Adaptive Synchronization of Uncertain Fractional-order Chaotic Systems Based on Projective Method
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摘要: 針對(duì)一類(lèi)具有未知參數(shù)、未知非線(xiàn)性函數(shù)及外部擾動(dòng)的分?jǐn)?shù)階混沌系統(tǒng)，基于分?jǐn)?shù)階系統(tǒng)穩(wěn)定性理論和Lyapunov穩(wěn)定性理論，該文提出一種基于滑模自適應(yīng)和投影法的同步控制策略。首先選取一類(lèi)穩(wěn)定的分?jǐn)?shù)階積分滑模面，運(yùn)用自適應(yīng)技術(shù)對(duì)不確定項(xiàng)進(jìn)行估計(jì)，設(shè)計(jì)了同步控制器。然后對(duì)自適應(yīng)設(shè)計(jì)中容易出現(xiàn)的增長(zhǎng)型自適應(yīng)律運(yùn)用投影法進(jìn)行修正，以保證參數(shù)有界，從而也保證控制輸入有界。最后數(shù)值仿真證明了所設(shè)計(jì)控制器的正確性和有效性。
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關(guān)鍵詞:
- 分?jǐn)?shù)階混沌系統(tǒng) /
- 滑模自適應(yīng)控制 /
- 投影法 /
- 參數(shù)有界
Abstract: Based on the stability theory of fractional-order system and Lyapunov stability theory, and using the sliding mode adaptive control and projective method, a synchronization control strategy is proposed for a class of fractional-order chaotic systems with uncertain parameters, uncertain nonlinear functions and external disturbances. A stable fractional-order integral sliding surface is selected and the adaptive laws are designed to estimate the uncertainties, consequently, the synchronization controller is obtained. Then, the projective method is introduced to modify above basic adaptive laws to prevent the adaptive parameters from diverging to infinite, thus, the boundedness of the control inputs is guaranteed. Finally, the numerical simulation result is presented to show the effectiveness and applicability of the proposed control strategy. -
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