Milan R. Rapaić

Time-varying PSO -- convergence analysis, convergence-related parameterization and new parameter adjustment schemes

In this paper, a formal convergence analysis of the conventional PSO algorithms with time-varying parameters is presented. Based on this analysis, a new convergence-related parametric model for the conventional PSO is introduced. Finally, several new schemes for parameter adjustment, providing significant performance benefits, are introduced. Performance of these schemes is empirically compared to conventional PSO algorithms on a set of selected benchmarks. The tests prove effectiveness of the newly introduced schemes, especially regarding their ability to efficiently explore the search space.

Generalized particle swarm optimization algorithm - Theoretical and empirical analysis with application in fault detection

A generalization of the particle swarm optimization (PSO) algorithm is presented in this paper. The novel optimizer, the Generalized PSO (GPSO), is inspired by linear control theory. It enables direct control over the key aspects of particle dynamics during the optimization process. A detailed theoretical and empirical analysis is presented, and parameter-tuning schemes are proposed. GPSO is compared to the classical PSO and genetic algorithm (GA) on a set of benchmark problems. The results clearly demonstrate the effectiveness of the proposed algorithm. Finally, an application of the GPSO algorithm to the fine-tuning of the support vector machines classifier for electrical machines fault detection is presented.

Variable-Order Fractional Operators for Adaptive Order and Parameter Estimation

Adaptive parameter estimation schemes for linear fractional-order processes of commensurate type are illustrated in the present note. A gradient-based scheme for commensurate order estimation is outlined first, and a combined gradient/least-squares scheme for simultaneously estimating the commensurate order and the remaining process parameters is finally considered. A key feature of the proposed schemes is the utilization of appropriate variable-order fractional filters. Theoretical results are validated by means of thoroughly discussed simulation examples.

Second-order sliding mode approaches to disturbance estimation and fault detection in fractional-order systems

Abstract This paper outlines some results concerning the application of second-order sliding-mode techniques to address estimation and fault detection problems involving fractional order (FO) dynamics. Perturbed and switched FO systems are dealt with throughout the paper. Simple tuning formulas for the suggested schemes are constructively developed along the paper by means of appropriate Lyapunov analysis. Simulation and experimental results confirm the expected performance.

A nonlinear two compartmental fractional derivative model

This study presents a new nonlinear two compartmental model and its application to the evaluation of valproic acid (VPA) pharmacokinetics in human volunteers after oral administration. We have used literature VPA concentrations. In the model, the integer order derivatives are replaced by derivatives of real order often called fractional order derivatives. Physically that means that the history (memory) of a biological process, realized as a transfer from one compartment to another, is taken into account with the mass balance conservation observed. Our contribution is the analysis of a specific nonlinear two compartmental model with the application in evaluation of VPA pharmacokinetics. The agreement of the values predicted by the proposed model with the values obtained through experiments is shown to be good. Thus, pharmacokinetics of VPA after oral application can be described well by a nonlinear two compartmental model with fractional derivatives of the same order proposed here. Parameters in the model are determined by the least-squares method and the particle swarm optimization (PSO) numerical procedure is used. The results show that the nonlinear fractional order two compartmental model for VPA pharmacokinetics is superior in comparison to the classical (integer order) linear two compartmental model and to the linear fractional order two compartmental model.

On-line adaptive clustering for process monitoring and fault detection

An adaptive clustering procedure specifically designed for process monitoring, fault detection and isolation is presented in this paper. The key feature of the proposed procedure can be identified as its underlying capability to detect novelties in the systems mode of operation and, thus, to identify previously unseen functioning modes of the process. Once a novelty is detected, relevant informations are used to enrich the knowledge-base of the algorithm and as a result the proposed clustering procedure evolves and learns the new features of the monitored process in accordance with the available process data. The suggested clustering procedure is theoretically illustrated and its effectiveness has been investigated experimentally. Particularly, the on-line implementation of the algorithm and its integration with a fault detection expert system have been considered by making reference to a pneumatic process.

Original articles: Discontinuous dynamical systems for fault detection. A unified approach including fractional and integer order dynamics

This paper considers a discontinuous dynamical observers stack and presents its possible application in the framework of fault detection and isolation (FDI) problems. Non-standard forms for the discontinuous observer injection signals, based on second-order sliding-mode techniques with dynamical sliding manifolds, are employed in the present work. A unified treatment covering at the same time integer-order and fractional-order (FO) dynamics is developed. Appropriate non-smooth Lyapunov analysis is made to support the theoretical properties of the suggested FDI observers, which yields simple tuning formulas for the corresponding parameters. Numerical implementation aspects are discussed. Finally, simulation and experimental results are presented to support the theoretical treatment, which confirm the expected performance.

Nonlinear fractional PI control of a class of fractional-order systems

Abstract This paper deals with the design of nonlinear PI control techniques for regulating a class of fractional-order dynamics governed by a commensurate-order model, possibly nonlinear, perturbed by an external disturbance. The suggested control algorithm is the combination between a fractional-order PI controller and a nonlinear robust version of it, namely a second-order sliding mode control algorithm called “super-twisting” controller in the literature. A key feature of the approach is the use of ad-hoc sliding manifolds whose construction involves fractional order derivatives. A constructive Lyapunov based synthesis is illustrated, which leads to simple tuning rules for the controller parameters guaranteeing the asymptotic rejection of the external disturbance under appropriate smoothness restrictions. Computer simulations illustrate the effectiveness of the proposed technique.

Analysis and shaping of the self-sustained oscillations in relay controlled fractional-order systems

This work deals with Single-Input-Single-Output (SISO) fractional order systems with a discontinuous relay control element in the feedback loop. Stable self-sustained oscillations often occur in the closed loop relay system, and this work takes advantage of Describing Function (DF) analysis and of another more accurate approach, called Locus of a Perturbed Relay System (LPRS) method, for analyzing in the frequency domain the characteristics of the limit cycle oscillations. The use of fractional lead compensator is also suggested for the purpose of shaping the characteristics of the limit cycle. The proposed analysis and design procedures will be supported by thoroughly discussed simulation examples.

Trapezoidal rule for numerical evaluation of fractional order integrals with applications to simulation and identification of fractional order systems

This paper presents an extension of the well-known trapezoidal (bilinear) integration rule, that in the present work is applied to the numerical evaluation of fractional-order integrals. Particularly, this approximation is exploited to derive viable numerical algorithms addressing two distinct problems: i) simulation of Linear Time-Invariant (LTI) Commensurate Fractional Order Systems (CFOS); ii) non-recursive parameter estimation in LTI-CFOS. More precisely, the problem of non-recursive parameter estimation is addressed in two different scenarios. The first one is when the commensurate order of the CFOS is known in advance, while the second, more general, one is that in which the commensurate order is unknown and is to be estimated. The effectiveness of the proposed methods is illustrated by numerical examples.