We propose an automatic and formally sound method for synthesising Lyapunov functions the asymptotic stability of autonomous non-linear systems. Traditional methods are either analytical require manual effort or numerical but lack formal soundness. Symbolic computational functions, which in between, give guarantees typically semi-automatic because they rely on user to provide appropriate function templates. a that finds fully automatically$-$using machine learning$-$while also providing...

This paper accompanies FOSSIL: a software tool for the synthesis of Lyapunov functions and barrier certificates (or functions) dynamical systems modelled as differential equations. are formal stability analysis, whereas safety models. FOSSIL is sound automatic thanks to counterexample-guided inductive loop. method exploits flexibility candidate generated by training neural network templates, assertions provided verifier (namely, an SMT solver), finally new procedures ease exchange...

Closed-loop stability of control systems can be undermined by actuator faults. Redundant sets and Fault-Tolerant Control (FTC) strategies exploited to enhance system resiliency loss efficiency, complete failures or jamming. Passive FTC methods entail designing a fixed-gain law that preserve the closed-loop when faults occur, compromising on performance faultless system. The use is particular interest in case underwater autonomous platforms, where extensive sensoring monitor status limited...

This paper presents Fossil 2.0, a new major release of software tool for the synthesis certificates (e.g., Lyapunov and barrier functions) dynamical systems modelled as ordinary differential difference equations. 2.0 is much improved from its original release, including interfaces, significantly expanded certificate portfolio, controller enhanced extensibility. We present these features part this paper. implements counterexample-guided inductive (CEGIS) loop ensuring soundness method. Our...

We propose a recursive least squares method with multiple forgetting schemes to track time-varying model parameters which change different rates. Our approach hinges on the reformulation of classic scheme as regularized problem. A simulation study shows effectiveness proposed method.

We introduce a novel approach for the construction of symbolic abstractions -simpler, finite-state models -which mimic behaviour system interest, and are commonly utilized to verify complex logic specifications. Such require an exhaustive knowledge concrete model, which can be difficult obtain in real-world applications. To overcome this, we propose sample finite length trajectories unknown build abstraction based on concept ℓ-completeness. this end, notion probabilistic behavioural...

Machine learning-based techniques have recently been adapted to solve control problems. The Neural Lyapunov Control (NLC) method is one such example. This approch combines Artificial Networks with Satisfiability Modulo Theories (SMT) solvers synthesise stabilising laws and prove their formal correctness. formers are trained over a dataset of state-space samples generate candidate functions, whilst the SMT tasked certifying correctness continuous domain or returning counterexample. Despite...

At the intersection of dynamical systems, control theory, and formal methods lies construction symbolic abstractions: these typically represent simpler, finite-state models whose behaviour mimics one an underlying concrete system but are easier to analyse. Building abstraction usually requires accurate knowledge model: this may be costly gather, especially in real-life applications. We aim bridge gap by building abstractions based on sampling finite length trajectories. Adding controller...

Multiple mature implementations of the actor model concurrency exist. Besides several ones available for Java Virtual Machine, there are others, example, written in SmallTalk or C++, targeting native platforms other virtual machines. Recently, runtime environments such as GPUs have also appeared. However, so far, no full-featured, distributed environment has allowed programs to run, unchanged, on both and JavaScript This paper describes our ongoing effort providing a portable implementation...

We employ the scenario approach to compute probably approximately correct (PAC) bounds on average inter-sample time (AIST) generated by an unknown PETC system, based a finite number of samples. extend optimisation multiclass SVM algorithms in order construct PAC map between concrete state-space and times. then build traffic model applying <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell $...

A common technique to verify complex logic specifications for dynamical systems is the construction of symbolic abstractions: simpler, finite-state models whose behaviour mimics one interest. Typically, abstractions are constructed exploiting an accurate knowledge underlying model: in real-life applications, this may be a costly assumption. By sampling random $\ell$-step trajectories unknown system, we build abstraction based on notion $\ell$-completeness. We newly define probabilistic...

An emerging branch of control theory specialises in certificate learning, concerning the specification a desired (possibly complex) system behaviour for an autonomous or model, which is then analytically verified by means function-based proof. However, synthesis controllers abiding these complex requirements general non-trivial task and may elude most expert engineers. This results need automatic techniques that are able to design analyse wide range elaborate specifications. In this paper,...

The increased relevance of renewable energy sources has modified the behaviour electrical grid. Some affect network in a very distributed manner: whilst each unit little influence, large population can have significant impact on global network, particularly case synchronised behaviour. This work investigates large, heterogeneous photovoltaic panels connected to We employ Markov models represent aggregated population, while rest (and its associated consumption) is modelled as single...

The increasing presence of solar energy sources has radically transformed the continental electrical network. While panels affect grid in a distributed manner, and an individual device negligible weight, large population engaged production can overall network dynamics. this effect might some scenarios be disruptive, offer potential for frequency regulation, if their power output is to controlled. In work, we present models aggregation heterogeneous connected grid. modeled centrally: model...

Common household devices, such as solar panels and refrigerators, offer a considerable potential for frequency regulation, given their aggregate power generation consumption. In this paper we present simple approach to control the contribution of population thermostatically controlled loads, via proportional control, in accordance with current primary practice. This is suitable decentralized implementation. addition, consider effect renewables on electricity network transfer function. We...

Performance and closed-loop stability of control systems can be jeopardised by actuator faults. Actuator redundancy in combination with appropriate laws increase the resiliency a system to both loss efficiency or jamming. Passive Fault-Tolerant Control (FTC) aim at designing unique law guaranteed nominal faulty scenarios. In this work, novel machine learning-based method is devised systematically synthesise for affected faults, whilst formally certifying stability. The learning architecture...

The abstraction of dynamical systems is a powerful tool that enables the design feedback controllers using correct-by-design framework. We investigate novel scheme to obtain data-driven abstractions discrete-time stochastic processes in terms richer discrete models, whose actions lead nondeterministic transitions over space probability measures. component proposed methodology lies fact we only assume samples from an unknown distribution. also rely on model underlying dynamics build our...