Related papers: Probabilistic Reach-Avoid Reachability in Nondeter…
When designing optimal controllers for any system, it is often the case that the true state of the system is unknown to the controller, for example due to noisy measurements or partially observable states. Incomplete state information must…
In this paper we propose a novel semi-definite programming approach that solves reach-avoid problems over open (i.e., not bounded a priori) time horizons for dynamical systems modeled by polynomial stochastic differential equations. The…
We present two data-driven methods for estimating reachable sets with probabilistic guarantees. Both methods make use of a probabilistic formulation allowing for a formal definition of a data-driven reachable set approximation that is…
Reachability analysis of hybrid systems has been used as a safety verification tool to assess offline whether the state of a system is capable of remaining within a designated safe region for a given time horizon. Although it has been…
This paper proposes an algorithm to maximize reachability probabilities for rectangular automata with random clocks via a history-dependent prophetic scheduler. This model class incorporates time-induced nondeterminism on discrete behavior…
The reachable sets of nonlinear control systems can in general only be numerically approximated, and are often very expensive to calculate. In this paper, we propose an algorithm that tracks only the boundaries of the reachable sets and…
Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…
Reachability analysis evaluates system safety, by identifying the set of states a system may evolve within over a finite time horizon. In contrast to model-based reachability analysis, data-driven reachability analysis estimates reachable…
We study the computation of lower and upper probabilities of hitting a target set of states for imprecise Markov chains, where transition uncertainty is modelled by a convex set of transition matrices. In the precise case, hitting…
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 this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of…
We present a data-driven framework for reachability analysis of nonlinear dynamical systems that requires no explicit model. A denoising diffusion probabilistic model learns the time-evolving state distribution of a dynamical system from…
Model predictive control solves a constrained optimization problem online in order to compute an implicit closed-loop control policy. Recursive feasibility -- guaranteeing that the optimal control problem will have a solution at every time…
This paper presents two stochastic model predictive control methods for linear time-invariant systems subject to unbounded additive uncertainties. The new methods are developed by formulating the chance constraints into deterministic form,…
A constant-rate multi-mode system is a hybrid system that can switch freely among a finite set of modes, and whose dynamics is specified by a finite number of real-valued variables with mode-dependent constant rates. Alur, Wojtczak, and…
We present ProbReach, a tool for verifying probabilistic reachability for stochastic hybrid systems, i.e., computing the probability that the system reaches an unsafe region of the state space. In particular, ProbReach will compute an…
Model predictive control allows solving complex control tasks with control and state constraints. However, an optimal control problem must be solved in real-time to predict the future system behavior, which is hardly possible on embedded…
This paper investigates one-step backward reachability for uncertain max-plus linear systems with additive disturbances. Given a target set, the problem is to compute the set of states from which there exists an admissible control input…
Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…
We consider finite horizon reach-avoid problems for discrete time stochastic systems. Our goal is to construct upper bound functions for the reach-avoid probability by means of tractable convex optimization problems. We achieve this by…