基于线性近似和神经网络逼近的模型预测控制

针对非线性系统的模型预测控制问题,提出了一种基于线性近似和神经网络逼近的控制算法。用Taylor级数展开法对非线性系统进行线性近似时,要求对象系统中的非线性函数必须连续可微。为了突破这一限制,引入了Stirling插值公式线性近似法,拓展了可处理的非线性系统范围。通过对线性化过程中产生的非线性高阶项进行径向基函数(radial basis function, RBF)神经网络逼近,显著提高了对象系统模型精确度。为了降低数值计算复杂度,将控制性能指标函数重构为易于处理的二次型最优化问题,通过对该二次型最优化问题的求解得到了最优控制序列。控制过程考虑了约束条件的影响以模拟真实的工业生产过程。仿真结果证明了所提出预测控制方案的有效性。

Model predictive control based on linearization and neural network approach

A constrained model predictive control algorithm is proposed based on linearization and neural network approach. The nonlinear system must be continuously differentiable when using the Taylor series expansion linearization method. In order to break through this restriction, we introduce Stirling’s interpolation formula method. In the interest of improving the precision of the model, we estimate the high-order terms associated with the linearization using a radial basis function (RBF) neural network. For the sake of reducing the complexity of computation, we reformulate the control performance index to a quadratic optimization problem, and obtain the optimization control sequences by solving the quadratic optimization problem. The constraint conditions are considered during the control process to simulate actual industrial production processes. The simulation results demonstrate the effectiveness of the proposed model predictive control scheme.