arXiv subjects

Andrew Sogokon

Publications and source records attributed to Andrew Sogokon.

5 recordsLinked to original sources

arXiv2026

TERA: A Unified Taylor Model Enabled Reachability Analysis Framework

Reachability analysis of safety-critical systems requires computing rigorous enclosures of all possible state trajectories. Taylor Model (TM)-based methods have proved effective at mitigating the so-called wrapping effect which leads to overly conservative enclosures of reachable sets. However, existing tools are often hard to extend or focused on narrow system classes (e.g. deterministic systems modelled by ODEs, or hybrid systems). We develop TERA: a Python-native framework for TM-based reachability analysis of continuous, hybrid and stochastic systems within a single symbolic-numeric workflow. TERA is free and open-source, enabling rapid prototyping of reachability analysis techniques with rigorous enclosures. At present, our implementation is able to compute tight reachable set over-approximations for non-linear ODEs and hybrid systems on difficult benchmark problems, and already supports analysis of continuous-time stochastic systems. Our goal is to develop a robust open-source Python infrastructure for rigorous reachability analysis supporting a broad class of systems, including stochastic hybrid systems.

eess.SY↗

arXiv2023

Specifying Autonomous System Behaviour

Specifying the intended behaviour of autonomous systems is becoming increasingly important but is fraught with many challenges. This technical report provides an overview of existing work on specifications of autonomous systems and places a particular emphasis on formal specification, i.e. mathematically rigorous approaches to specification that require an appropriate formalism. Given the breadth of this domain, our coverage is necessarily incomplete but serves to provide a brief introduction to some of the difficulties that specifying autonomous systems entails, as well as existing approaches to addressing these difficulties currently pursued in academia and industry.

eess.SY↗

arXiv2021

Characterizing Positively Invariant Sets: Inductive and Topological Methods

We present two characterizations of positive invariance of sets under the flow of systems of ordinary differential equations. The first characterization uses inward sets which intuitively collect those points from which the flow evolves within the set for a short period of time, whereas the second characterization uses the notion of exit sets, which intuitively collect those points from which the flow immediately leaves the set. Our proofs emphasize the use of the real induction principle as a generic and unifying proof technique that captures the essence of the formal reasoning justifying our results and provides cleaner alternative proofs of known results. The two characterizations presented in this article, while essentially equivalent, lead to two rather different decision procedures (termed respectively LZZ and ESE) for checking whether a given semi-algebraic set is positively invariant under the flow of a system of polynomial ordinary differential equations. The procedure LZZ improves upon the original work by Liu, Zhan and Zhao (EMSOFT 2011). The procedure ESE, introduced in this article, works by splitting the problem, in a principled way, into simpler sub-problems that are easier to check, and is shown to exhibit substantially better performance compared to LZZ on problems featuring semi-algebraic sets described by formulas with non-trivial Boolean structure.

cs.CG↗

arXiv2020

Pegasus: Sound Continuous Invariant Generation

Continuous invariants are an important component in deductive verification of hybrid and continuous systems. Just like discrete invariants are used to reason about correctness in discrete systems without having to unroll their loops, continuous invariants are used to reason about differential equations without having to solve them. Automatic generation of continuous invariants remains one of the biggest practical challenges to the automation of formal proofs of safety for hybrid systems. There are at present many disparate methods available for generating continuous invariants; however, this wealth of diverse techniques presents a number of challenges, with different methods having different strengths and weaknesses. To address some of these challenges, we develop Pegasus: an automatic continuous invariant generator which allows for combinations of various methods, and integrate it with the KeYmaera X theorem prover for hybrid systems. We describe some of the architectural aspects of this integration, comment on its methods and challenges, and present an experimental evaluation on a suite of benchmarks.

cs.SC↗

arXiv2019

A Formal Safety Net for Waypoint Following in Ground Robots

We present a reusable formally verified safety net that provides end-to-end safety and liveness guarantees for 2D waypoint-following of Dubins-type ground robots with tolerances and acceleration. We: i) Model a robot in differential dynamic logic (dL), and specify assumptions on the controller and robot kinematics, ii) Prove formal safety and liveness properties for waypoint-following with speed limits, iii) Synthesize a monitor, which is automatically proven to enforce model compliance at runtime, and iv) Our use of the VeriPhy toolchain makes these guarantees carry over down to the level of machine code with untrusted controllers, environments, and plans. The guarantees for the safety net apply to any robot as long as the waypoints are chosen safely and the physical assumptions in its model hold. Experiments show these assumptions hold in practice, with an inherent trade-off between compliance and performance.

cs.RO↗