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Abstract: Evolutionary algorithms (EAs) refer to a broad class of optimization algorithms, which take some inspiration from evolutionary systems in the natural world. In recent years, a new class of EAs called estimation of distribution algorithms (EDAs) has emerged based on probabilistic modeling of the search space. Instances of EDAs include population based incremental learning (PBIL) algorithm. The PBIL algorithm is an easy to understand heuristic optimization technique that is inspired by the genetic algorithm and the competitive learning paradigm. PBIL includes many of the features from the genetic algorithm such as binary string representation, the notion of individuals, fitness measures and mutations. Contrary to the genetic algorithm it does not maintain a population of individuals but instead PBIL contains a probability vector. At each generation a new population of individuals is sampled according to the probabilities specified in the probability vector. The population is evaluated and the probability vector is updated by dragging it towards the best individual in the population. In recent years, the investigation of synchronization of chaotic systems has attracted much attention of researchers. Chaos synchronization has been applied in many fields such as secure communication, chemical, engineering, and biological systems, among others. This paper presents the synchronization of two identical discrete chaotic systems subject the different initial conditions by designing a proportional–integral–derivative (PID) controller. In addition, the tuning of the PID controller based on a modified PBIL algorithm using similarity analysis is also investigated in this paper. Simulation results show the good performance of the modified PBIL algorithm for synchronization of chaotic systems. [Copyright &y& Elsevier]

Abstract: Nowadays, a variety of controllers used in process industries are still of the proportional–integral–derivative (PID) types. PID controllers have the advantage of simple structure, good stability, and high reliability. A relevant issue for PID controllers design is the accurate and efficient tuning of parameters. In this context, several approaches have been reported in the literature for tuning the parameters of PID controllers using evolutionary algorithms, mainly for single-input single-output systems. The systematic design of multi-loop (or decentralized) PID control for multivariable processes to meet certain objectives simultaneously is still a challenging task. This paper proposes a new chaotic firefly algorithm approach based on Tinkerbell map (CFA) to tune multi-loop PID multivariable controllers. The firefly algorithm is a metaheuristic algorithm based on the idealized behavior of the flashing characteristics of fireflies. To validate the performance of the proposed PID control design, a multi-loop multivariable PID structure for a binary distillation column plant (Wood and Berry column model) and an industrial-scale polymerization reactor are taken. Simulation results indicate that a suitable set of PID parameters can be calculated by the proposed CFA. Besides, some comparison results of a genetic algorithm, a particle swarm optimization approach, traditional firefly algorithm, modified firefly algorithm, and the proposed CFA to tune multi-loop PID controllers are presented and discussed. [Copyright &y& Elsevier]

Abstract: This paper investigates a neuro-wavelet control (NWC) system to address the problem of synchronization control of uncertain chaotic systems. In this NWC system, a wavelet neural network (WNN) controller is the principal tracking controller designed to mimic the perfect control law and an auxiliary compensation controller is used to recover the residual approximation error so that the favorable synchronization can be achieved. Moreover, the proportional-integral (PI) training algorithms of the control system are derived from the Lyapunov stability theorem, which are utilized to update the adjustable parameters of WNN controller on-line for further assuring system stability and obtaining a fast convergence. In addition, to relax the requirement of unknown uncertainty bound, a bound estimation law is derived to estimate the uncertainty bound. Finally, some numerical simulations are presented to illustrate the effectiveness of the proposed control strategy. The simulation results demonstrate that the proposed NWC with PI training algorithms can synchronize the chaotic systems more accurately than the other control strategies. [Copyright &y& Elsevier]