Related papers: Data-Driven Reachability Analysis from Noisy Data
This paper poses a theoretical characterization of the stochastic reachability problem in terms of probability measures, capturing the probability measure of the state of the system that satisfies the reachability specification for all…
We study the verification problem for closed-loop dynamical systems with neural-network controllers (NNCS). This problem is commonly reduced to computing the set of reachable states. When considering dynamical systems and neural networks in…
In this paper, we introduce a set representation called polynomial logical zonotopes for performing exact and computationally efficient reachability analysis on logical systems. We prove that through this polynomial-like construction, we…
Hybrid systems - more precisely, their mathematical models - can exhibit behaviors, like Zeno behaviors, that are absent in purely discrete or purely continuous systems. First, we observe that, in this context, the usual definition 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…
In the context of data-driven control of nonlinear systems, many approaches lack of rigorous guarantees, call for nonconvex optimization, or require knowledge of a function basis containing the system dynamics. To tackle these drawbacks, we…
Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Reachability analysis works by iteratively applying continuous…
This paper investigates the application of zonotope-based reachability analysis to low-thrust spacecraft in both two-body and cislunar environments. Reachable sets are generated under two-body and circular restricted three-body (CR3BP)…
This paper presents a robust data-driven controller design based on the noisy input-output data without assumptions on the statistical properties of the noises. We start with the direct data-representation of system models that take…
We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounded norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all…
This work presents a method of efficiently computing inner and outer approximations of forward reachable sets for nonlinear control systems with changed dynamics and diminished control authority, given an a priori computed reachable set for…
Neural networks (NNs) have been shown to learn complex control laws successfully, often with performance advantages or decreased computational cost compared to alternative methods. Neural network controllers (NNCs) are, however, highly…
This paper proposes an algorithm capable of driving a system to follow a piecewise linear trajectory without prior knowledge of the system dynamics. Motivated by a critical failure scenario in which a system can experience an abrupt change…
This paper presents a new data-driven robust predictive control law, for linear systems affected by unknown-but-bounded process disturbances. A sequence of input-state data is used to construct a suitable uncertainty representation based on…
Validating and controlling safety-critical systems in uncertain environments necessitates probabilistic reachable sets of future state evolutions. The existing methods of computing probabilistic reachable sets normally assume that…
We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a…
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…
We derive an algorithm of optimal complexity which determines whether a given matrix is a Cauchy matrix, and which exactly recovers the Cauchy points defining a Cauchy matrix from the matrix entries. Moreover, we study how to approximate a…
Determining the reachable set for a given nonlinear system is critically important for autonomous trajectory planning for reach-avoid applications and safety critical scenarios. Providing the reachable set is generally impossible when 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…