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

Second-order sliding modes and soft computing techniques for fault detection

This paper outlines some results concerning the combined application of secondorder sliding-mode and soft-computing techniques in the framework of fault-detection problems. A method for estimating the discrete state of an LTI affine switched system is developed to that end. Simple controller/observer tuning formulas are constructively developed along the paper by Lyapunov analysis. Simulation and experimental results confirm the expected performance

Adaptive unit-vector law with time-varying gain for finite-time parameter estimation in LTI systems

A continuation of previous authors' work on adaptive parameter estimation for linear dynamical systems having irrational transfer function is presented in this work. An original modification of the gradient algorithm, inspired by the variable structure control techniques and additionally featuring a time-varying adaptation gain, is presented and analyzed using Lyapunov techniques. The exposition is illustrated by several numerical examples which illustrate the effectiveness of the proposed algorithm

Adaptive parameter estimation for infinite-dimensional LTI systems with finite-time convergence

A novel adaptive algorithm to address the on-line identification of constant uncertain parameters in linear timeinvariant dynamical systems is proposed. The approach can be applied to a broad class of linear dynamical processes including, e.g., delay systems, fractional-order systems, and distributedparameter systems. The proposed scheme takes advantage of a nonlinear adaptation rule inspired by the unit-vector variable-structure control strategy and provides the finite-time parameter estimation. Convergence properties of the algorithm are investigated through Lyapunov analysis, that constructively yields explicit convergence conditions which generalize the wellknown Persistence of Excitation (P.E.) and identifiability requirements arising in conventional adaptive estimation. The theoretical findings are substantiated by extensive simulation examples

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 system's 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

Pseudo-Recursive Trapezoidal Rule for the Numerical Solution of Linear Fractional Differential Equations

This paper presents an extension of the trapezoidal integration rule, that in the present work is applied to devise a pseudo-recursive numerical algorithm for the numerical evaluation of fractional-order integrals. The main benefit of pseudo recursive implementation arises in terms of higher accuracy when the algorithm is run in the "short memory" version. The rule is suitably generalized in order to build a numerical solver for a class of fractional differential equations. The algorithm is also specialized to derive an efficient numerical algorithm for the on-line implementation of linear fractional order controllers. The accuracy of the method is theoretically analyzed and its effectiveness is illustrated by simulation examples

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

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

Mechanism and Convergence Analysis of a Multi-Robot Swarm Approach Based on Natural Selection

The Darwinian Particle Swarm Optimization (DPSO) is an evolutionary algorithm that extends the Particle Swarm Optimization (PSO) using natural selection, or survival-of-the-fittest, to enhance the ability to escape from local optima. An extension of the DPSO to multi-robot applications has been recently proposed and denoted as Robotic Darwinian PSO (RDPSO), benefiting from the dynamical partitioning of the whole population of robots. Therefore, the RDPSO decreases the amount of required information exchange among robots, and is scalable to large populations of robots. This paper presents a stability analysis of the RDPSO to better understand the relationship between the algorithm parameters and the robot’s convergence. Moreover, the analysis of the RDPSO is further extended for real robot constraints (e.g., robot dynamics, obstacles and communication constraints) and experimental assessment with physical robots. The optimal parameters are evaluated in groups of physical robots and a larger population of simulated mobile robots for different target distributions within larger scenarios. Experimental results show that robots are able to converge regardless of the RDPSO parameters within the defined attraction domain. However, a more conservative parametrization presents a significant influence on the convergence time. To further evaluate the herein proposed approach, the RDPSO is further compared with four state-of-the-art swarm robotic alternatives under simulation. It is observed that the RDPSO algorithm provably converges to the optimal solution faster and more accurately than the other approaches.info:eu-repo/semantics/publishedVersio