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Policy-based computing is one of the software and knowledge engineering methods (along with Artificial Neural Networks, Fuzzy Logic, etc.) that allows incorporating a specified expert knowledge into various kind of decision making processes. In this paper a preliminary study is undertaken in order to determine applicability of this technology supported by selected trend analysis methods for the problem...
The paper presents a comparative analysis of extended horizon model predictive control deployed for two various state prediction algorithms designed for discrete-time fractional-order state space systems. The first one is a finite fractional difference state predictor derived on the basis of a finite-length approximation of the fractional-order state space system. The second one is a BTA-based integer-order...
In this paper, controversial views on the use of an integer- and fractional-order derivatives in the theory and practice of electric circuits are discussed. Maxwell's equations are definitely useful in classical circuit analyses but empirical, fractional-order modeling is advocated in specific applications, including an exemplary supercapacitor charging circuit. Thus, both methodologies can be employed...
This paper presents new results in simulation analysis of Al-Alaloui-based discretization scheme for fractional-order derivative. The analysis is performed both in frequency and time domains. A series of simulation analyses provide to formulation of some implementation highlights related to approximation of fractional-order derivative with the Al-Alaloui operator.
This paper introduces a method for modeling and identification of a simple dynamical system described by fractional-order differential equation. The Grünwald-Letnikov fractional-order derivative is approximated by a discrete-time Laguerre-based model, giving rise to a new discrete-time integerorder equation modeling the considered system. An application example involves a supercapacitor charging circuit...
This paper presents a new method for modeling and identification of a simple electric circuit described by fractional-order differential equation. The Grunwald-Letnikov fractional-order derivative is approximated by its effective discrete-time model based on Laguerre filters, giving rise to a new discrete-time integer-order equation modeling the considered electric circuit. High accuracy of modeling...
In this paper, a Grünwald-Letnikov-originated fractional-order difference (FD) is modeled with finite-length approximators called a finite fractional difference (FFD) and a normalized finite fractional difference (NFFD), whose time-domain structure enables their effective employment in the prediction process for linear discrete-time fractional-order state-space systems. The main, original contribution...
This paper presents a general, modified framework for various time-domain approximations to the Grünwald-Letnikov fractional difference, namely finite fractional and Laguerre-based differences. The approximations are applied in the modeling problem for linear fractional-order state space systems, with two different implementation schemes presented.
This paper presents a new implementable strategy for modeling and identification of a fractional-order discrete-time nonlinear block-oriented SISO Wiener system. The concept of modeling of a linear dynamics by means of orthonormal basis functions (OBF) is employed to separate linear and nonlinear submodels, which enables a linear regression formulation of the parameter estimation problem. Finally,...
This paper presents new results in the reduction of a steady-state error in modeling of the Grünwald-Letnikov (GL) discrete-time fractional difference by means of discrete-time Laguerre filters. A discussion of various approximation criteria contributes to the steady-state accuracy problem. The paper is culminated with the presentation of finite fractional/Laguerre-based difference (FFLD), whose excellent...
This paper presents a new simple form of a polynomial matrix σ-inverse introduced as a result of research works on minimum variance control (MVC) for LTI MIMO nonsquare systems. A new approach to construction of a σ-inverse of a nonsquare polynomial matrix can result in e.g. pole-free design of MVC, which is provided by specially selected degrees of freedom of the σ-inverse. A simulation example in...
This paper presents a new concept of modeling of LTI SISO discrete-time fractional-order systems, in which the Laguerre filters are employed to model both 1) the Grünwald-Letnikov fractional difference and 2) a dynamics of the LTI SISO fractional-order system. Such a ‘double-Laguerre’ concept yields original accuracy and computational results at both modeling stages, illustrated with a series of simulation...
Normalized finite fractional differences are considered as an approximation to the Grunwald-Letnikov fractional difference. In particular, adaptive finite fractional difference (AFFD) is recalled and effectively modified by the introduction of a time-varying forgetting factor. The modified AFFD is shown in simulations to provide an excellent approximation performance, both in terms of the modeling...
This paper presents new results in finite-memory modeling of a discrete-time fractional derivative. The introduced normalized finite fractional derivative is shown to properly approximate its fractional derivative original, in particular in terms of the steady-state properties. A stability analysis is also presented as well as a recursive computation algorithm is offered for finite fractional derivatives.
This paper presents a comparison of five algorithms used to control acyclic traffic lights at intersections of roads in an urban road network. The following algorithms are selected: Most Cars characterized by low computational complexity, the author's algorithm called In-and-Outbound Lane Control, which is an efficient modification of the Most Cars, Local Hill-Climbing algorithm (LHC), the reinforcement...
This paper presents (structurally stable) pole-free control designs for (a deterministic version of) generalized minimum variance control and linear quadratic regulation for nonsquare LTI MIMO systems. For both discrete-time control strategies, two alternative approaches are offered, the numerical one related with limiting control solutions as control weighting matrices tend to the zero ones and the...
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