An efficient sequential linear quadratic algorithm for solving nonlinear optimal control problems
An efficient sequential linear quadratic algorithm for solving nonlinear optimal control problems
复制标题
求解非线性最优控制问题的高效顺序线性二次算法
DOI：
--
复制
发表时间：
2005
期刊：
影响因子：
--
通讯作者：
J. Bobrow
中科院分区：
文献类型：
--
作者：
Athanasios Sideris;J. Bobrow
我们开发了一个数值上有效的算法计算控制的非线性系统，最小化的二次性能指标。我们将最优控制问题表述为离散时间，但许多连续时间问题也可以在离散化后求解。我们的方法是类似于序列二次规划的有限维优化问题，我们解决的非线性最优控制问题，使用序列的线性二次子问题。每个子问题有效地解决了Riccati差分方程。我们表明，每次迭代产生的性能指标的下降方向，并控制序列收敛到一个解决方案，满足众所周知的必要条件的最优控制。
We develop a numerically efficient algorithm for computing controls for nonlinear systems that minimize a quadratic performance measure. We formulate the optimal control problem in discrete-time, but many continuous-time problems can be also solved after discretization. Our approach is similar to sequential quadratic programming for finite-dimensional optimization problems in that we solve the nonlinear optimal control problem using sequence of linear quadratic subproblems. Each subproblem is solved efficiently using the Riccati difference equation. We show that each iteration produces a descent direction for the performance measure, and that the sequence of controls converges to a solution that satisfies the well-known necessary conditions for the optimal control.