Related papers: Compile-Time Extensions to Hybrid ODEs
The spatially discretized magnetic vector potential formulation of magnetoquasistatic field problems is transformed from an infinitely stiff differential algebraic equation system into a finitely stiff ordinary differential equation (ODE)…
We study SMT problems over the reals containing ordinary differential equations. They are important for formal verification of realistic hybrid systems and embedded software. We develop delta-complete algorithms for SMT formulas that are…
Quantum speed-ups for dynamical simulation usually demand unitary time-evolution, whereas the large ODE/PDE systems encountered in realistic physical models are generically non-unitary. We present a universal moment-fulfilling dilation that…
The satisfiability problem for branching-time temporal logics like CTL*, CTL and CTL+ has important applications in program specification and verification. Their computational complexities are known: CTL* and CTL+ are complete for doubly…
In programming, better tools often yield better results. For that, modern programming environments offer mechanisms to allow for their extensibility. The closer those tools are to the code, the easier it is for programmers to map the…
Reachability analysis is important for studying optimal control problems and differential games, which are powerful theoretical tools for analyzing and modeling many practical problems in robotics, aircraft control, among other application…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…
We consider the problem of symbolic reachability analysis of higher-order context-free processes. These models are generalizations of the context-free processes (also called BPA processes) where each process manipulates a data structure…
Ensuring the correctness of critical real-time systems, involving concurrent behaviours and timing requirements, is crucial. Timed automata extend finite-state automata with clocks, compared in guards and invariants with integer constants.…
For any given spacetime the choice of time coordinate is undetermined. A particular choice is the absolute time associated with a preferred vector field. Using the absolute time Hamilton's equations are $- (\delta H_{c})/(\delta…
We consider pushdown timed automata (PTAs) that are timed automata (with dense clocks) augmented with a pushdown stack. A configuration of a PTA includes a control state, dense clock values and a stack word. By using the pattern technique,…
Building on the work by Fainekos and Pappas and the one by Donze and Maler, we introduce AvSTL, an extension of metric interval temporal logic by averaged temporal operators. Its expressivity in capturing both space and time robustness…
This paper presents algorithms for performing data-driven reachability analysis under temporal logic side information. In certain scenarios, the data-driven reachable sets of a robot can be prohibitively conservative due to the inherent…
Controlling hybrid systems is mostly very challenging due to the variety of dynamics these systems can exhibit. Inspired by the concept of differential flatness of nonlinear continuous systems and their inherent invertibility property, the…
Reachability analysis is used to determine all possible states that a system acting under uncertainty may reach. It is a critical component to obtain guarantees of various safety-critical systems both for safety verification and controller…
A transient magneto-quasistatic vector potential formulation involving nonlinear material is spatially discretized using the finite element method of first and second polynomial order. By applying a generalized Schur complement the…
Verifying the correct behavior of robots in contact tasks is challenging due to model uncertainties associated with contacts. Standard methods for testing often fall short since all (uncountable many) solutions cannot be obtained. Instead,…
The model-checking problem for hybrid systems is a well known challenge in the scientific community. Most of the existing approaches and tools are limited to safety properties only, or operates by transforming the hybrid system to be…
Imitation learning has demonstrated impressive results in robotic manipulation but fails under out-of-distribution (OOD) states. This limitation is particularly critical in Deformable Object Manipulation (DOM), where the near-infinite…
We present a new technique for demonstrating the reachability of states in deterministic finite automata representing the concatenation of two languages. Such demonstrations are a necessary step in establishing the state complexity of the…