多關聯(lián)運動體的合作運動分析與控制

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的動力學分析與控制的基本目標，研究空間多關聯(lián)運動體的編隊控制，具有切換、非線性、異構多關聯(lián)運動體分布式一致控制，邏輯動態(tài)網(wǎng)絡中多關聯(lián)運動體分析與控制，以及加權多模型自適應控制等關鍵問題。通過綜合運用復雜系統(tǒng)控制理論、圖論、以及非線性系統(tǒng)控制理論等相關知識，分析了多關聯(lián)運動體的動態(tài)性質，得到了分布式協(xié)調控制的條件和設計方法。主要研究內(nèi)容和結果如下。對于多關聯(lián)體自驅動編隊的合并與分離問題，目前文獻中大多采用的方案是利用關聯(lián)體之間的長程吸引和短程排斥相互作用實現(xiàn)系統(tǒng)整體的空間有界穩(wěn)態(tài)分布構型。本課題通過在關聯(lián)體之間引入中程排斥作用，并利用混合拓撲結構實現(xiàn)了系統(tǒng)隊形的分裂和合并。關于非線性因素對多關聯(lián)運動體編隊控制的影響，本課題結合有向網(wǎng)絡拓撲中非線性一階多關聯(lián)運動體的一致控制問題進行了研究，建立了控制器的設計條件?？紤]到由于技術限制或外界干擾等因素，應用中通常難以實現(xiàn)基于全信息狀態(tài)反饋的實際情況。本課題研究了未知速度量測信息和不同拓撲連接結構情形下的異構多關聯(lián)運動體分布式一致控制。另外，還討論了分布式有限時間一致性控制問題。在加權多模型自適應控制系統(tǒng)的分析與設計方面，進一步完善了前期的研究工作。得到了連續(xù)時間隨機不確定系統(tǒng)的加權多模型自適應控制的穩(wěn)定性條件，設計出新的加權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，而收斂條件進一步減弱，應用范圍擴大。同時，對課題前期開發(fā)的多自由度運動控制器進行了完善升級，進一步加強了系統(tǒng)的穩(wěn)定性和實時性等方面的性能，滿足了課題研究工作發(fā)展的需要。另外，研究了多關聯(lián)動態(tài)邏輯系統(tǒng)的狀態(tài)反饋鎮(zhèn)定和最優(yōu)控制問題，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)反饋的變換和設計步驟。對于含不確定性的概率布爾網(wǎng)絡，得到了穩(wěn)態(tài)概率分布最優(yōu)控制問題可解的充分必要條件，討論了相關的多目標優(yōu)化問題并給出可行的計算方法。對于布爾網(wǎng)絡控制系統(tǒng)的能觀性問題，在不假設系統(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)絡的擾動解耦控制問題。以上研究結果對于理解和控制空間合作目標的復雜運動具有重要的意義。

關鍵詞：多關聯(lián)體；協(xié)調運動；編隊控制；一致性協(xié)議；自適應估計；邏輯動態(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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