趙麗萍 樓旭陽
摘 要:文章利用神經(jīng)動態(tài)優(yōu)化方法研究離散時滯系統(tǒng)預(yù)測控制問題,首先將離散時滯系統(tǒng)的模型預(yù)測控制問題轉(zhuǎn)化為帶約束的優(yōu)化問題,再采用梯度神經(jīng)網(wǎng)絡(luò)進行在線求解。該神經(jīng)網(wǎng)絡(luò)具有較少的狀態(tài)變量,結(jié)構(gòu)簡單,優(yōu)化速度快,能夠有效的解決帶有約束的規(guī)劃問題。仿真結(jié)果表明該神經(jīng)動態(tài)優(yōu)化方法可提高模型預(yù)測控制的在線計算能力。
關(guān)鍵詞:離散時滯系統(tǒng);梯度神經(jīng)網(wǎng)絡(luò);模型預(yù)測控制
中圖分類號:TP273 文獻標志碼:A 文章編號:2095-2945(2018)13-0025-04
Abstract: In this paper, the neural dynamic optimization method is used to study the predictive control problem for discrete time-delay systems. Firstly, the model predictive control problem for discrete time-delay systems is transformed into an optimization problem with constraints, and then the gradient neural network is used to solve the problem online. The neural network has fewer state variables, simple structure as well as fast optimization speed, and can effectively solve the programming problem with constraints. The simulation results show that the neural dynamic optimization method can improve the on-line computing ability of the model predictive control.
Keywords: discrete time-delay systems; gradient neural networks; model predictive control
1 概述
模型預(yù)測控制(Model Predictive Control,簡稱MPC)是一種基于預(yù)測模型的,在有限的時間內(nèi)彌補現(xiàn)代控制理論最優(yōu)控制缺點的閉環(huán)計算機控制算法。MPC主要有預(yù)測模型、滾動優(yōu)化和反饋校正三個部分,預(yù)測模型主要是利用當前信息對未來輸出做出預(yù)測,滾動優(yōu)化則主要是隨時間在線優(yōu)化,使預(yù)測輸出與給定的期望輸出接近,然后通過反饋校正,使預(yù)測輸出達到最佳。自20世紀70年代以來,模型預(yù)測控制在工業(yè)過程中已得到廣泛應(yīng)用[1-3],顯現(xiàn)出其優(yōu)于經(jīng)典控制解決多變量、有約束工業(yè)過程控制問題的性能。
早期的模型預(yù)測控制研究中,系統(tǒng)模型大都是線性的,而大多數(shù)工業(yè)過程都是非線性的,因此盡管MPC在國內(nèi)外工業(yè)應(yīng)用中取得了廣泛應(yīng)用,在作為解決當前社會的約束優(yōu)化問題時,仍存在不足。從已有算法來看,由于最終求解的優(yōu)化問題包含模型和約束條件,求解過程中需要重復(fù)迭代,因此使得模型預(yù)測控制具有較大的在線計算量和較長的計算時間,限制了模型預(yù)測控制的實際應(yīng)用范圍。在應(yīng)用對象方面,主要還是應(yīng)用于線性和弱非線性系統(tǒng),對于強非線性系統(tǒng),用一個近似線性模型去逼近可能會導(dǎo)致控制性能的惡化,而目前對非線性的建模還比較困難。從應(yīng)用方式看,由于現(xiàn)實物理條件約束的存在,我們目前還是很難得到精確的優(yōu)化問題的解析式。因此,模型預(yù)測控制在優(yōu)化問題還有很多限制,加大對模型預(yù)測控制在線優(yōu)化的研究仍具有重要意義。
常規(guī)的控制理論研究需要預(yù)先知道被控對象的數(shù)學模型,而實際研究工業(yè)對象具有不確定性、時變性和非線性等特征。神經(jīng)網(wǎng)絡(luò)是一種黑箱建模方法,作為非線性系統(tǒng)建模的有力工具,可以以任意精度逼近任意非線性函數(shù)。此外,人工神經(jīng)網(wǎng)絡(luò)由大量神經(jīng)元組成,在處理問題時可以以分布式進行并行操作,不隨優(yōu)化問題維數(shù)的增加而降低處理速度,并且人工神經(jīng)網(wǎng)絡(luò)在硬件上可以實現(xiàn),較大的提高了優(yōu)化速度,因此是一個很有前景的優(yōu)化工具。Hopfield和Tank首先提出了Hopfield遞歸神經(jīng)網(wǎng)絡(luò)模型并解決了旅行商的優(yōu)化問題[4],在[5]中,Kennedy和Chua通過梯度和懲罰函數(shù)方法提出了一個原始神經(jīng)網(wǎng)絡(luò)用于解決非線性規(guī)劃問題,基于對偶和投影方法,Wang等人提出了幾種求解優(yōu)化問題的神經(jīng)網(wǎng)絡(luò);如簡化對偶神經(jīng)網(wǎng)絡(luò)[6],時滯神經(jīng)網(wǎng)絡(luò)[7],投影神經(jīng)網(wǎng)絡(luò)[8]等,仿真顯示這些神經(jīng)網(wǎng)絡(luò)在解決優(yōu)化問題方面都取得了很好的效果。
神經(jīng)動態(tài)優(yōu)化方法主要是通過將神經(jīng)網(wǎng)絡(luò)的平衡點和優(yōu)化問題的最優(yōu)解相同或近似,利用神經(jīng)網(wǎng)絡(luò)收斂到平衡點從而求解優(yōu)化問題的一種新方法。目前神經(jīng)動態(tài)優(yōu)化的理論研究較多,其核心思想是設(shè)計神經(jīng)網(wǎng)絡(luò)的學習法則,主要設(shè)計方法包括投影法、拉格朗日函數(shù)法、對偶定理和罰函數(shù)法等[9]。文獻[10]給出了兩種具有全局收斂性的遞歸神經(jīng)網(wǎng)絡(luò)用于求解離散系統(tǒng)的模型預(yù)測控制優(yōu)化問題。文獻[11]則提出了一種簡化對偶神經(jīng)網(wǎng)絡(luò)來解決非線性仿射系統(tǒng)的模型預(yù)測控制問題,而對帶有魯棒的系統(tǒng)的模型預(yù)測控制優(yōu)化問題。文獻[12]提出了一種兩層神經(jīng)網(wǎng)絡(luò),在[13]中則利用投影神經(jīng)網(wǎng)絡(luò)求解仿射系統(tǒng)的模型預(yù)測控制優(yōu)化問題并將其應(yīng)用于連續(xù)攪拌釜式反應(yīng)器(CSTR)驗證該神經(jīng)動態(tài)優(yōu)化方法的可行性和有效性,Lu等人則利用離散神經(jīng)網(wǎng)絡(luò)求解預(yù)測控制并通過硬件實現(xiàn)該優(yōu)化方法[14]。
2 離散系統(tǒng)預(yù)測控制
考慮如下離散時滯系統(tǒng):
文獻[15]證明了該梯度神經(jīng)網(wǎng)絡(luò)是Lyapunov穩(wěn)定且是指數(shù)收斂。根據(jù)神經(jīng)網(wǎng)絡(luò)的收斂條件,當目標函數(shù)是帶有不等式約束的二次規(guī)劃形式時,仍能滿足收斂要求,此時該神經(jīng)網(wǎng)絡(luò)仍是Lyapunov穩(wěn)定和指數(shù)收斂,因此可以用來求解優(yōu)化問題(10)。
綜上,基于離散時滯系統(tǒng)梯度神經(jīng)網(wǎng)絡(luò)模型預(yù)測控制優(yōu)化算法如下:
4 結(jié)束語
本文針對離散時滯系統(tǒng)的模型預(yù)測控制問題,提出了基于梯度神經(jīng)網(wǎng)絡(luò)的神經(jīng)動態(tài)優(yōu)化方法。該方法擴大了模型預(yù)測控制優(yōu)化的應(yīng)用范圍,較好的提高了在線計算速度,減少了在線計算時間。此外,該神經(jīng)動態(tài)優(yōu)化方法也可以用于其他非線性凸規(guī)劃問題,豐富了模型預(yù)測控制在更多領(lǐng)域的應(yīng)用和應(yīng)用場合的推廣。
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