基于信赖域二次规划的非线性模型预测控制优化算法

Nonlinear model predictive control optimization algorithm based on the trust-region quadratic programming

针对非线性预测控制如何在有限时域内有效的求解非凸非线性规划这一关键问题,本文采用序列二次规划方法,将非线性规划转化为一系列二次子规划求解.首先根据非线性规划联立方法将系统状态和控制量同时作为优化变量,得到以控制量步长为优化变量,只包含不等式约束的子二次规划问题,并用它取代原SQP子规划,减小了子问题的规模;随后采用基于信赖域二次规划的方法求解子规划问题,保证每次迭代的可行性;同时采用一种能够保持SQP问题Hessian矩阵稀疏结构的更新方法,也在一定程度上降低了算法的复杂程度.最后的仿真结果表明了该方法的有效性.

The nonlinear model predictive control（NMPC） requires the optimal or suboptimal solution of a nonlinear non-convex optimization problem at each sampling time, and the sequential-quadratic-programming（SQP） is the conventional algorithm for solving such a problem. By means of the simultaneous approach in nonlinear programming, an SQP sub-problem of NMPC is built, which considers the system state and the control as optimization variables simultaneously. Then, a new quadratic-programming（QP） sub-problem is established for which the step-length in each iteration is treated as an optimization variable and the linear inequalities are treated as constraints. After that, a trust-region-quadratic- programming approach is used to solve this sub-problem, and an update method that maintains the sparse structure for the Hessian matrix is used to reduce the computational complexity. Finally, simulation examples show the effectiveness of the presented approach.