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

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

A graph theoretic approach to input-to-state stability of switched systems

This article deals with input-to-state stability (ISS) of discrete-time switched systems. Given a family of nonlinear systems with exogenous inputs, we present a class of switching signals under which the resulting switched system is ISS. We allow non-ISS systems in the family and our analysis involves graph-theoretic arguments. A weighted digraph is associated to the switched system, and a switching signal is expressed as an infinite walk on this digraph, both in a natural way. Our class of stabilizing switching signals (infinite walks) is periodic in nature and affords simple algorithmic construction.Comment: 14 pages, 1 figur

Global controllability tests for geometric hybrid control systems

Hybrid systems are characterized by having an interaction between continuous dynamics and discrete events. The contribution of this paper is to provide hybrid systems with a novel geometric formulation so that controls can be added. Using this framework we describe some new global controllability tests for hybrid control systems exploiting the geometry and the topology of the set of jump points, where the instantaneous change of dynamics take place. Controllability is understood as the existence of a feasible trajectory for the system joining any two given points. As a result we describe examples where none of the continuous control systems are controllable, but the associated hybrid system is controllable because of the characteristics of the jump set.Comment: 27 pages, 5 figure

A Family of Iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control

This paper introduces a family of iterative algorithms for unconstrained nonlinear optimal control. We generalize the well-known iLQR algorithm to different multiple-shooting variants, combining advantages like straight-forward initialization and a closed-loop forward integration. All algorithms have similar computational complexity, i.e. linear complexity in the time horizon, and can be derived in the same computational framework. We compare the full-step variants of our algorithms and present several simulation examples, including a high-dimensional underactuated robot subject to contact switches. Simulation results show that our multiple-shooting algorithms can achieve faster convergence, better local contraction rates and much shorter runtimes than classical iLQR, which makes them a superior choice for nonlinear model predictive control applications.Comment: 8 page

Coordinating views for data visualisation and algorithmic profiling

A number of researchers have designed visualisation systems that consist of multiple components, through which data and interaction commands flow. Such multistage (hybrid) models can be used to reduce algorithmic complexity, and to open up intermediate stages of algorithms for inspection and steering. In this paper, we present work on aiding the developer and the user of such algorithms through the application of interactive visualisation techniques. We present a set of tools designed to profile the performance of other visualisation components, and provide further functionality for the exploration of high dimensional data sets. Case studies are provided, illustrating the application of the profiling modules to a number of data sets. Through this work we are exploring ways in which techniques traditionally used to prepare for visualisation runs, and to retrospectively analyse them, can find new uses within the context of a multi-component visualisation system