输入受限LQ控制的参变量变分原理和算法

摘要

Based on the theory of analogy, the parametric variational principle derived from plastic mechanics and contact mechanics is developed and applied to the theory of optimal control. New coupled equations of Hamilton canonical equation and linear complementarity equation are established for the problem of LQ optimal control with constrained control input. By dividing the continuous time into a series of equidistant intervals,a new numerical algorithm based on the parametric quadratic programming method for solving the coupledequations is proposed in the discrete time domain. Numerical simulations show that the algorithm given in this paper is effective for the problem of LQ optimal control with constrained control input and the convergence speed and accuracy of the algorithm is satisfactory.%在最优控制理论中根据模拟理论思想发展了塑性力学和接触力学中的参变量变分原理,并建立了控制输入受限的线性二次(linear quadratic,LQ)最优控制问题的求解新方程-耦合的Hamilton正则方程与线性互补方程.通过将连续时间离散成一系列等间距时间区段,在离散时域内采用参数二次规划方法给出数值求解输入受限的LQ最优控制问题的新算法.数值仿真验证了该算法在求解控制输入受限的LQ最优控制问题中的有效性,并且该算法具有较快的收敛性,在大步长下具有较高的计算精度.