Raffaele Iervolino

Cone-Copositive Piecewise Quadratic Lyapunov Functions for Conewise Linear Systems

In this technical note, cone-copositive piecewise quadratic Lyapunov functions (PWQ-LFs) for the stability analysis of conewise linear systems are proposed. The existence of a PWQ-LF is formulated as the feasibility of a cone-copositive programming problem which is represented in terms of linear matrix inequalities. A constructive procedure for its solution is provided. Examples show the effectiveness of the approach, also in the case of uncertain conewise linear systems.

Stability analysis of conewise linear systems with sliding modes

In this paper cone-copositive piecewise quadratic Lyapunov functions (PWQ-LFs) for the stability analysis of conewise linear systems with the possible presence of sliding modes are proposed. The existence of a PWQ-LF is formulated as the feasibility of a cone-copositive programming problem which is represented in terms of linear matrix inequalities with equality constraints. An algorithm for the construction of a PWQ-LF is provided. Examples show the effectiveness of the approach in the presence of stable and unstable sliding modes.

New Results on Robot Modeling and Simulation

In this paper the possibility of simulating the robot forward dynamics by making use of the inertia matrix and of the kinetic energy gradient only is demonstrated. Such method is shown to be simpler and numerically more efficient than the classical approaches. In the case of planar robots with revolute joints and link centers of mass belonging to the plane containing the rotating axes of the joints, theorems are formulated and demonstrated providing a relatively fast and simple method of calculation for both the inertia matrix and the gradient of the kinetic energy. This allows obtaining a simple and efficient tool to simulate practical robots with rigid links and can also be particularly useful for studying robots with flexible links. By using the proposed approach, the model of a practical planar robot, designed by the computer aided design software package CATIA™, is easily developed and implemented. The simulation results when the gradient of the kinetic energy is computed analytically versus numerically are compared to illustrate that the computational costs are relatively low and the accuracy is high.

Lyapunov stability for piecewise affine systems via cone-copositivity

Cone-copositive piecewise quadratic Lyapunov functions (PWQ-LFs) for the stability analysis of continuous-time piecewise affine (PWA) systems are proposed. The state space is assumed to be partitioned into a finite number of convex, possibly unbounded, polyhedra. Preliminary conditions on PWQ functions for their sign in the polyhedra and continuity over the common boundaries are provided. The sign of each quadratic function is studied by means of cone-constrained matrix inequalities which are translated into linear matrix inequalities (LMIs) via cone-copositivity. The continuity is guaranteed by adding equality constraints over the polyhedra intersections. An asymptotic stability result for PWA systems is then obtained by finding a continuous PWQ-LF through the solution of a set of constrained LMIs. The effectiveness of the proposed approach is shown by analyzing an opinion dynamics model and two saturating control systems.

Piecewise quadratic stability of consensus in heterogeneous opinion dynamics

A piecewise quadratic Lyapunov function approach for the consensus in heterogeneous opinion dynamics is proposed. The connections among the agents are influenced by different thresholds which characterize the heterogeneity of the network. The continuous-time opinion dynamics model is represented as a piecewise affine system with the state space partitioned into convex polyhedra defined by the agents influence functions. Conditions on piecewise quadratic functions for their sign in the polyhedra and continuity over the common boundaries are given. A sufficient condition for the local asymptotic stability, i.e., the consensus, is formulated as a set of LMIs whose solution provides a continuous piecewise quadratic Lyapunov function. Numerical results show the effectiveness of the proposed approach.

Coopetition and Cooperosity over Opinion Dynamics

In the heterogeneous Hegselmann–Krause (HK) opinion dynamics network, the existence of edges among the agents depend on different connectivity thresholds. A new version of this model is here presented, by using the notions of coopetition and cooperosity. Such concepts are defined by combining the representation of the cooperation, competition and generosity behaviours. The proposed HK model is recast as a piecewise linear system with the state space partitioned into convex polyhedra defined by the agents influence functions. A sufficient condition for the local asymptotic stability, i.e., the consensus, is formulated as a set of linear matrix inequalities whose solution provides a continuous piecewise quadratic Lyapunov function. Numerical results show the effectiveness of the proposed approach.

Trajectory tracking of a class of uncertain systems applied to vehicle platooning and antenna scanning systems

ABSTRACT The tracking problem is considered for a recurring class of systems, such as the Cartesian robots with real actuators, some transportation systems, and scanning devices used for medical and engineering applications. Some theorems are proved to design a PD type controller, with a possible compensation signal, in order to track sufficiently smooth trajectories with a prescribed maximum error. The developed design methodology is illustrated through two engineering examples. The first example concerns the safety distance control of an electric vehicles fleet. The second example deals with the identification of an antenna scanning system and the prototype design of a new controller that provides better performance than the current one.

Modeling, Simulation and Control of a 4WD Electric Vehicle with In-Wheel Motors

A relatively new technology for the electric vehicles considers the use of brushless permanent magnet motors directly connected to the car wheels (in-wheel motors or hub motors). In order to evaluate the performance that can be obtained, a complete dynamic model of a four-wheel drive (4WD) electric vehicle equipped with four in-wheel motors is developed and a correspondent parametric simulator is implemented in Matlab/SimulinkTM. The simulator is also employed for designing, testing and comparing various control logics which reproduce the handling behavior of a real vehicle.

A wearable device for sport performance analysis and monitoring

In this paper the use of a wearable device is considered in order to evaluate the performance of an athlete during her/his sport activities. The preliminary step consists of recording the motion variables at a sufficiently high sampling rate throughout the experimental campaign. The collected data are then elaborated by a PC-based application to identify the system dynamics and derive some synthetic performance indicators, by taking into account also the experience of the sport professionals. The extraction of the indicators is based on basic signal processing that can be implemented in algorithms run directly on the microcontroller unit (MCU) of the device. The key indicators values can be sent to other electronic devices by using one of the available wireless network connections at a reduced transmission rate. Some experimental data are also reported to illustrate the effectiveness of the approach.

A control oriented approach to the time-discretization of delay systems

There are many examples of systems with delays, mainly due to transport phenomena, to the information transmission, to the calculation time of the integration digital devices, and so on. These systems, being infinite dimensional, are very difficult to analyze and to control. If they are forced by piecewise constant signals in time ranges of appropriate constant amplitude, such systems can be modeled by finite dimensional discrete-time systems. In this paper, theorems are stated that allow discretizing an LTI system with state, input and output delays, with an appropriate sampling period. A method is also proposed for the design of reduced order discrete-time controllers that allow assigning a set of arbitrary poles to the overall system. The accuracy of the discrete-time models and the effectiveness of the proposed controllers are illustrated by two interesting examples.