# Biography:I. Michael Ross

**Isaac Michael Ross** is a Distinguished Professor and Program Director of Control and Optimization at the Naval Postgraduate School in Monterey, CA. He has published a highly-regarded textbook on optimal control theory^{[1]} and seminal papers in pseudospectral optimal control theory,^{[2]}^{[3]}^{[4]}^{[5]}^{[6]}
energy-sink theory,^{[7]}^{[8]} the optimization and deflection of near-Earth asteroids and comets,^{[9]}^{[10]}
robotics,^{[11]}^{[12]} attitude dynamics and control,^{[13]} orbital mechanics,^{[14]}^{[15]}^{[16]} real-time optimal control^{[17]}^{[18]} and
unscented optimal control.^{[19]}^{[20]}^{[21]} The Kang–Ross–Gong theorem,^{[22]}^{[23]} Ross' π lemma, Ross' time constant, the Ross–Fahroo lemma, and the Ross–Fahroo pseudospectral method are all named after him.^{[24]}^{[25]}^{[26]}^{[27]}^{[28]} According to a report published by Stanford University,^{[29]} Ross is one of the world's top 2% of scientists.

## Theoretical contributions

Although Ross has made contributions to energy-sink theory, attitude dynamics and control and planetary defense, he is best known^{[24]}^{[25]}^{[26]}^{[28]}^{[30]} for work on pseudospectral optimal control. In 2001, Ross and Fahroo announced^{[2]} the covector mapping principle, first, as a special result in pseudospectral optimal control, and later^{[5]} as a general result in optimal control. This principle was based on the Ross–Fahroo lemma which proves^{[25]} that dualization and discretization are not necessarily commutative operations and that certain steps must be taken to promote commutation. When discretization is commutative with dualization, then, under appropriate conditions, Pontryagin's minimum principle emerges as a consequence of the convergence of the discretization.
Together with F. Fahroo, W. Kang and Q. Gong, Ross proved a series of results on the convergence of pseudospectral discretizations of optimal control problems.^{[23]} Ross and his coworkers showed that the Legendre and Chebyshev pseudospectral discretizations converge to an optimal solution of a problem under the mild condition of boundedness of variations.^{[23]}

## Software contributions

In 2001, Ross created DIDO, a software package for solving optimal control problems.^{[31]}^{[32]}^{[33]} Powered by pseudospectral methods, Ross created a user-friendly set of objects that required no knowledge of his theory to run DIDO. This work was used in on pseudospectral methods for solving optimal control problems.^{[34]} DIDO is used for solving optimal control problems in aerospace applications,^{[35]}^{[36]} search theory,^{[37]} and robotics. Ross' constructs have been licensed to other software products, and have been used by NASA to solve flight-critical problems on the International Space Station.^{[38]}

## Flight contributions

In 2006, NASA used DIDO to implement zero propellant maneuvering^{[39]} of the International Space Station. In 2007, *SIAM News* printed a page 1 article^{[38]} announcing the use of Ross' theory. This led other researchers^{[34]} to explore the mathematics of pseudospectral optimal control theory. DIDO is also used to maneuver the Space Station and operate various ground and flight equipment to incorporate autonomy and performance efficiency for nonlinear control systems.^{[22]}

## Awards and distinctions

In 2010, Ross was elected a Fellow of the American Astronautical Society for "his pioneering contributions to the theory, software and flight demonstration of pseudospectral optimal control." He also received (jointly with Fariba Fahroo), the AIAA Mechanics and Control of Flight Award for "fundamentally changing the landscape of flight mechanics". His research has made headlines in *SIAM News*,^{[38]} *IEEE Control Systems Magazine*,^{[40]} *IEEE Spectrum*,^{[27]} and *Space Daily*.^{[41]}

## See also

- Ross' π lemma
- Caratheodory-π solution
- Ross–Fahroo pseudospectral methods
- Ross–Fahroo lemma
- Covector mapping principle
- Bellman pseudospectral method
- Flat pseudospectral methods
- DIDO (optimal control)

## References

- ↑ I. M. Ross,
*A Primer on Pontryagin’s Principle in Optimal Control,*Second Edition, Collegiate Publishers, San Francisco, CA, 2015. - ↑
^{2.0}^{2.1}I. M. Ross and F. Fahroo, A Pseudospectral Transformation of the Covectors of Optimal Control Systems, Proceedings of the First IFAC Symposium on System Structure and Control, Prague, Czech Republic, 29–31 August 2001. - ↑ I. M. Ross and F. Fahroo, Legendre Pseudospectral Approximations of Optimal Control Problems,
*Lecture Notes in Control and Information Sciences*, Vol. 295, Springer-Verlag, 2003. - ↑ Ross, I. M.; Fahroo, F. (2004). "Pseudospectral Knotting Methods for Solving Optimal Control Problems".
*Journal of Guidance, Control and Dynamics***27**(3): 3. doi:10.2514/1.3426. https://zenodo.org/record/1235937. - ↑
^{5.0}^{5.1}I. M. Ross and F. Fahroo, Discrete Verification of Necessary Conditions for Switched Nonlinear Optimal Control Systems, Proceedings of the American Control Conference, Invited Paper, June 2004, Boston, MA. - ↑ Ross, I. M.; Fahroo, F. (2004). "Pseudospectral Methods for the Optimal Motion Planning of Differentially Flat Systems".
*IEEE Transactions on Automatic Control***49**(8): 1410–1413. doi:10.1109/tac.2004.832972. https://zenodo.org/record/1265714. - ↑ Ross, I. M. (1996). "Formulation of Stability Conditions for Systems Containing Driven Rotors".
*Journal of Guidance, Control and Dynamics***19**(2): 305–308. doi:10.2514/3.21619. Bibcode: 1996JGCD...19..305R. - ↑ Ross, I. M. (1993). "Nutational Stability and Core Energy of a Quasi-rigid Gyrostat".
*Journal of Guidance, Control and Dynamics***16**(4): 641–647. doi:10.2514/3.21062. Bibcode: 1993JGCD...16..641R. - ↑ Ross, I. M.; Park, S. Y.; Porter, S. E. (2001). "Gravitational Effects of Earth in Optimizing Delta-V for Deflecting Earth-Crossing Asteroids".
*Journal of Spacecraft and Rockets***38**(5): 759–764. doi:10.2514/2.3743. - ↑ Park, S. Y.; Ross, I. M. (1999). "Two-Body Optimization for Deflecting Earth-Crossing Asteroids".
*Journal of Guidance, Control and Dynamics***22**(3): 415–420. doi:10.2514/2.4413. Bibcode: 1999JGCD...22..415P. - ↑ M. A. Hurni, P. Sekhavat, and I. M. Ross, "An Info-Centric Trajectory Planner for Unmanned Ground Vehicles," Dynamics of Information Systems: Theory and Applications, Springer Optimization and its Applications, 2010, pp. 213–232.
- ↑ Gong, Q.; Lewis, L. R.; Ross, I. M. (2009). "Pseudospectral Motion Planning for Autonomous Vehicles".
*Journal of Guidance, Control and Dynamics***32**(3): 1039–1045. doi:10.2514/1.39697. Bibcode: 2009JGCD...32.1039G. - ↑ Fleming, A.; Sekhavat, P.; Ross, I. M. (2010). "Minimum-Time Reorientation of a Rigid Body".
*Journal of Guidance, Control and Dynamics***33**(1): 160–170. doi:10.2514/1.43549. Bibcode: 2010JGCD...33..160F. - ↑ Ross, I. Michael (2003-07-01). "Linearized Dynamic Equations for Spacecraft Subject to J2 Perturbations".
*Journal of Guidance, Control, and Dynamics***26**(4): 657–659. doi:10.2514/2.5095. Bibcode: 2003JGCD...26..657R. https://arc.aiaa.org/doi/10.2514/2.5095. - ↑ Ross, I. Michael (2002-07-01). "Mechanism for Precision Orbit Control with Applications to Formation Keeping".
*Journal of Guidance, Control, and Dynamics***25**(4): 818–820. doi:10.2514/2.4951. Bibcode: 2002JGCD...25..818R. https://arc.aiaa.org/doi/10.2514/2.4951. - ↑ I. M. Ross, H. Yan and F. Fahroo, "A Curiously Outlandish Problem in Orbital Mechanics," American Astronautical Society, AAS Paper 01-430, July–Aug. 2001
- ↑ Ross, I. M.; Fahroo, F. (2006). "Issues in the Real-Time Computation of Optimal Control".
*Mathematical and Computer Modelling***43**(9–10): 1172–1188. doi:10.1016/j.mcm.2005.05.021. - ↑ Ross, I. M.; Sekhavat, P.; Fleming, A.; Gong, Q. (2008). "Optimal Feedback Control: Foundations, Examples and Experimental Results for a New Approach".
*Journal of Guidance, Control and Dynamics***31**(2): 307–321. doi:10.2514/1.29532. Bibcode: 2008JGCD...31..307R. - ↑ I. M. Ross, R. J. Proulx, and M. Karpenko, "Unscented Optimal Control for Space Flight,"
*Proceedings of the 24th International Symposium on Space Flight Dynamics (ISSFD)*, May 5–9, 2014, Laurel, MD. - ↑ I. M. Ross, R. J. Proulx, M. Karpenko, and Q. Gong, "Riemann–Stieltjes Optimal Control Problems for Uncertain Dynamic Systems,"
*Journal of Guidance, Control, and Dynamics*, Vol. 38, No. 7 (2015), pp. 1251-1263. doi: 10.2514/1.G000505. - ↑ I. M. Ross, R. J. Proulx, M. Karpenko, "Unscented guidance,"
*American Control Conference,*2015, pp.5605-5610, 1–3 July 2015 doi: 10.1109/ACC.2015.7172217. - ↑
^{22.0}^{22.1}Ross, I. M.; Karpenko, M. (2012). "A Review of Pseudospectral Optimal Control: From Theory to Flight".*Annual Reviews in Control***36**(2): 182–197. doi:10.1016/j.arcontrol.2012.09.002. - ↑
^{23.0}^{23.1}^{23.2}W. Kang, I. M. Ross, Q. Gong, Pseudospectral optimal control and its convergence theorems, Analysis and Design of Nonlinear Control Systems, Springer, pp. 109–124, 2008. - ↑
^{24.0}^{24.1}B. S. Mordukhovich, Variational Analysis and Generalized Differentiation, I: Basic Theory, Vol. 330 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] Series, Springer, Berlin, 2005. - ↑
^{25.0}^{25.1}^{25.2}W. Kang, "Rate of Convergence for the Legendre Pseudospectral Optimal Control of Feedback Linearizable Systems",*Journal of Control Theory and Application*, Vol.8, No.4, 2010. pp.391-405. - ↑
^{26.0}^{26.1}Jr-; Li, S; Ruths, J.; Yu, T-Y; Arthanari, H.; Wagner, G. (2011). "Optimal Pulse Design in Quantum Control: A Unified Computational Method".*Proceedings of the National Academy of Sciences***108**(5): 1879–1884. doi:10.1073/pnas.1009797108. PMID 21245345. Bibcode: 2011PNAS..108.1879L. - ↑
^{27.0}^{27.1}N. Bedrossian, M. Karpenko, and S. Bhatt, "Overclock My Satellite: Sophisticated Algorithms Boost Satellite Performance on the Cheap",*IEEE Spectrum*, November 2012. - ↑
^{28.0}^{28.1}Stevens, R. E.; Wiesel, W. (2008). "Large Time Scale Optimal Control of an Electrodynamic Tether Satellite".*Journal of Guidance, Control and Dynamics***32**(6): 1716–1727. doi:10.2514/1.34897. Bibcode: 2008JGCD...31.1716S. https://zenodo.org/record/1235939. - ↑ Ioannidis, John P. A. (2023-10-04). "“October 2023 data-update for "Updated science-wide author databases of standardized citation indicators"”" (in en).
*Elsevier Data Repository, V6, doi: 10.17632/btchxktzyw.6***6**. doi:10.17632/btchxktzyw.6. https://elsevier.digitalcommonsdata.com/datasets/btchxktzyw/6. - ↑ P. Williams, "Application of Pseudospectral Methods for Receding
Horizon Control,"
*Journal of Guidance, Control and Dynamics*, Vol.27, No.2, pp.310-314, 2004. - ↑ Conway, Bruce A. (2011-09-15). "A Survey of Methods Available for the Numerical Optimization of Continuous Dynamic Systems".
*Journal of Optimization Theory and Applications***152**(2): 271–306. doi:10.1007/s10957-011-9918-z. ISSN 0022-3239. http://dx.doi.org/10.1007/s10957-011-9918-z. - ↑ B. Honegger, "NPS Professor's Software Breakthrough Allows Zero-Propellant Maneuvers in Space." Navy.mil. United States Navy. April 20, 2007. (Sept. 11, 2011) http://www.elissarglobal.com/wp-content/uploads/2011/07/Navy_News.pdf .
- ↑ Ross, Isaac (2020). "Enhancements to the DIDO Optimal Control Toolbox". arXiv:2004.13112 [math.OC].
- ↑
^{34.0}^{34.1}Q. Gong, W. Kang, N. Bedrossian, F. Fahroo, P. Sekhavat and K. Bollino, Pseudospectral Optimal Control for Military and Industrial Applications, 46th IEEE Conference on Decision and Control, New Orleans, LA, pp. 4128–4142, Dec. 2007. - ↑ A. M. Hawkins,
*Constrained Trajectory Optimization of a Soft Lunar Landing From a Parking Orbit,*S.M. Thesis, Dept. of Aeronautics and Astronautics, Massachusetts Institute of Technology, 2005. http://dspace.mit.edu/handle/1721.1/32431 - ↑ J. R. Rea,
*A Legendre Pseudospectral Method for Rapid Optimization of Launch Vehicle Trajectories,*S.M. Thesis, Dept. of Aeronautics and Astronautics, Massachusetts Institute of Technology, 2001. http://dspace.mit.edu/handle/1721.1/8608 - ↑ Stone, Lawrence; Royset, Johannes; Washburn, Alan (2016).
*Optimal Search for Moving Targets*. Switzerland: Springer. pp. 155–188. ISBN 978-3-319-26897-2. - ↑
^{38.0}^{38.1}^{38.2}W. Kang and N. Bedrossian, "Pseudospectral Optimal Control Theory Makes Debut Flight",*SIAM News*, Vol. 40, Page 1, 2007. - ↑ "International Space Station Zero-Propellant Maneuver (ZPM) Demonstration (ZPM) - 07.29.14". NASA.
- ↑ N. S. Bedrossian, S. Bhatt, W. Kang, and I. M. Ross, Zero-Propellant Maneuver Guidance,
*IEEE Control Systems Magazine*, October 2009 (Feature Article), pp 53–73. - ↑ TRACE Spacecraft's New Slewing Procedure,
*Space Daily*, December 28, 2010

## External links

Original source: https://en.wikipedia.org/wiki/I. Michael Ross.
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