Outline
- Abstract
- 1. Introduction
- 2. Preliminaries on Fractional Calculus
- 3. the Example Systems Description
- 3.1. the Fractional Order Energy Resources Demand–supply System
- 3.2. the Fractional Order Chen System
- 4. Neuro-Fuzzy Network Estimator
- 5. Problem Formulation and the Proposed Hybrid Adaptive Intelligent Controller Design
- 6. Simulation Results
- 7. Conclusions
- References
رئوس مطالب
- چکیده
- 1. مقدمه
- 2. اصول اولیه در مورد محاسبه های کسری
- 3. توصیف سیستم های نمونه
- 4. تخمین زننده های شبکه ای عصبی فازی
- 5. فرمولاسیون مسئله و طراحی کنترل کننده هوشمند وقفی ترکیبی پیشنهاد شده
- 6. نتایج شبیه سازی ها
- 7. جمع بندی
Abstract
This paper precedes chaos control of fractional-order chaotic systems in presence of uncertainty and external disturbances. Based on some basic properties on fractional calculus and the stability theorems, we present a hybrid adaptive intelligent backstepping-sliding mode controller (FAIBSMC) for the finite-time control of such systems. The FAIBSMC is proposed based on the concept of active control technique. The asymptotic stability of the controller is shown based on Lyapunov theorem and the finite time reaching to the sliding surfaces is also proved. Illustrative and comparative examples and simulation results are given to confirm the effectiveness of the proposed procedure, which consent well with the analytical results.
Conclusions
In this paper, in order for stabilization of the fractional uncertain chaotic systems, a novel hybrid fractional-order robust adaptive intelligent control scheme which is comprised of sliding mode control, backstepping control, adaptive control, and neuro-fuzzy network is proposed. An SMC law has been synthesized to guarantee the reachability of the specified sliding surface. The neuro-fuzzy network is employed to estimate the unknown continuous function. To cope with lumped uncertainties generated by NFN approximation errors and extra disturbances a robust structure with adaptive gains is used which on-line adaptive laws of the control system are derived based on the Lyapunov stability theorem so that the global asymptotic stability of the dynamical system can be achieved. Furthermore, the finite reaching time to the sliding surfaces has been proved. As some examples, the proposed technique is applied to control the energy resources demand–supply fractional order chaotic system and Chen fractional order chaotic system, these examples demonstrate the validity, effectiveness and good performance of the proposed FAIBSMC method. Based on the formulations, presented approach can be applied for stabilization for a large class of fractional uncertain chaotic systems with unknown system dynamics.