Related papers: A Sample-Driven Solving Procedure for the Repeated…
Inductive bias refers to restrictions on the hypothesis class that enable a learning method to generalize effectively from limited data. A canonical example in control is linearity, which underpins low sample-complexity guarantees for…
In this paper, a method to achieve smooth transitions between sequential reachability tasks for a continuous time mobile robotic system is presented. Control barrier functions provide formal guarantees of forward invariance of safe sets and…
In the real world a graph is often fragmented and distributed across different sites. This highlights the need for evaluating queries on distributed graphs. This paper proposes distributed evaluation algorithms for three classes of queries:…
Random walks (or Markov chains) are models extensively used in theoretical computer science. Several tools, including analysis of quantities such as hitting and mixing times, are helpful for devising randomized algorithms. A notable example…
Piecewise affine maps (PAMs) are frequently used as a reference model to show the openness of the reachability questions in other systems. The reachability problem for one-dimentional PAM is still open even if we define it with only two…
Writing formal specifications for distributed systems is difficult. Even simple consistency requirements often turn out to be unrealizable because of the complicated information flow in the distributed system: not all information is…
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…
Control Barrier Functions (CBFs) are a powerful tool for ensuring robotic safety, but designing or learning valid CBFs for complex systems is a significant challenge. While Hamilton-Jacobi Reachability provides a formal method for…
In this paper, we study the problem of model-checking quantum pushdown systems from a computational complexity point of view. We arrive at the following equally important, interesting new results: We first extend the notions of the {\it…
Markov decision processes model systems subject to nondeterministic and probabilistic uncertainty. A plethora of verification techniques addresses variations of reachability properties, such as: Is there a scheduler resolving the…
Reachability analysis is a powerful tool for computing the set of states or outputs reachable for a system. While previous work has focused on systems described by state-space models, we present the first methods to compute reachable sets…
One of the most important problems in hybrid systems is the {\em reachability problem}. The reachability problem has been shown to be undecidable even for a subclass of {\em linear} hybrid systems. In view of this, the main focus in the…
Verifying correctness of deep neural networks (DNNs) is challenging. We study a generic reachability problem for feed-forward DNNs which, for a given set of inputs to the network and a Lipschitz-continuous function over its outputs,…
We consider here systems with piecewise linear dynamics that are periodically sampled with a given period {\tau} . At each sampling time, the mode of the system, i.e., the parameters of the linear dynamics, can be switched, according to a…
While quantum speed-up in solving certain decision problems by a fault-tolerant universal quantum computer has been promised, a timely research interest includes how far one can reduce the resource requirement to demonstrate a provable…
Forward reachability analysis is a dominant approach for verifying reach-avoid specifications in neural feedback systems, i.e., dynamical systems controlled by neural networks, and a number of directions have been proposed and studied. In…
Contact-rich robotic systems, such as legged robots and manipulators, are often represented as hybrid systems. However, the stability analysis and region-of-attraction computation for these systems are often challenging because of the…
We present an algorithm for data-driven reachability analysis that estimates finite-horizon forward reachable sets for general nonlinear systems using level sets of a certain class of polynomials known as Christoffel functions. The level…
In this work, we present a numerical optimal control framework for reachable set computation using \emph{normotopes}, a new set representation as a norm ball with a shaping matrix. In reachable set computations, we expect to continuously…
Analyses of serially-sampled data often begin with the assumption that the observations represent discrete samples from a latent continuous-time stochastic process. The continuous-time Markov chain (CTMC) is one such generative model whose…