Robust Stability Analysis of Nonlinear Hybrid Systems

We present a methodology for robust stability analysis of nonlinear hybrid systems, through the algorithmic construction of polynomial and piecewise polynomial Lyapunov-like functions using convex optimization and in particular the sum of squares decomposition of multivariate polynomials. Several improvements compared to previous approaches are discussed, such as treating in a unified way polynomial switching surfaces and robust stability analysis for nonlinear hybrid systems

Decision algorithm for the stability of planar switching linear systems

This paper presents a decision algorithm for the analysis of the stability of a class of planar switched linear systems, modeled by hybrid automata. The dynamics in each location of the hybrid automaton is assumed to be linear and asymptotically stable; the guards on the transitions are hyper planes in the state space. We show that for every pair of an ingoing and an outgoing transition related to a location, the exact gain in the norm of the vector induced by the dynamics in that location can be computed. These exact gains are used in defining a gain automaton which forms the basis of an algorithmic criterion to determine if a planar hybrid automaton is stable or not

Tools for Stability of Switching Linear Systems: Gain Automata and Delay Compensation.

The topic of this paper is the analysis of stability for a class of switched linear systems, modeled by hybrid automata. In each location of the hybrid automaton the dynamics is assumed to be linear and asymptotically stable; the guards on the transitions are hyperplanes in the state space. For each location an estimate is made of the gain via a Lyapunov function for the dynamics in that location, given a pair of ingoing and outgoing transitions. It is shown how to obtain the best possible estimate by optimizing the Lyapunov function. The estimated gains are used in defining a so-called gain automaton that forms the basis of an algorithmic criterion for the stability of the hybrid automaton. The associated gain automaton provides a systematic tool to detect potential sources of instability as well as an indication on to how to stabilize the hybrid systems by requiring appropriate delays for specific transitions

A mollified Ensemble Kalman filter

It is well recognized that discontinuous analysis increments of sequential data assimilation systems, such as ensemble Kalman filters, might lead to spurious high frequency adjustment processes in the model dynamics. Various methods have been devised to continuously spread out the analysis increments over a fixed time interval centered about analysis time. Among these techniques are nudging and incremental analysis updates (IAU). Here we propose another alternative, which may be viewed as a hybrid of nudging and IAU and which arises naturally from a recently proposed continuous formulation of the ensemble Kalman analysis step. A new slow-fast extension of the popular Lorenz-96 model is introduced to demonstrate the properties of the proposed mollified ensemble Kalman filter.Comment: 16 pages, 6 figures. Minor revisions, added algorithmic summary and extended appendi

Recommender systems in industrial contexts

This thesis consists of four parts: - An analysis of the core functions and the prerequisites for recommender systems in an industrial context: we identify four core functions for recommendation systems: Help do Decide, Help to Compare, Help to Explore, Help to Discover. The implementation of these functions has implications for the choices at the heart of algorithmic recommender systems. - A state of the art, which deals with the main techniques used in automated recommendation system: the two most commonly used algorithmic methods, the K-Nearest-Neighbor methods (KNN) and the fast factorization methods are detailed. The state of the art presents also purely content-based methods, hybridization techniques, and the classical performance metrics used to evaluate the recommender systems. This state of the art then gives an overview of several systems, both from academia and industry (Amazon, Google ...). - An analysis of the performances and implications of a recommendation system developed during this thesis: this system, Reperio, is a hybrid recommender engine using KNN methods. We study the performance of the KNN methods, including the impact of similarity functions used. Then we study the performance of the KNN method in critical uses cases in cold start situation. - A methodology for analyzing the performance of recommender systems in industrial context: this methodology assesses the added value of algorithmic strategies and recommendation systems according to its core functions.Comment: version 3.30, May 201

Stability and robustness of planar switching linear systems

This paper presents a decision algorithm for the analysis of the stability of a class of planar switched linear systems, modeled by hybrid automata. The dynamics in each location of the hybrid automaton is assumed to be linear and asymptotically stable; the guards on the transitions are hyperplanes in the state space. We show that for every pair of an ingoing and an outgoing transition related to a location, the exact gain in the norm of the vector induced by the dynamics in that location can be computed. These exact gains are used in defining a gain automaton which forms the basis of an algorithmic criterion to determine if a planar hybrid automaton is stable or not

Finite Bisimulations of Controllable Linear Systems

Finite abstractions of infinite state models have been critical in enabling and applying formal and algorithmic verification methods to continuous and hybrid systems. This has triggered the study and characterization of classes of continuous dynamics which can be abstracted by finite transition systems. In this paper, we focus on synthesis rather than analysis. In this spirit, we show that given any discrete-time, linear control system satisfying a generic controllability property, and any finite set of observations restricted to the boolean algebra of Brunovsky sets, a finite bisimulation always exists and can be effectively computed

Algorithmic Verification of Continuous and Hybrid Systems

We provide a tutorial introduction to reachability computation, a class of computational techniques that exports verification technology toward continuous and hybrid systems. For open under-determined systems, this technique can sometimes replace an infinite number of simulations.Comment: In Proceedings INFINITY 2013, arXiv:1402.661

Computer Aided Verification

This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications