Adaptive Optimal Dynamic Control for Nonholonomic Systems

In this paper two different control methods are combined for controlling a typical nonholonomic device (a bicycle) the dynamic model and parameters of which are only approximately known. Most of such devices suffer from the problem that the time-derivatives of the coordinates of their location and orientation cannot independently be set so an arbitrarily prescribed trajectory cannot precisely be traced by them. For tackling this difficulty Optimal Control is proposed that can find acceptable compromise between the tracking error of the various coordinates. Further problem is that the solution proposed by the optimal controller cannot exactly be implemented in the lack of precise information on the dynamic model of the system. Based on the decoupled nature of the dynamic model of the longitudinal and lateral behavior of the engine special fixed point transformations are proposed to achieve adaptive tracking. These transformations were formerly successfully applied for the control of holonomic systems. It is the first time that the combined method is checked for various trajectories and dynamic model errors via simulation. It yielded promising results

Modelling and Control of Freeway Traffic

This paper presents the most recent developments of the Simulator of Intelligent Transportation Systems (SITS). The SITS is based on a microscopic simulation approach to reproduce real traffic conditions in an urban or non-urban network. In order to analyse the quality of the microscopic traffic simulator SITS a benchmark test was performed. A dynamical analysis of several traffic phenomena, applying a new modelling formalism based on the embedding of statistics and Laplace transform, is then addressed. The paper presents also a new traffic control concept applied to a freeway traffic system

Approximating fractional derivatives through the generalized mean

This paper addresses the calculation of fractional order expressions through rational fractions. The article starts by analyzing the techniques adopted in the continuous to discrete time conversion. The problem is re-evaluated in an optimization perspective by tacking advantage of the degree of freedom provided by the generalized mean formula. The results demonstrate the superior performance of the new algorithm

Adaptive vibration damping based on casual time-invariant green-functions and fractional order derivates

In this paper a simple nonlinear, adaptive control using causal time-invariant Green-functions and fractional order derivatives is applied for damping the vibration of a car forced during passing along a bumpy road. Its key idea is the replacement of the integer order derivates in a Green-functions-based nonlinear controller with a time-shift invariant, causal approximation of the Riemann-Liouville fractional derivative that also behaves like a Green-function. Since its physical essence is rather frequency filtering than providing inter order derivatives in limit cases, the approximation applied numerically is quite convinent. In this way simple kinematic design of the desired damping becomes possible. The adaptive part of the controller guarantees the realization of this kinematic design without making it necessary for the designer to have accurate and complete dynamic model of the system to be controlled or to design a sophisticated linear "CRONE" controller that has to take the responsability for the unknown dynamics of the system. The applicability of the approach is illustrated via simulations for a paradigm that is a rough model of a car. It was found that both adaptivity and the use of fractional order derivatives in the control are essential parts of the success of the method.info:eu-repo/semantics/publishedVersio

Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms

This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms

Simple Geometric Approach of Identification and Control Using Floating Basis Vectors for Representation

As a plausible alternative of certain sophisticated soft computing approaches trying to identify complete and static system models, a simple adaptive controller is outlined that creates only a temporal model. This model can be built up and maintained step-by-step on the basis of slowly fading information by the use of simple updating rules consisting of finite algebraic steps of lucid geometric interpretation. The method may be used for filling in the lookup tables or rule bases of the above representations experimentally. The method is tested by the use of a simple dynamic system as a typical paradigm via simulation.N/

Improved Numerical Simulation for a Novel Adaptive Control Using Fractional Order Derivatives

A novel control technique is investigated in the adaptive control of a typical paradigm, an approximately and partially modeled cart plus double pendulum system. In contrast to the traditional approaches that try to build up ”complete” and ”permanent” system models it develops ”temporal” and ”partial” ones that are valid only in the actual dynamic environment of the system, that is only within some ”spatio-temporal vicinity” of the actual observations. This technique was investigated for various physical systems via ”preliminary” simulations integrating by the simplest 1st order finite element approach for the time domain. In 2004 INRIA issued its SCILAB 3.0 and its improved numerical simulation tool ”Scicos” making it possible to generate ”professional”, ”convenient”, and accurate simulations. The basic principles of the adaptive control, the typical tools available in Scicos, and others developed by the authors, as well as the improved simulation results and conclusions are presented in the contribution

Fractional Dynamics and Control of Distributed Parameter Systems

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses a FC perspective in the study of the dynamics and control of some distributed parameter systems

Simple Kinematic Design for Evading the Forced Oscillation of a Car-Wheel Suspension System

An adaptive control damping the forced vibration of a car while passing along a bumpy road is investigated. It is based on a simple kinematic description of the desired behavior of the damped system. A modified PID controller containing an approximation of Caputo’s fractional derivative suppresses the high-frequency components related to the bumps and dips, while the low frequency part of passing hills/valleys are strictly traced. Neither a complete dynamic model of the car nor ’a priori’ information on the surface of the road is needed. The adaptive control realizes this kinematic design in spite of the existence of dynamically coupled, excitable internal degrees of freedom. The method is investigated via Scicos-based simulation in the case of a paradigm. It was found that both adaptivity and fractional order derivatives are essential parts of the control that can keep the vibration of the load at bay without directly controlling its motion

Scicos Based Investigation of an Adaptive Vibration Damping Technique Using Fractional Order Derivatives

Detailed investigation of a simple nonlinear, active, adaptive approach of controlling the oscillation of a car proceeding on a bumpy road is presented. Its key idea is a frequency dependent control of the strictness of a traditional PID controller by applying fractional order derivatives in a simple kinematic design without any respect to the dynamic model of the system. The adaptive part of the controller relieves the designer of dealing with the system’s dynamics within the frames of some linear control, and guarantees the implementation of this design. The operation of the approach is illustrated by the use of INRIA’s scientific co-simulator Scicos for a rough model of a car. Well interpretable trends were revealed regarding the effect of the variation of the order of derivation, and that of the sampling time of the adaptive loop. These results seem to be promising for actively damping the vibration of systems having unmodeled, uncontrolled internal degrees of freedom.N/