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Research Output

2020

On Algebraic Proofs of Stability for Homogeneous Vector Fields

Ahmadi, A. A. & El Khadir, B., Jan 2020, In : IEEE Transactions on Automatic Control. 65, 1, p. 325-332 8 p., 8706528.

Princeton University

Research output: Contribution to journalArticle

On the complexity of detecting convexity over a box

Ahmadi, A. A. & Hall, G., Jul 1 2020, In : Mathematical Programming. 182, 1-2, p. 429-443 15 p.

Princeton University

Research output: Contribution to journalArticle

2019
1 Scopus citations
2 Scopus citations

Polynomial norms

Ahmadi, A. A. L. I., Klerk, E. D. E. & Hall, G., 2019, In : SIAM Journal on Optimization. 29, 1, p. 399-422 24 p.

Princeton University

Research output: Contribution to journalArticle

2018
1 Scopus citations

DC decomposition of nonconvex polynomials with algebraic techniques

Ahmadi, A. A. & Hall, G., May 1 2018, In : Mathematical Programming. 169, 1, p. 69-94 26 p.

Princeton University

Research output: Contribution to journalArticle

4 Scopus citations

Improving efficiency and scalability of sum of squares optimization: Recent advances and limitations

Ahmadi, A. A., Hall, G., Papachristodoulou, A., Saunderson, J. & Zheng, Y., Jan 18 2018, 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Institute of Electrical and Electronics Engineers Inc., p. 453-462 10 p. (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; vol. 2018-January).

Princeton University

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations
2017

A Characterization of Lyapunov Inequalities for Stability of Switched Systems

Jungers, R. M., Ahmadi, A. A., Parrilo, P. A. & Roozbehani, M., Jun 1 2017, In : IEEE Transactions on Automatic Control. 62, 6, p. 3062-3067 6 p., 7858590.

Princeton University

Research output: Contribution to journalArticle

18 Scopus citations

Geometry of 3D environments and sum of squares polynomials

Ahmadi, A. A., Hall, G., Makadia, A. & Sindhwani, V., Jan 1 2017, Robotics: Science and Systems XIII, RSS 2017. Srinivasa, S., Ayanian, N., Amato, N. & Kuindersma, S. (eds.). MIT Press Journals, (Robotics: Science and Systems; vol. 13).

Princeton University

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Optimization over structured subsets of positive semidefinite matrices via column generation

Ahmadi, A. A., Dash, S. & Hall, G., May 1 2017, In : Discrete Optimization. 24, p. 129-151 23 p.

Princeton University

Research output: Contribution to journalArticle

4 Scopus citations

Some recent directions in algebraic methods for optimization and lyapunov analysis

Ahmadi, A. A. & Parrilo, P. A., 2017, Springer Tracts in Advanced Robotics. Springer Verlag, p. 89-112 24 p. (Springer Tracts in Advanced Robotics; vol. 117).

Princeton University

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations

Sum of squares basis pursuit with linear and second order cone programming

Ahmadi, A. A. & Hall, G., 2017, Contemporary Mathematics. American Mathematical Society, p. 27-53 27 p. (Contemporary Mathematics; vol. 685).

Princeton University

Research output: Chapter in Book/Report/Conference proceedingChapter

8 Scopus citations

Sum of Squares Certificates for Stability of Planar, Homogeneous, and Switched Systems

Ahmadi, A. A. & Parrilo, P. A., Oct 1 2017, In : IEEE Transactions on Automatic Control. 62, 10, p. 5269-5274 6 p., 7803555.

Princeton University

Research output: Contribution to journalArticle

2 Scopus citations
2016

Lower bounds on complexity of Lyapunov functions for switched linear systems

Ahmadi, A. A. & Jungers, R. M., Aug 1 2016, In : Nonlinear Analysis: Hybrid Systems. 21, p. 118-129 12 p.

Princeton University

Research output: Contribution to journalArticle

3 Scopus citations
11 Scopus citations
2015

Robust-to-dynamics linear programming

Ahmadi, A. A. & Günluk, O., Feb 8 2015, 54rd IEEE Conference on Decision and Control,CDC 2015. Institute of Electrical and Electronics Engineers Inc., p. 5915-5919 5 p. 7403149. (Proceedings of the IEEE Conference on Decision and Control; vol. 54rd IEEE Conference on Decision and Control,CDC 2015).

Princeton University

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations
2014

Control and verification of high-dimensional systems with DSOS and SDSOS programming

Majumdar, A., Ahmadi, A. A. & Tedrake, R., Jan 1 2014, In : Proceedings of the IEEE Conference on Decision and Control. 2015-February, February, p. 394-401 8 p., 7039413.

Princeton University

Research output: Contribution to journalConference article

38 Scopus citations
40 Scopus citations

Joint spectral radius and path-complete graph Lyapunov functions

Ahmadi, A. A., Jungers, R. M., Parrilo, P. A. & Roozbehani, M., Mar 28 2014, In : SIAM Journal on Control and Optimization. 52, 1, p. 687-717 31 p.

Research output: Contribution to journalArticle

53 Scopus citations

On complexity of Lyapunov functions for switched linear systems

Ahmadi, A. A. & Jungers, R. M., 2014, 19th IFAC World Congress IFAC 2014, Proceedings. Boje, E. & Xia, X. (eds.). IFAC Secretariat, p. 5992-5997 6 p. (IFAC Proceedings Volumes (IFAC-PapersOnline); vol. 19).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Towards scalable algorithms with formal guarantees for Lyapunov analysis of control systems via algebraic optimization

Ahmadi, A. A. & Parrilo, P. A., Jan 1 2014, In : Proceedings of the IEEE Conference on Decision and Control. 2015-February, February, p. 2272-2281 10 p., 7039734.

Princeton University

Research output: Contribution to journalConference article

12 Scopus citations
2013

A complete characterization of the gap between convexity and sos-convexity

Ahmadi, A. A. & Parrilo, P. A., Aug 1 2013, In : SIAM Journal on Optimization. 23, 2, p. 811-833 23 p.

Research output: Contribution to journalArticle

35 Scopus citations

Complexity of ten decision problems in continuous time dynamical systems

Ahmadi, A. A., Majumdar, A. & Tedrake, R., 2013, 2013 American Control Conference, ACC 2013. Institute of Electrical and Electronics Engineers Inc., p. 6376-6381 6 p. 6580838. (Proceedings of the American Control Conference).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Control design along trajectories with sums of squares programming

Majumdar, A., Ahmadi, A. A. & Tedrake, R., Nov 14 2013, 2013 IEEE International Conference on Robotics and Automation, ICRA 2013. p. 4054-4061 8 p. 6631149. (Proceedings - IEEE International Conference on Robotics and Automation).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

63 Scopus citations

NP-hardness of deciding convexity of quartic polynomials and related problems

Ahmadi, A. A., Olshevsky, A., Parrilo, P. A. & Tsitsiklis, J. N., 2013, In : Mathematical Programming. 137, 1-2, p. 453-476 24 p.

Princeton University

Research output: Contribution to journalArticle

53 Scopus citations

Switched stability of nonlinear systems via SOS-convex Lyapunov functions and semidefinite programming

Ahmadi, A. A. & Jungers, R. M., Jan 1 2013, 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013. Institute of Electrical and Electronics Engineers Inc., p. 727-732 6 p. 6759968. (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations
2012

A convex polynomial that is not sos-convex

Ahmadi, A. A. & Parrilo, P. A., Oct 1 2012, In : Mathematical Programming. 135, 1-2, p. 275-292 18 p.

Research output: Contribution to journalArticle

31 Scopus citations

Feasibility checks and control laws for reconfigurations of spacecraft clusters

Moshtagh, N., Ahmadi, A. A. & Mesbahi, M., Jan 1 2012, 2012 American Control Conference, ACC 2012. Institute of Electrical and Electronics Engineers Inc., p. 961-966 6 p. 6315644. (Proceedings of the American Control Conference).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Joint spectral radius of rank one matrices and the maximum cycle mean problem

Ahmadi, A. A. & Parrilo, P. A., Dec 1 2012, In : Proceedings of the IEEE Conference on Decision and Control. p. 731-733 3 p., 6425992.

Research output: Contribution to journalConference article

7 Scopus citations

On the difficulty of deciding asymptotic stability of cubic homogeneous vector fields

Ahmadi, A. A., Nov 26 2012, 2012 American Control Conference, ACC 2012. p. 3334-3339 6 p. 6315687. (Proceedings of the American Control Conference).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Scopus citations

When is a set of LMIs a sufficient condition for stability

Ahmadi, A. A., Jungers, R. M., Parrilo, P. A. & Roozbehani, M., Sep 17 2012, ROCOND'12 - 7th IFAC Symposium on Robust Control Design. PART 1 ed. p. 313-318 6 p. (IFAC Proceedings Volumes (IFAC-PapersOnline); vol. 7, no. PART 1).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations
2011

A globally asymptotically stable polynomial vector field with no polynomial Lyapunov function

Ahmadi, A. A., Krstic, M. & Parrilo, P. A., Dec 1 2011, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. p. 7579-7580 2 p. 6161499. (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

35 Scopus citations

Analysis of the joint spectral radius via Lyapunov functions on path-complete graphs

Ahmadi, A. A., Jungers, R. M., Parrilo, P. A. & Roozbehani, M., May 20 2011, HSCC'11 - Proceedings of the 2011 ACM/SIGBED Hybrid Systems: Computation and Control. p. 13-22 10 p. (HSCC'11 - Proceedings of the 2011 ACM/SIGBED Hybrid Systems: Computation and Control).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

26 Scopus citations

Converse results on existence of sum of squares Lyapunov functions

Ahmadi, A. A. & Parrilo, P. A., Dec 1 2011, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. p. 6516-6521 6 p. 6161493. (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

21 Scopus citations

On higher order derivatives of Lyapunov functions

Ahmadi, A. A. & Parrilo, P. A., Sep 29 2011, Proceedings of the 2011 American Control Conference, ACC 2011. p. 1313-1314 2 p. 5991573. (Proceedings of the American Control Conference).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

13 Scopus citations
2010

On the equivalence of algebraic conditions for convexity and quasiconvexity of polynomials

Ali Ahmadi, A. & Parrilo, P. A., Dec 1 2010, 2010 49th IEEE Conference on Decision and Control, CDC 2010. p. 3343-3348 6 p. 5717510. (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Piecewise polynomial Lyapunov functions with guaranteed accuracy

Ahmadi, A. A., Jungers, R. M., Parrilo, P. & Roozbehani, M., Dec 1 2010, 2010 IEEE 26th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2010. 1 p. 5662189. (2010 IEEE 26th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2010).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2009

A positive definite polynomial Hessian that does not factor

Ahmadi, A. A. & Parrilo, P. A., Dec 1 2009, Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. p. 1195-1200 6 p. 5400519. (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations
2008

Non-monotonic Lyapunov functions for stability of discrete time nonlinear and switched systems

Ahmadi, A. A. & Parrilo, P. A., Dec 1 2008, Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008. p. 614-621 8 p. 4739402. (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

75 Scopus citations
2006

High-speed broadband polarization-independent optical clock recovery in a silicon detector

Ahmadi, A. A., Salem, R. & Murphy, T. E., Dec 14 2006, Proceedings - Thirteenth International Symposium on Temporal Representation and Reasoning, TIME 2006. Vol. 2006. 1636694

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Two-photon absorption for optical clock recovery in OTDM networks

Salem, R., Ahmadi, A. A., Tudury, G. E., Carter, G. M. & Murphy, T. E., Sep 1 2006, In : Journal of Lightwave Technology. 24, 9, p. 3353-3361 9 p.

Research output: Contribution to journalArticle

14 Scopus citations