楚天廣+楊萌+李睿+張琦+張維存

摘要：本研究圍繞空間合作目標(biāo)的動(dòng)力學(xué)分析與控制的基本目標(biāo)，研究空間多關(guān)聯(lián)運(yùn)動(dòng)體的編隊(duì)控制，具有切換、非線性、異構(gòu)多關(guān)聯(lián)運(yùn)動(dòng)體分布式一致控制，邏輯動(dòng)態(tài)網(wǎng)絡(luò)中多關(guān)聯(lián)運(yùn)動(dòng)體分析與控制，以及加權(quán)多模型自適應(yīng)控制等關(guān)鍵問(wèn)題。通過(guò)綜合運(yùn)用復(fù)雜系統(tǒng)控制理論、圖論、以及非線性系統(tǒng)控制理論等相關(guān)知識(shí)，分析了多關(guān)聯(lián)運(yùn)動(dòng)體的動(dòng)態(tài)性質(zhì)，得到了分布式協(xié)調(diào)控制的條件和設(shè)計(jì)方法。主要研究?jī)?nèi)容和結(jié)果如下。對(duì)于多關(guān)聯(lián)體自驅(qū)動(dòng)編隊(duì)的合并與分離問(wèn)題，目前文獻(xiàn)中大多采用的方案是利用關(guān)聯(lián)體之間的長(zhǎng)程吸引和短程排斥相互作用實(shí)現(xiàn)系統(tǒng)整體的空間有界穩(wěn)態(tài)分布構(gòu)型。本課題通過(guò)在關(guān)聯(lián)體之間引入中程排斥作用，并利用混合拓?fù)浣Y(jié)構(gòu)實(shí)現(xiàn)了系統(tǒng)隊(duì)形的分裂和合并。關(guān)于非線性因素對(duì)多關(guān)聯(lián)運(yùn)動(dòng)體編隊(duì)控制的影響，本課題結(jié)合有向網(wǎng)絡(luò)拓?fù)渲蟹蔷€性一階多關(guān)聯(lián)運(yùn)動(dòng)體的一致控制問(wèn)題進(jìn)行了研究，建立了控制器的設(shè)計(jì)條件?？紤]到由于技術(shù)限制或外界干擾等因素，應(yīng)用中通常難以實(shí)現(xiàn)基于全信息狀態(tài)反饋的實(shí)際情況。本課題研究了未知速度量測(cè)信息和不同拓?fù)溥B接結(jié)構(gòu)情形下的異構(gòu)多關(guān)聯(lián)運(yùn)動(dòng)體分布式一致控制。另外，還討論了分布式有限時(shí)間一致性控制問(wèn)題。在加權(quán)多模型自適應(yīng)控制系統(tǒng)的分析與設(shè)計(jì)方面，進(jìn)一步完善了前期的研究工作。得到了連續(xù)時(shí)間隨機(jī)不確定系統(tǒng)的加權(quán)多模型自適應(yīng)控制的穩(wěn)定性條件，設(shè)計(jì)出新的加權(quán)算法并在理論上證明了其收斂性。新算法的收斂速度有明顯提高，而收斂條件進(jìn)一步減弱，應(yīng)用范圍擴(kuò)大。同時(shí)，對(duì)課題前期開(kāi)發(fā)的多自由度運(yùn)動(dòng)控制器進(jìn)行了完善升級(jí)，進(jìn)一步加強(qiáng)了系統(tǒng)的穩(wěn)定性和實(shí)時(shí)性等方面的性能，滿足了課題研究工作發(fā)展的需要。另外，研究了多關(guān)聯(lián)動(dòng)態(tài)邏輯系統(tǒng)的狀態(tài)反饋鎮(zhèn)定和最優(yōu)控制問(wèn)題，利用新近發(fā)展的矩陣半張量積理論，得到了全局狀態(tài)反饋鎮(zhèn)定控制器存在的代數(shù)充分必要條件，并給出了從代數(shù)表示到邏輯形式狀態(tài)反饋的變換和設(shè)計(jì)步驟。對(duì)于含不確定性的概率布爾網(wǎng)絡(luò)，得到了穩(wěn)態(tài)概率分布最優(yōu)控制問(wèn)題可解的充分必要條件，討論了相關(guān)的多目標(biāo)優(yōu)化問(wèn)題并給出可行的計(jì)算方法。對(duì)于布爾網(wǎng)絡(luò)控制系統(tǒng)的能觀性問(wèn)題，在不假設(shè)系統(tǒng)的能控性條件下，給出了系統(tǒng)能觀性的充分必要條件。另外，還討論了布爾網(wǎng)絡(luò)的擾動(dòng)解耦控制問(wèn)題。以上研究結(jié)果對(duì)于理解和控制空間合作目標(biāo)的復(fù)雜運(yùn)動(dòng)具有重要的意義。

關(guān)鍵詞：多關(guān)聯(lián)體；協(xié)調(diào)運(yùn)動(dòng)；編隊(duì)控制；一致性協(xié)議；自適應(yīng)估計(jì)；邏輯動(dòng)態(tài)系統(tǒng)

Dynamics Analysis and Control of Coordinated Motion in Multiagent Systems

Abstract：This study is concerned with issues concerning the dynamic analysis and control of multiagent systems， including formation control of the systems， distributed consensus control of switching， non-linear， and heterogeneous systems respectively， weighted multi model adaptive control， and analysis and control of logic dynamic networks etc. Based on approaches and methods from system and control theory， graph theory， and nonlinear system theory， it carries out dynamics analysis of the multiagent systems and establishes conditions of distributed coordination control and the corresponding design procedures. The main results are as follows. For the issue of formation control of self-driven multiagent systems， an approach making use of mid-range repulsive interactions and mixed topological structures is developed to realize the aggregation and splitting formation in the systems. This improves the existing methods in the literature that assume long-range attraction and short-range repulsion between a pair of agents in the systems so as to obtain bounded configurations. To study the influence of nonlinearities on collective motion of the systems， the consensus control of first-order nonlinear multiagent systems with directed network topology is considered and consensus conditions are derived， which suggest the controller design procedures. The problem of distributed control of consensus in heterogeneous multiagent systems is discussed under the assumption that only measured velocity information is available. In addition， the finite time consensus control problem is also discussed. For the issue of analysis and design of weighted multi-model adaptive control systems， the present work establishes stability conditions for continuous time systems， and gives a new algorithm for weight designed algorithm and proves its convergence. Compared with previous results， the new algorithm has a more quickly convergence speed and milder convergence conditions. The multi-degree-of-freedom motion controller that developed before is updated by enhancing the stability and real-time performance to meet the need of the project. Finally， issues of stabilization and optimal control of dynamic logic systems are investigated using the newly developed semi tensor product theory， necessary and sufficient algebraic conditions for global state feedback stabilization are obtained.

Keywords：Multiagent system； Coordinated motion； Formation control； Consensus protocol； Adaptive estimation； Dynamic logic system

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