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Research Output 2006 2019

2019

On the complexity of detecting convexity over a box

Ahmadi, A. A. & Hall, G., Jan 1 2019, In : Mathematical Programming.

Princeton University

Research output: Contribution to journalArticle

Convexity
NP-complete problem
Polynomial
Testing
Positive semidefinite
Nonlinear Optimization
Polynomials
Testing
NP-complete problem
Semidefinite Programming

Polynomial norms

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

Princeton University

Research output: Contribution to journalArticle

Polynomials
Norm
Polynomial
Positive definite
Sum of squares
2018
1 Citation (Scopus)
Lyapunov functions
Polynomials
1 Citation (Scopus)

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

Convex Decomposition
Polynomials
Decomposition
Decompose
Polynomial
6 Citations (Scopus)

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

Sum of squares
Scalability
Sparsity
Optimization
Second-order Cone
2017
15 Citations (Scopus)

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

Stability criteria
2 Citations (Scopus)

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

Computer vision
Robotics
Polynomials
Geometry
Experiments
2 Citations (Scopus)

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

Column Generation
Positive Semidefinite Matrix
Set theory
Cones
Cone
1 Citation (Scopus)

Some recent directions in algebraic methods for optimization and lyapunov analysis

Ahmadi, A. A. & Parrilo, P. A., Jan 1 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

Collision avoidance
Lyapunov functions
Hybrid systems
Scalability
Polynomials
6 Citations (Scopus)

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

Ahmadi, A. A. & Hall, G., Jan 1 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

Basis Pursuit
Second-order Cone Programming
Sum of squares
Linear Order
Second-order Cone
1 Citation (Scopus)

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

Lyapunov functions
Polynomials
Derivatives
Linear systems
2016
3 Citations (Scopus)

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

Switched Linear Systems
Lyapunov functions
Lyapunov Function
Linear systems
Lower bound
6 Citations (Scopus)
Operations Research
Decision Making
Real-time
Unmanned Vehicles
Polynomial
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

Linear programming
Dynamic Optimization Problems
Linear Program
Optimization Problem
Dynamic Optimization
2014
30 Citations (Scopus)

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

Sum of squares
Cones
Second-order Cone Programming
High-dimensional
Programming
36 Citations (Scopus)
Computer programming
Set theory
Linear programming
Scalability
Cones
39 Citations (Scopus)

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.

Princeton University

Research output: Contribution to journalArticle

Joint Spectral Radius
Lyapunov functions
Complete Graph
Lyapunov Function
Path
3 Citations (Scopus)

On complexity of Lyapunov functions for switched linear systems

Ahmadi, A. A. & Jungers, R. M., Jan 1 2014, 19th IFAC World Congress IFAC 2014, Proceedings. Xia, X. & Boje, E. (eds.). IFAC Secretariat, p. 5992-5997 6 p. (IFAC Proceedings Volumes (IFAC-PapersOnline); vol. 19).

Princeton University

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

Switched Linear Systems
Lyapunov Function
Finiteness
Joint Spectral Radius
Imply
12 Citations (Scopus)

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

Lyapunov
Control System
Control systems
Lyapunov Theory
Worst-case Performance
2013
28 Citations (Scopus)

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.

Princeton University

Research output: Contribution to journalArticle

Sum of squares
Convexity
Polynomials
Polynomial
Non-negative
7 Citations (Scopus)

Complexity of ten decision problems in continuous time dynamical systems

Ahmadi, A. A., Majumdar, A. & Tedrake, R., Sep 11 2013, 2013 American Control Conference, ACC 2013. p. 6376-6381 6 p. 6580838. (Proceedings of the American Control Conference).

Princeton University

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

Dynamical systems
Polynomials
Invariance
Differential equations
Trajectories
57 Citations (Scopus)

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).

Princeton University

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

Trajectories
Controllers
Torque
Pendulums
Invariance
41 Citations (Scopus)

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

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

Princeton University

Research output: Contribution to journalArticle

NP-hardness
Quartic
Pseudoconvexity
Quasiconvexity
Convexity
4 Citations (Scopus)

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).

Princeton University

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

Semidefinite Programming
Lyapunov functions
Lyapunov Function
Convex function
Nonlinear systems
2012
26 Citations (Scopus)

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

Convexity
Polynomials
Polynomial
Trivariate
Semidefinite Program

Feasibility checks and control laws for reconfigurations of spacecraft clusters

Moshtagh, N., Ahmadi, A. A. & Mesbahi, M., Nov 26 2012, 2012 American Control Conference, ACC 2012. p. 961-966 6 p. 6315644. (Proceedings of the American Control Conference).

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

Spacecraft
Debris
Orbits
Earth (planet)
Topology
6 Citations (Scopus)

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

Joint Spectral Radius
Directed graphs
Cycle
Exact Computation
Directed Graph
8 Citations (Scopus)

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).

Princeton University

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

Asymptotic stability
Lyapunov functions
Polynomials
Byproducts
Linear systems
6 Citations (Scopus)

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).

Princeton University

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

Switching systems
Stability criteria
Byproducts
2011
32 Citations (Scopus)

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).

Princeton University

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

Stable Polynomials
Polynomial Vector Fields
Globally Asymptotically Stable
Lyapunov functions
Polynomial function
26 Citations (Scopus)

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).

Princeton University

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

Joint Spectral Radius
Complete Graph
Lyapunov Function
Quadratic Function
Path
18 Citations (Scopus)

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).

Princeton University

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

Square Functions
Sum of squares
Lyapunov functions
Converse
Lyapunov Function
11 Citations (Scopus)

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

Lyapunov functions
Derivatives
Asymptotic stability
Dynamical systems
2010
4 Citations (Scopus)

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).

Princeton University

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

Quasiconvexity
Convexity
Equivalence
Polynomials
Polynomial

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).

Princeton University

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

Lyapunov functions
Computational complexity
Polynomials
2009
7 Citations (Scopus)

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).

Princeton University

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

Positive definite
Polynomials
Polynomial
Convexity
Trivariate
2008
61 Citations (Scopus)

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).

Princeton University

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

Switched Systems
Lyapunov functions
Discrete-time Systems
Lyapunov Function
Nonlinear Systems
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

clocks
recovery
high speed
broadband
detectors
14 Citations (Scopus)

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

clocks
dynamic range
recovery
vibration
photons