# A Descent Algorithm for the Optimal Control of Constrained Nonlinear Switched Dynamical Systems: Appendix

### Humberto Gonzalez, Ram Vasudevan, Maryam Kamgarpour, S. Shankar Sastry, Ruzena Bajcsy and Claire Tomlin

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/EECS-2010-9

January 26, 2010

### http://www.eecs.berkeley.edu/Pubs/TechRpts/2010/EECS-2010-9.pdf

This document is an appendix to the paper "A Descent Algorithm for the Optimal Control of Constrained Nonlinear Switched Dynamical Systems", presented at the 13th International Conference on Hybrid Systems: Computation and Control (HSCC'10), and contains the proofs of all the propositions and theorems in Section 4 of that paper. The reader is advised to read this document after covering the first three sections of the original paper, as the notation and the problem formulation are not covered in this appendix. The numbering of the equations, propositions, and theorems is consistent with the numbering used in the original paper.

BibTeX citation:

@techreport{Gonzalez:EECS-2010-9, Author = {Gonzalez, Humberto and Vasudevan, Ram and Kamgarpour, Maryam and Sastry, S. Shankar and Bajcsy, Ruzena and Tomlin, Claire}, Title = {A Descent Algorithm for the Optimal Control of Constrained Nonlinear Switched Dynamical Systems: Appendix}, Institution = {EECS Department, University of California, Berkeley}, Year = {2010}, Month = {Jan}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2010/EECS-2010-9.html}, Number = {UCB/EECS-2010-9}, Abstract = {This document is an appendix to the paper "A Descent Algorithm for the Optimal Control of Constrained Nonlinear Switched Dynamical Systems", presented at the 13th International Conference on Hybrid Systems: Computation and Control (HSCC'10), and contains the proofs of all the propositions and theorems in Section 4 of that paper. The reader is advised to read this document after covering the first three sections of the original paper, as the notation and the problem formulation are not covered in this appendix. The numbering of the equations, propositions, and theorems is consistent with the numbering used in the original paper.} }

EndNote citation:

%0 Report %A Gonzalez, Humberto %A Vasudevan, Ram %A Kamgarpour, Maryam %A Sastry, S. Shankar %A Bajcsy, Ruzena %A Tomlin, Claire %T A Descent Algorithm for the Optimal Control of Constrained Nonlinear Switched Dynamical Systems: Appendix %I EECS Department, University of California, Berkeley %D 2010 %8 January 26 %@ UCB/EECS-2010-9 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/2010/EECS-2010-9.html %F Gonzalez:EECS-2010-9