Parameter Estimation of Lorenz Chaotic System Based on a Hybrid Jaya-Powell Algorithm

Li Zhuang,Long Wang,Yonghong Zhong,Wengang Zheng,Longpeng Cao,Yong Wu,Lili Zhangzhong

doi:10.1109/access.2020.2968106

Abstract

Parameter estimation of Lorenz chaotic system using a novel hybrid Jaya-Powell algorithm is proposed in this paper. Since the nonlinear dynamic system is complex with multi-dimension parameters, estimating parameters of the system can be considered as a muti-objective optimization task. The proposed Jaya-Powell algorithm combines the Jaya and Powell algorithm to search for the relatively global optimum and local optimum respectively, which offers a more accurate and effective estimation. The searching strategy of the proposed algorithm facilitates the balance of the exploration and exploitation in the optimization procedure. Due to no algorithm-specific parameters are required in the Jaya and Powell algorithm, the proposed Jaya-Powell can avoid deliberate fine-tuning of corresponding parameters. To validate the accuracy and robustness of the proposed algorithm in parameter estimation, the simulation of Lorenz chaotic system and comparative experiments are conducted. Seven algorithms, including Jaya algorithm, Powell algorithm, Teaching-learning-based optimization (TLBO) algorithm, particle swarm optimization (PSO), genetic algorithm (GA), covariance matrix adaptation evolution strategy (CMA-ES), and cluster-chaotic-optimization algorithm (CCO), are considered as benchmarking algorithms in the comparison. The proposed hybrid Jaya-Powell algorithm outperforms seven benchmarking algorithms with the more accurate estimation and the relatively faster convergence. Based on the embedded system Raspberry pi 3, the proposed algorithm achieves the similar performance by comparing with the experiments conducted on the computer. The successful implementation via Raspberry pi 3 facilitates the application of the proposed algorithm in edge computing.

Highlights

As a prominent complex behavior in nonlinear dynamical systems, chaos has attracted much attention from researchers and been widely studied over the past three decades
In this paper, a novel hybrid algorithm combining Jaya algorithm and the Powell method named Jaya-Powell was proposed for parameter estimation of Lorenz chaotic system
The proposed hybrid algorithm focused on efficiently searching for a satisfactory solution via balancing the exploration and exploitation, which avoided to fall into the local optimum

Summary

INTRODUCTION

As a prominent complex behavior in nonlinear dynamical systems, chaos has attracted much attention from researchers and been widely studied over the past three decades. To achieve the feasibility in parameter estimation of chaotic systems, evolutionary computation based methods have been applied in this field and address parameter estimation as an optimization problem. Tao et al [11] applied genetic algorithm (GA) into parameter estimation of chaotic time series He et al [12] developed particle swarm optimization (PSO) to estimate parameters of chaos systems and achieved more accurate solutions by comparing with GA. Based on classical evolutionary computation algorithms, hybrid methods which combine two different evolutionary algorithms have been developed to obtain better estimation results. Jaya algorithm, a population-based method proposed by Rao [22] free of algorithm-specific parameters, is applied to optimize parameters of Lorenz chaotic system.

PROBLEM FORMULATION

POWELL METHOD

BENCHMARKING ALGORITHMS

CONCLUSION