Rodrigo H. Ordóñez-Hurtado

Finding common quadratic Lyapunov functions for switched linear systems using particle swarm optimisation

It is undoubtedly important to be able to ensure the existence of a common quadratic Lyapunov function (CQLF) for a given switched system because this is proof of its asymptotic stability, but equally important is the ability to calculate it in order to obtain more specific information about the behaviour of the switched system under analysis. This article describes the development of a new methodology for calculating a CQLF based on particle swarm optimisation (PSO) once the existence of a CQLF has been assured. Several comparative analyses are presented to show the strengths and advantages of the proposed methodology.

A method for determining the non-existence of a common quadratic Lyapunov function for switched linear systems based on particle swarm optimisation

The existence of a common quadratic Lyapunov function (CQLF) for a switched linear system guarantees its global asymptotic stability. Even if progress in finding the conditions for the existence/non-existence of a CQLF is significant, especially in switched linear systems consisting of N second-order systems or two systems of order n, the general case of N systems of order n still remains open. In this article, a sufficient condition for the non-existence of a CQLF for N systems of order n is derived. Based on the condition, a new method for determining the non-existence of a CQLF, using particle swarm optimisation, was designed and is described. Examples illustrating the proposed method are introduced at the end of this article.

Intelligent Speed Advising Based on Cooperative Traffic Scenario Determination

A novel system for safe speed recommendation, based on a cooperative method for vehicular density estimation and on the intelligent determination of the traffic scenario, is presented.

A Distributed and Privacy-Aware Speed Advisory System for Optimizing Conventional and Electric Vehicle Networks

One of the key ideas to make intelligent transportation systems work effectively is to deploy advanced communication and cooperative control technologies among vehicles and road infrastructures. In this spirit, we propose a consensus-based distributed speed advisory system that optimally determines a recommended common speed for a given area in order that the group emissions, or group battery consumptions, are minimized. Our algorithms achieve this in a privacy-aware manner; that is, individual vehicles do not reveal in-vehicle information to other vehicles or to infrastructure. A mobility simulator is used to illustrate the efficacy of the algorithm, and hardware-in-the-loop tests involving a real vehicle are given to illustrate user acceptability and ease of deployment.

On interconnected systems, passivity and some generalisations

A sufficient condition for the stability of large-scale interconnections of N linear time-variant systems is presented. Such a condition represents important extensions to passivity criteria and ensures stability by means of the existence of a positive definite (full-block) matrix P which is a common solution to Lyapunov equations involving a diagonal stacking of the N systems and the interconnection structure matrix. An experimental methodology for the verification of the sufficient condition also is proposed, based on evolutionary computation techniques. Applications of the new stability results are provided through illustrative examples, which are developed using particle swarm optimisation and genetic algorithms.

Characterising discrete-time linear systems with the “mixed” positive real and bounded real property☆

Abstract In this paper, we present characterisations of linear, shift-invariant, discrete-time systems that exhibit mixtures of small gain-type properties and positive real-type behaviours in a certain manner. These “mixed” systems are already fairly well characterised in the continuous-time domain, but the widespread adoption of digital controllers makes it necessary to verify whether commonly used discretisation procedures preserve the characteristic of “mixedness”. First, we analyse the effects of classical discretisation methods on the “mixed” property using Nyquist methods. A frequency domain feedback stability result is then presented. Finally, we develop a spectral-based characterisation of “mixed” discrete-time systems which provides a practical computational test that can also be applied to the MIMO case. Several examples validate the developed theory.

Evaluation of a new intelligent speed advisory system using hardware-in-the-loop simulation

In this paper we present a recently developed speed advisory system for ITS applications. A real vehicle embedded in a large scale SUMO simulation is used to demonstrate the efficacy of such a system.

A Methodology for Determining the Non-existence of Common Quadratic Lyapunov Functions for Pairs of Stable Systems

The existence of a common quadratic Lyapunov function (CQLF) for a switched linear system guarantees its global asymptotic stability. Although the progress in finding conditions for existence/non-existence of a CQLF has been significant in the last years, especially in switched linear systems with N subsystems of second order or two non-arbitrary subsystems of order n, the general case of N systems of order n still remains open. In this paper, based on a sufficient condition for the nonexistence of a CQLF for a pair of general subsystems of order n obtained from a lemma by Shorten et al., a new method for determining the non-existence of a CQLF, using Particle Swarm Optimization, is designed. A example illustrating the proposed method is introduced towards the end of the paper.

Using stationary vehicles to enhance cooperative positioning in Vehicular Ad-hoc Networks

A new approach to enhance Cooperative Positioning (CP) in Vehicular Ad-hoc Networks (VANETs) using stationary vehicles is presented. Tests using SUMO simulations show some preliminary benefits of the approach.

Design of adaptive laws for discrete-time systems based on Particle Swarm Optimization

A wide variety of linear/nonlinear adaptive systems in continuous/discrete time can be represented by error models, thus facilitating their analysis. The solution obtained for a given error model can be applied to different systems represented by the error model. This paper presents a methodology for adjusting the parameters of a discrete-time adaptive system represented by a Type 1 Error Model, which is based on Particle Swarm Optimization (PSO) and that allows using it in on-line applications. The performance of the proposed methodology is compared with the traditional gradient and least squares methods through simulations.