertain dynamics. Due to the computational intractability of exact reachability analysis for general nonlinear, high-dimensional…