基于线性近似和神经网络逼近的模型预测控制

Model predictive control based on linearization and neural network approach

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。

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 ex- pansion 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 asso- ciated 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 con- ditions are considered during the control process to simulate actual industrial production processes. The simula- tion results demonstrate the effectiveness of the proposed model predictive control scheme.