Differential dynamic programming

Differential Dynamic Programming (DDP) is a second-order iterative algorithm of trajectory optimization. The algorithm was was introduced by Jacobson and Mayne^[1]. The algorithm uses locally-quadratic models of a dynamics function ${\displaystyle f(\mathbf {x} ,u)}$

Given a fixed initial state ${\displaystyle x_{0}}$, DDP finds a locally-optimal control sequence ${\displaystyle U=\{u_{i}\}_{i=1}^{N}}$.

${\displaystyle {\begin{bmatrix}0&Q_{\mathbf {x} }^{\mathsf {T}}&Q_{\mathbf {u} }^{\mathsf {T}}\\Q_{\mathbf {x} }&Q_{\mathbf {x} \mathbf {x} }&Q_{\mathbf {x} \mathbf {u} }\\Q_{\mathbf {u} }&Q_{\mathbf {u} \mathbf {x} }&Q_{\mathbf {u} \mathbf {u} }\end{bmatrix}}}$

References

1. Mayne, David H. and Jacobson, David Q. (1970). Differential dynamic programming. New York: American Elsevier Pub. Co. ISBN 0444000704.

See also

• optimal control

External links

• A Python implementation of DDP
• A MATLAB implementation of DDP