This letter describes an extension of the classic Lazy Probabilistic Roadmaps algorithm (Lazy PRM), which results from pairing PRM and a novel Branch-And-Cut (BC) algorithm. Cuts are dynamically generated constraints that are imposed on minimum cost paths over the geometric graphs selected by PRM. Cuts eliminate paths that cannot be mapped into smooth plans that satisfy suitably defined geometric and differential constraints. We generate candidate smooth plans by fitting splines to vertices in a minimum-cost path. Plans are validated with a recently proposed algorithm that maps them into finite traces, without the need to choose a fixed discretization step. A trace records the exact sequence of constraint boundaries crossed by the plan, modulo arithmetic precision. We evaluate several planners using our methods over the recently proposed BARN benchmark, reporting evidence of the scalability of our approach.

In this study, a control theoretic description of resilience is provided to quantify the characteristics of a resilient system. The aim is to establish a paradigm for resilient control design based on tangible control objectives that yield desirable attributes for safety-critical systems. In that regard, durability and recoverability properties are identified as key components of the proposed resilience framework and, to offer a methodology to enforce these attributes, the notion of finite-time robust control barrier function (FR-CBF) is introduced. Furthermore, to offer a comprehensive treatment of the problem, resilient control design is investigated for both continuous and sampled-data systems. To that end, FR-CBF-based design conditions for both continuous and piece-wise constant zero-order hold (ZOH) control inputs are included. Moreover, to provide a concrete example of how the proposed framework could be adopted for safety-critical control applications, in this study we also investigate the voltage regulation problem for inverter-interfaced radial power distribution networks subject to adversarial injections. In that regard, sufficient conditions for both the continuous and sampled-data ZOH control are derived to guarantee finite-time recovery and safe operation of the distribution grid in accordance with the proposed resilience framework. Finally, the efficacy of the proposed results is advocated using a simulation study showing resilient grid performance in the presence of the 'worst-case' power injection attack, as reported in (Lindstr & ouml;m et al. 2021).

Motivated by the need to localise faults along electrical power lines, this paper adopts a frequency-domain approach to parameter estimation for an infinite-dimensional linear dynamical system with one spatial variable. Since the time of the fault is unknown, and voltages and currents are measured at only one end of the line, distance information must be extracted from the post-fault transients. To properly account for high-frequency transient behaviour, the line dynamics is modelled directly by the Telegrapher's equation, rather than the more commonly used lumped-parameter approximations. First, the governing equations are non-dimensionalised to avoid ill-conditioning. A closed-form expression for the transfer function is then derived. Finally, nonlinear least-squares optimisation is employed to search for the fault location. Requirements on fault bandwidth, sensor bandwidth and simulation time-step are also presented. The result is a novel end-to-end algorithm for data generation and fault localisation, the effectiveness of which is demonstrated via simulation.

The asymptotic implausibility problem is introduced from the perspective of an adversary that seeks to drive the belief of a recursive Bayesian estimator away from a particular set of parameter values. It is assumed that the adversary controls all sensors informing the estimator, and can transmit false measurements stochastically according to a fixed distribution of its choice. First, we outline a method for verifying whether a given distribution solves the problem. We then consider the class of spoofing attacks, and show that the asymptotic implausibility problem has a solution if and only if it can be solved by a spoofing attack. Attention is restricted to finite parameter and observation spaces.

A Metric Interval Temporal Logic (MITL) verification algorithm is presented. It verifies continuous-time signals without relying on high frequency sampling. Instead, it is assumed that collections of over- and under-approximating intervals are available for the times at which the individual atomic propositions hold true for a given signal. These are combined inductively to generate corresponding over- and under-approximations for the specified MITL formula. The gap between the over- and under-approximations reflects timing uncertainty with respect to the signal being verified, thereby providing a quantitative measure of the conservativeness of the algorithm. The verification is exact when the over-approximations for the atomic propositions coincide with the under-approximations. Numerical examples are provided to illustrate.

This paper concerns the verification of continuous-time polynomial spline trajectories against linear temporal logic specifications (LTL without 'next’). Each atomic proposition is assumed to represent a state space region described by a multivariate polynomial inequality. The proposed approach samples a trajectory strategically, to capture every one of its region transitions. This yields a discrete word called a trace, which is amenable to established formal methods for path checking. The original continuous-time trajectory is shown to satisfy the specification if and only if its trace does. General topological conditions on the sample points are derived that ensure a trace is recorded for arbitrary continuous paths, given arbitrary region descriptions. Using techniques from computer algebra, a trace generation algorithm is developed to satisfy these conditions when the path and region boundaries are defined by polynomials. The proposed PolyTrace algorithm has polynomial complexity in the number of atomic propositions, and is guaranteed to produce a trace of any polynomial path. Its performance is demonstrated via numerical examples and a case study from robotics.

This letter considers the iterative numerical optimization of time-varying cost functions where no gradient information is available at each iteration. In this case, the proposed algorithm estimates a directional derivative by finite differences. The main contributions are the derivation of error bounds for such algorithms and proposal of optimal algorithm parameter values, e.g., step-sizes, for strongly convex cost functions. The algorithm is applied to tackle a source localization problem using a sensing agent where the source actively evades the agent. Numerical examples are provided to illustrate the theoretical results.

This paper analyses the performance of projected gradient descent on optimisation problems with cost functions and constraints that vary in discrete time. Specifically, strongly convex cost functions with Lipschitz gradient, and a sequence of convex constraints are assumed. Error bounds and suboptimality bounds are derived for a variety of cases, which show convergence to a steady-state. Conditions on the constraint sequence are also presented for guaranteeing finite-time feasibility, and for bounding the distance between successive minimisers. Numerical examples are then presented to validate the analytical results.