Equivalence Of Nonlinear Systems To Prime Systems Under Generalized Output Transformations

. Within a linear algebraic framework, we present a new characterization of the class of nonlinear systems which are equivalent to a prime system. We then introduce a class of generalized output transformations that can be thought of as a generalization to the nonlinear setting of a unimodular transformation in the output space. Our main result gives necessary and sufficient conditions for equivalence to a prime system under a certain group of transformations that includes generalized output transformations. Key words. nonlinear systems, output transformation, prime systems, differential forms AMS subject classifications. 93C10, 93B17, 58A10 PII. S0363012996307060 1. Introduction. The problem of characterizing the class of linear systems that are equivalent to prime systems was first posed and solved by Morse [12]. The group of transformations considered in [12] included, besides state space change of coordinates and linear state feedback, output space change of coordinates. Marino,..

Non-Collision Conditions in Multi-Agent Virtual Leader-Based Formation Control

Formation control is one of the most important issues of group coordination for multi-agent robots systems. Some schemes are based on the leader-followers approach where some robots are considered as group leaders which influence the group behaviour. In this work, we address a formation strategy using a virtual leader which has communication with the rest of the follower robots, considered as omnidirectional robots. The virtual leader approach presents advantages such as analysis simplification and fewer sensing requirements in the control law implementation. The formation control is based on attractive potential functions only. The control law guarantees the convergence to the desired formation but, in principle, does not avoid inter-agent collisions. A set of necessary and sufficient non-collision conditions based on the explicit solution of the closed-loop system is derived. The conditions allow concluding from the initial conditions whether or not the agents will collide. The results are extended to the case of unicycle-type robots

Infinitesimal Brunovský form for nonlinear systems with applications to Dynamic Linearization

We define, in an infinite-dimensional differential geometric framework, the 'infinitesimal Brunovský form' which we previously introduced in another framework and link it with equivalence via diffeomorphism to a linear system, which is the same as linearizability by 'endogenous dynamic feedback'

Control mediante modos deslizantes en tiempo discreto para el seguimiento de trayectorias de un robot móvil1

Resumen: En este trabajo se presenta una estrategia de control en tiempo discreto para el seguimiento de trayectorias de un robot móvil tipo (2,0) controlado remotamente. La estrategia de control se desarrolló mediante un enfoque de modos deslizantes, considerando el modelo discreto exacto del vehículo en el cual se incluyen los efectos del retardo de transporte causado por la propagación de las señales sobre una red de comunicación. El esquema de control garantiza el seguimiento de trayectorias predeterminadas obteniéndose convergencia asintótica de los errores de seguimiento. La estrategia propuesta es evaluada mediante una serie de resultados por simulación. Palabras clave: Robot móvil, retardos de transporte, control en tiempo discreto, modos deslizante

Discretización exacta de un robot móvil con retardo de transporte

An exact discrete time model of a mobile robot of the type (2,0) that includes the time-delay induced by a communication network between the sensors and actuators on the mobile robot and the remote control system is presented. Simulations results are provided to show the performance of the proposed exact discrete time model. The performance of obtained model is better compared to the approximate model because it does not need a sampling period sufficiently small.En este trabajo se presenta la obtención del modelo exacto en tiempo discreto de un robot móvil tipo (2,0), bajo la consideración de la existencia de retardos de transporte en la señal de control, producidos por la propagación de las señales entre los sensores y actuadores del robot y el control remoto. El modelo obtenido es evaluado mediante simulación, comparando su desempeño con un modelo discreto aproximado que incluye también retardos de transporte y con el modelo en tiempo continuo del mismo sistema