ILC-Based Fixed-Structure Controller Design for Output PDF Shaping in Stochastic Systems Using LMI Techniques
ILC-Based Fixed-Structure Controller Design for Output PDF Shaping in Stochastic Systems Using LMI Techniques
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DOI：
10.1109/tac.2009.2014934
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发表时间：
2009-03
影响因子：
6.8
通讯作者：
Hong Wang;P. Afshar
中科院分区：
文献类型：
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作者：
Hong Wang;P. Afshar
针对非高斯动态随机系统，提出了一种用于输出概率密度函数整形的广义状态空间控制器设计。采用径向基函数（RBF）神经网络逼近系统输出的PDF。这种神经网络由若干权重和相应的基函数组成。利用这种近似，原始随机系统的动力学可以表示为控制输入与RBF神经网络权值之间的动力学。因此，输出PDF控制的任务可以简化为RBF权重控制，并对基函数参数（即基函数的中心和宽度）进行自适应调整。为了达到这一目的，控制水平被分成一定的间隔，以下称为批次。利用这些定义，整个控制策略包括三个阶段，即(a)动态非线性模型的子空间参数辨识（将控制信号与RBF神经网络的权值联系起来）；(b)采用基于lmi的凸优化技术设计权值跟踪控制器；(c)使用迭代学习控制（ILC）框架根据其中心和宽度进行RBF基函数形状调谐。在上述阶段中，前两个阶段在每个批次中进行，而阶段(c)在任何两个相邻批次之间进行。该算法具有逐批提高闭环输出PDF跟踪性能的优点。此外，阶段(b)中提到的控制器是状态空间形式的通用控制器。通过稳定性分析和仿真结果验证了该方法的有效性，并取得了令人鼓舞的结果。
In this paper, a generalized state-space controller design for the shaping of the output probability density function (PDF) is presented for non-Gaussian dynamical stochastic systems. A radial basis function (RBF) neural network is used to approximate the output PDF of the system. Such a neural network consists of a number of weights and corresponding basis functions. Using such an approximation, the dynamics of the original stochastic system can be expressed as the dynamics between the control input and the weights of the RBF neural network. The task of output PDF control can therefore be reduced to a RBF weight control together with an adaptive tuning of the basis function parameters (i.e., the centers and widths of the basis functions). To achieve this aim, the control horizon is divided into certain intervals hereinafter called batches. Using these definitions, the whole control strategy consists of three stages, namely (a) sub-space parameter identification of the dynamic nonlinear model (that relates the control signal to the weights of the RBF neural network); (b) Weight tracking controller design using an LMI-based convex optimization technique; and (c) RBF basis functions shape tuning in terms of their centers and widths using an iterative learning control (ILC) framework. Among the above stages, the first two are performed within each batch, while stage (c) is carried out between any two adjacent batches. Such an algorithm has the advantage of the batch-by-batch improvement of the closed-loop output PDF tracking performance. Moreover, the controller mentioned in stage (b) is a general controller in a state-space form. Stability analysis has been performed and simulation results are included to show the effectiveness of the proposed method, where encouraging results have been made.