Integration of Soft Computing and Fractional Derivatives in Adaptive Control

Realizing that generality and uniformity of the usual Soft Computing (SC) structures exclude the application of plausible simplifications relevant in the case of whole problem classes resulted in the idea that a novel branch of soft computing could be developed by the use of which far simpler and more lucid uniform structures and procedures could be applied than in the traditional ones. Such a novel approach to computational cybernetics akin to SC was developed at Budapest Tech to control inaccurately and incompletely modelled dynamic systems under external disturbances. Hydraulic servo valve controlled differential cylinders as non-linear, strongly coupled multivariable electromechanical tools serve as excellent paradigms of such difficulties. Their control has to cope with the problem of instabilities due to the friction forces between the piston and the cylinder, as well as with uncertainties and variation of the hydrodynamic parameters that makes it unrealistic to develop an accurate static model for them. In this paper a combination of this novel method with the use of fractional derivatives is applied for the control of a hydraulic differential cylinder. Simulation results well exemplifying the conclusions are also presented

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

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

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

Preliminary Sketch of Possible Fixed Point Transformations for Use in Adaptive Control

In this paper a further step towards a novel approach to adaptive nonlinear control developed at Budapest Tech in the past few years is reported. Its main advantage in comparison with the complicated Lyapunov function based techniques is that it is based on simple geometric considerations on the basis of which the control task can be formulated as a Fixed Point Problem for the solution of which a Contractive Mapping is created that generates an Iterative Cauchy Sequence for Single Input - Single Output (SISO) systems. Consequently it converges to the fixed point that is the solution of the control task. In the formerly developed approaches for monotone increasing or monotone decreasing systems the proper fixed points had only a finite basin of attraction outside of which the iteration might become divergent. The here sketched potential solutions apply a special function built up of the “response function” of the excited system under control and of a few parameters. This function has almost constant value apart from a finite region in which it has a “wrinkle” in the vicinity of the desired solution that is the “proper” fixed point of this function. By the use of an affine approximation of the response function around the solution it is shown that at one of its sides this fixed point is repulsive, while at the opposite side it is attractive. It is shown, too, that at the repulsive side another, so called “false” fixed point is present that is globally attractive, with the exception of the basin of attraction of the “proper” one. This structure is advantageous because a) no divergence can occur in the iteration, b) the convergence to the “false” value can easily be detected, and c) by using some ancillary tricks in the most of the cases the solution can be kicked from the wrong fixed point into the basin of attraction of the “proper one”. In the paper preliminary calculations are presented.N/

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