ADAPTIVE CONTROL BASED ON THE APPLICATION OF A SIMPLIFIED UNIFORM STRUCTURES AND LEARNING PROCEDURES

The present state of creating a new branch of Soft Computing (SC) for particular problem classes, possibly wider than the control of mechanical systems, is reported in this article. Like "traditional" SC il evades the development of analytical system models, and uses uniform structures, but these structures originate from various Lie groups. The advantages are a drastic reduction in size and an increase in lucidity. The generally "stochastic or semistochastic" "learning" or parameter tuning seems to be replaceable by simple explicit algebraic procedures of limited steps, too. The idea originated from mechanical systems\u27 control while considering their general internal symmetry group, and later it was further developed by using specific general features of it on a much wider scale. Convergence considerations are given for MIMO and SISO systems, too. Simulation examples are presented for the control of the inverted pendulum with the use of the Generalized Lorentzian Matrices. It is concluded that the me/hod is promising and probably imposes acceptable convergence requirements in many cases

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

Application of Luenberger's observer in RFPT-based adaptive control - 2014; A case study

The traditional way of thinking in controller design prefers the use of the “state space representation” introduced by R. Kalman in the early sixties of the past century. This system description is in close relationship with linear or at least partly linear system in which the linear part can be used in forming a quadratic Lyapunov function in the stability proof. In the standard model of such systems it is assumed that the state of the system is not directly observable, only certain linear functions of the state variable are directly measurable. Since such approaches introduce certain feedback gains for the state variable, observers are needed that calculate the estimation of the state variable on the basis of directly measurable quantities. The Luenberger observers solve this task via introducing a differential equation for the estimated state. In order to avoid the mathematical difficulties of Lya- punov’s “direct method” the “ Robust Fixed Point Transforma- tions (RFPT) ” were introduced in a novel adaptive technique that instead of the state space representation directly utilized the available approximate model of the system to estimate its “response function”. In this approach it was assumed that the system’s response is directly observable and an iterative sequence was generated by the use of “ Banach’s Fixed Point Theorem ” that converged to an appropriate deformation of the rough initial model to obtain precise trajectory tracking. In the present paper it is shown that the Luenberger observers and the RFPT-based mathod can be combined in a more con- ventional approach of the adaptive controllers that are designed on the basis of finding appropriate feedback gains. Illustrative simulation examples are presented to substantiate this statement

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