Differential dynamic programming: Difference between revisions

Revision as of 02:23, 16 December 2023

Revision as of 12:38, 4 January 2024

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:<math>\ell(\mathbf{x},\mathbf{u}) + V(\mathbf{f}(\mathbf{x},\mathbf{u}),i+1)</math>

is the argument of the <math>\min[\cdot]</math> operator in {{EquationNote|2|Eq. 2}}, let <math>Q</math> be the variation of this quantity around the <math>i</math>-th <math>(\mathbf{x},\mathbf{u})</math> pair:

:<math>\begin{align}Q(\delta\mathbf{x},\delta\mathbf{u})\equiv &\ell(\mathbf{x}+\delta\mathbf{x},\mathbf{u}+\delta\mathbf{u})&&{}+V(\mathbf{f}(\mathbf{x}+\delta\mathbf{x},\mathbf{u}+\delta\mathbf{u}),i+1)

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== Regularization and line-search ==

Differential dynamic programming is a second-order algorithm like [[Newton's method]]. It therefore takes large steps toward the minimum and often requires [[regularization (mathematics)|regularization]] and/or [[line-search]] to achieve convergence.<ref>

{{Cite journal |last=Liao |first=L. Z |author2=C. A Shoemaker |author2-link=Christine Shoemaker |year=1991 |title=Convergence in unconstrained discrete-time differential dynamic programming |journal=IEEE Transactions on Automatic Control |volume=36 |issue=6 |page=692 |doi=10.1109/9.86943}}

<ref>

</ref><ref>{{Cite journalthesis

| volume = 36

| issue = 6

| page = 692

| last = Liao

| first = L. Z

|author2=C. A Shoemaker | author2-link = Christine Shoemaker

| title = Convergence in unconstrained discrete-time differential dynamic programming

| journal = IEEE Transactions on Automatic Control

| year = 1991

| doi = 10.1109/9.86943

}}

</ref>

.<ref>{{Cite thesis

| publisher = Hebrew University

| last = Tassa