离散约束系统最优控制中的内点法

摘要

Aimed at optimal control of mechanical systems, Discrete Mechanics and Optimal Control for Constrained Sys-tems(DMOCC)adopt methods of variation after discretization. The discretized equations expressed as optimal problem with nonlinear equality constraints, combined with discrete null space method, finely maintain the physical characteristics of the system, while the standard Sequence Quadratic Program(SQP)algorithm can be applied to the numerical computation. Due to the large scale constraints, SQP algorithm suffers its inefficient. Meanwhile, interior point algorithm has been widely used in the optimal control benefited from its good convergence and stability. Based on the analysis of the features of constraints of DMOCC, interior point algorithm is applied to the numerical computation and the calculation efficiency can be improved. Numerical simulation of crank slider shows that the internal point algorithm has advantage of efficiency in case of same accuracy.%对于带约束的力学系统的最优控制，约束系统离散力学最优控制（Discrete Mechanics and Optimal Con-trol for Constrained Systems，DMOCC）采用了“先离散，后变分”的方法，结合离散零空间法，能很好地保持系统的物理特性，其模型方程可表示为非线性等式约束的优化问题，通常采用标准序列二次规划（Sequence Quadratic Pro-gram，SQP）算法求解。由于约束条件的规模大，SQP算法的计算效率不高。相对于SQP，内点法具有收敛性好、稳定性强的特点。在对DMOCC约束条件的特点进行分析之后，将内点法用于DMOCC的数学模型进行数值计算，能有效提高计算效率。曲柄滑块的数值仿真证明了在数值精度一致的情况下，内点法具有效率上的优势。