高阶多智能体系统一致性问题的控制增益优化设计

发布时间：2018-05-30 11:06

本文选题：多智能体系统 + 最小均方差　；参考：《中国科学技术大学》2016年硕士论文

【摘要】：近些年来,多智能体系统得到了越来越多的关注。本文针对受过程噪声干扰的离散高阶多智能体系统,研究其一致性控制增益优化设计问题。文中主要考虑了两种情况,分别为状态反馈下的一致性控制策略和输出反馈下的一致性控制策略。对于状态反馈控制策略下的多智能体系统,我们选取系统状态的极限均方差作为性能指标,通过最小化该性能指标来设计相应的控制增益。这个优化问题具有非线性矩阵不等式的形式,很难直接求解。为应对这一问题,本文提出了一种迭代算法来求解这个优化问题。在每次迭代中,首先给定一个可行的控制增益,这个控制增益要保证能够使多智能体系统实现均方有界一致性,在这种情况下,非线性矩阵不等式问题成为线性矩阵不等式问题,很容易求解出相应的中间变量。在求解的中间变量和给定的控制增益的基础上,利用扰动法求解一个近似的可行的一致性控制增益变化方向,在该方向上移动控制增益,系统的一致性性能指标得到优化,并通过线搜索方法,得到局部最优的一致性控制增益。求解出的新的一致性控制增益显然能够使系统实现均方有界一致性,可以作为下一次迭代的初始条件,进行迭代直到满足截止条件为止。对于输出反馈控制策略下的多智能体系统,本文使用一种基于状态观测的一致性控制策略,系统的性能指标为系统状态和观测状态的极限均方差的和,通过优化性能指标求解控制增益和观测器参数,优化问题同样具有非线性矩阵不等式形式,针对于状态反馈情况而设计的迭代算法同样适用于输出反馈情况下的优化问题。本文提出的一致性控制增益设计方法不但能保证多智能体系统的均方有界一致性,而且能够优化系统的一致性性能,有效地消减了过程噪声对于系统的干扰。除了理论证明,还进行了仿真实验,验证了算法的正确性和有效性。
[Abstract]:In recent years, more and more attention has been paid to multi-agent system. In this paper, the optimal design of the uniform control gain for discrete high order multi-agent systems with process noise interference is studied. In this paper, two kinds of cases are considered, one is consistency control strategy based on state feedback and the other is consistency control strategy under output feedback. For the multi-agent system under the state feedback control strategy, we select the limit mean square error of the system state as the performance index, and design the corresponding control gain by minimizing the performance index. This optimization problem has the form of nonlinear matrix inequality and is difficult to solve directly. To solve this problem, an iterative algorithm is proposed to solve the optimization problem. In each iteration, a feasible control gain is first given, which ensures that the multi-agent system can achieve a bounded mean square, in which case, The nonlinear matrix inequality problem is a linear matrix inequality problem, and it is easy to solve the corresponding intermediate variables. On the basis of the intermediate variable and the given control gain, the perturbation method is used to solve the change direction of an approximate consistent control gain. In this direction, the control gain is moved and the system consistency performance index is optimized. The local optimal consistency control gain is obtained by line search method. It is obvious that the new consistency control gain can make the system realize mean-square bounded consistency, which can be used as the initial condition of the next iteration until the cut-off condition is satisfied. For the multi-agent system with output feedback control strategy, this paper uses a consistency control strategy based on state observation. The performance index of the system is the sum of the limit mean square deviation of the system state and the observed state. By solving the control gain and observer parameters by optimizing performance index, the optimization problem also has the form of nonlinear matrix inequality, and the iterative algorithm designed for the case of state feedback is also suitable for the optimization problem under the condition of output feedback. The gain design method of consistency control proposed in this paper not only can guarantee the mean square bounded consistency of multi-agent system, but also can optimize the consistency performance of the system and effectively reduce the interference of process noise to the system. In addition to theoretical proof, simulation experiments are carried out to verify the correctness and effectiveness of the algorithm.
【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TP18

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