计及不定等价输入矩阵的多输入多输出非仿射系统鲁棒控制研究

In a multiple-input-multiple-output (MIMO) nonaffine system, controls affect evolution of system states by an implicit and nonlinear manner. Comparing with affine systems, nonaffine systems are more general and accurate in modeling complex dynamics, and bring new challenge of control design. The main difficulties of controlling such systems stem from that we can hardly solve an analytical inversion of control, and the equivalent input matrix of nonaffine systems is frequently indefinite and unsymmetrical. In addition, many practical systems process inherent uncertain characteristics, which further enhance the difficulty of control. Therefore, control of MIMO nonaffine systems is a challenge topic in nonlinear control theory. This project aim at exploring robust control design for MIMO nonaffine systems based on a self-organized neural network structure and an event-trigger switch control strategy. At first, dynamic transformation and leading-principle-minor-based matrix decomposition are studied for the purpose of transforming the original systems into an affine-in-input and semi-decoupled model. Secondly, to deal with the system uncertainties, a self-organized neural-network with a damping-term-free update law of weights is studied. The aim is to minimize the number of neurons while achieving the prescribed control requirement. And then, in the face of unknown direction coefficients of equivalent input matrix, a switch control triggered by convergence function of error is studied, to achieve stable convergence after finite switching. Finally, a testbed of UAV helicopter is set up to verify the feasibility and effectiveness of the proposed control scheme. The results and outcome will enrich the nonlinear control study, and provide theoretical guidance for practical application.

多输入多输出非仿射系统具有输入隐式表达特征，相较于仿射系统，可更精确模型化复杂被控对象，更具普适性，同时也增加了控制设计难度：输入的隐式表达导致难以求解其可逆解耦映射，且等价输入矩阵一般为非对称不定矩阵，加之广泛存在的未知动态，使其控制设计成为非线性控制领域的一项挑战性课题。为此，本项目研究基于自重构神经网络和事件驱动切换控制的鲁棒控制算法：首先，采用动态变换和基于顺序主子式的矩阵分解方法实现多输入变量显式映射及半解耦处理；其次，兼顾控制精度和运算效率，构建自重构神经网络和不依赖权值衰减项的权值更新算法，实现系统未知动态的有效处理；再次，面向不定等价输入矩阵具有未知方向参数的系统，研究误差收敛性能函数驱动的控制器切换策略，以实现经有限次切换后达到稳定控制；最后，搭建实验平台，验证所构建控制算法的有效性。研究成果将丰富非线性控制理论，为工程应用奠定基础，具有重要学术价值和实用价值。

多输入多输出非仿射系统具有输入隐式表达特征，相较于仿射系统，可更精确模型化复杂被控对象，更具普适性，同时也增加了控制设计难度：输入的隐式表达导致难以求解其可逆解耦映射，且等价输入矩阵一般为非对称不定矩阵，加之广泛存在的未知动态，使其控制设计成为非线性控制领域的一项挑战性课题。为此，本项目重点研究基于自重构神经网络和光滑切换的鲁棒控制算法：针对非对称矩阵的多输入多输出模型，采用动态变换和基于顺序主子式的矩阵分解方法实现了多输入变量显式映射及半解耦处理，并基于此构造了自适应神经网络及以死区误差驱动的新型的自适应更新算法，随后，引入切换机制，进一步解决了顺序主子式未知的难题；针对非仿射结构模型，构造新型的自适应神经网络，对系统等价有效控制变量直接进行学习，避免了对原系统的变型处理；针对多输入多输出非仿射系统中常见的控制方向未知问题，提出了一种新型的光滑Nussbaum函数，首次分析了相关李雅普诺夫函数的理论上界，并证明了其在多通道控制方向未知问题上的优势；搭建了实验平台，验证所构建控制算法的实践有效性。研究成果将丰富非线性控制理论，为工程应用奠定基础，具有重要学术价值和实用价值。