A Hybrid Differential Dynamic Programming Algorithm for Constrained Optimal Control Problems. Part 1: Theory

作者：Lantoine Gregory^*; Russell Ryan P

来源：Journal of Optimization Theory and Applications, 2012, 154(2): 382-417.

DOI：10.1007/s10957-012-0039-0

• Optimal control
• Differential dynamic programming
• Nonlinear optimization
• Large-scale problem
• Trust region
• Augmented Lagrangian

A new algorithm is presented to solve constrained nonlinear optimal control problems, with an emphasis on highly nonlinear dynamical systems. The algorithm, called HDDP, is a hybrid variant of differential dynamic programming, a proven second-order technique that relies on Bellman's Principle of Optimality and successive minimization of quadratic approximations. The new hybrid method incorporates nonlinear mathematical programming techniques to increase efficiency: quadratic programming subproblems are solved via trust region and range-space active set methods, an augmented Lagrangian cost function is utilized, and a multiphase structure is implemented. In addition, the algorithm decouples the optimization from the dynamics using first- and second-order state transition matrices. A comprehensive theoretical description of the algorithm is provided in this first part of the two paper series. Practical implementation and numerical evaluation of the algorithm is presented in Part 2.

• 出版日期2012-8