Isaac Michael Ross is a Distinguished Professor and Program Director of Control and Optimization at the

Naval Postgraduate School Naval Postgraduate School (NPS) is a Naval command with a graduate university mission, operated by the United States Navy and located in Monterey, California. The NPS mission is to provide "defense-focused graduate education, including clas ...

in Monterey, CA. He has published a highly-regarded textbook on optimal control theoryI. M. Ross,
A Primer on Pontryagin’s Principle in Optimal Control
'' Second Edition, Collegiate Publishers, San Francisco, CA, 2015. and seminal papers in

pseudospectral optimal control Pseudospectral optimal control is a joint theoretical-computational method for solving optimal control problems. It combines pseudo-spectral method, pseudospectral (PS) theory with optimal control theory to produce a PS optimal control theory. ...

theory,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. 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. energy-sink theory, the optimization and deflection of near-Earth asteroids and comets,

robotics Robotics is the interdisciplinary study and practice of the design, construction, operation, and use of robots. Within mechanical engineering, robotics is the design and construction of the physical structures of robots, while in computer s ...

,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.

attitude dynamics and control Spacecraft attitude control is the process of controlling the orientation of a spacecraft (vehicle or satellite) with respect to an inertial frame of reference or another entity such as the celestial sphere, certain fields, and nearby objects, ...

, orbital mechanics, real-time optimal control, unscented optimal controlI. 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. and continuous optimization. The Kang–Ross–Gong theorem, Ross' lemma, Ross' time constant, the

Ross–Fahroo lemma Named after I. Michael Ross and F. Fahroo, the Ross–Fahroo lemma is a fundamental result in optimal control theory. I. M. Ross and F. Fahroo, A Pseudospectral Transformation of the Covectors of Optimal Control Systems, Proceedings of the First I ...

, and the

Ross–Fahroo pseudospectral method Introduced by I. Michael Ross and F. Fahroo, the Ross–Fahroo pseudospectral methods are a broad collection of pseudospectral methods for optimal control.N. Bedrossian, M. Karpenko, and S. Bhatt, "Overclock My Satellite: Sophisticated Algorit ...

are all named after him.B. S. Mordukhovich, Variational Analysis and Generalized Differentiation, I: Basic Theory, Vol. 330 of Grundlehren der Mathematischen Wissenschaften undamental Principles of Mathematical SciencesSeries, Springer, Berlin, 2005.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.N. Bedrossian, M. Karpenko, and S. Bhatt, "Overclock My Satellite: Sophisticated Algorithms Boost Satellite Performance on the Cheap", ''

IEEE Spectrum ''IEEE Spectrum'' is a magazine edited and published by the Institute of Electrical and Electronics Engineers. The first issue of ''IEEE Spectrum'' was published in January 1964 as a successor to ''Electrical Engineering''. In 2010, ''IEEE Spe ...

'', November 2012. According to a report published by Stanford University, Ross is one of the world's top 2% of scientists.

Theoretical contributions

Although Ross has made contributions to energy-sink theory,

and

planetary defense Asteroid impact avoidance encompasses the methods by which near-Earth objects (NEO) on a potential collision course with Earth could be diverted, preventing destructive impact events. An impact by a sufficiently large asteroid or other NEOs w ...

, he is best knownP. Williams, "Application of Pseudospectral Methods for Receding Horizon Control," ''Journal of Guidance, Control and Dynamics'', Vol.27, No.2, pp.310-314, 2004. for work on

. In 2001, Ross and Fahroo announced the

covector mapping principle The covector mapping principle is a special case of Riesz' representation theorem, which is a fundamental theorem in functional analysis. The name was coined by Ross and coauthors,Ross, I. M., “A Historical Introduction to the Covector Mapping ...

, first, as a special result in

, and later as a general result in

optimal control Optimal control theory is a branch of control theory that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations ...

. This principle was based on the

which proves that dualization and

discretization In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numeri ...

are not necessarily

commutative operation In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Perhaps most familiar as a pr ...

s and that certain steps must be taken to promote commutation. When

is commutative with dualization, then, under appropriate conditions,

Pontryagin's minimum principle Pontryagin's maximum principle is used in optimal control theory to find the best possible control for taking a dynamical system from one state to another, especially in the presence of constraints for the state or input controls. It states that i ...

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.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. Ross and his coworkers showed that the Legendre and

Chebyshev Pafnuty Lvovich Chebyshev ( rus, Пафну́тий Льво́вич Чебышёв, p=pɐfˈnutʲɪj ˈlʲvovʲɪtɕ tɕɪbɨˈʂof) ( – ) was a list of Russian mathematicians, Russian mathematician and considered to be the founding father o ...

pseudospectral discretizations converge to an optimal solution of a problem under the mild condition of boundedness of variations.

Software contributions

In 2001, Ross created

DIDO Dido ( ; , ), also known as Elissa ( , ), was the legendary founder and first queen of the Phoenician city-state of Carthage (located in Tunisia), in 814 BC. In most accounts, she was the queen of the Phoenician city-state of Tyre (located ...

, a software package for solving

problems. 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.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. DIDO is used for solving optimal control problems in aerospace applications,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 search theory, and

. Ross' constructs have been licensed to other software products, and have been used by

NASA The National Aeronautics and Space Administration (NASA ) is an independent agencies of the United States government, independent agency of the federal government of the United States, US federal government responsible for the United States ...

to solve flight-critical problems on the

International Space Station The International Space Station (ISS) is a large space station that was Assembly of the International Space Station, assembled and is maintained in low Earth orbit by a collaboration of five space agencies and their contractors: NASA (United ...

.W. Kang and N. Bedrossian, "Pseudospectral Optimal Control Theory Makes Debut Flight", ''

SIAM Thailand, officially the Kingdom of Thailand and historically known as Siam (the official name until 1939), is a country in Southeast Asia on the Mainland Southeast Asia, Indochinese Peninsula. With a population of almost 66 million, it spa ...

News'', Vol. 40, Page 1, 2007.

Flight contributions

In 2006, NASA used

to implement zero propellant maneuvering"International Space Station Zero-Propellant Maneuver (ZPM) Demonstration (ZPM) - 07.29.14"
NASA. of the

. In 2007, ''

News'' printed a page 1 article announcing the use of Ross' theory. This led other researchers to explore the mathematics of

theory. DIDO is also used to maneuver the Space Station and operate various ground and flight equipment to incorporate

autonomy In developmental psychology and moral, political, and bioethical philosophy, autonomy is the capacity to make an informed, uncoerced decision. Autonomous organizations or institutions are independent or self-governing. Autonomy can also be ...

and performance efficiency for nonlinear control systems.

Awards and distinctions

In 2010, Ross was elected a Fellow of the

American Astronautical Society Formed in 1954, the American Astronautical Society (AAS) is an independent scientific and technical group in the United States dedicated to the advancement of space science and space exploration. AAS supports NASA The National Aeronau ...

for "his pioneering contributions to the theory, software and flight demonstration of

." He also received (jointly with

Fariba Fahroo Fariba Fahroo is an American Persian mathematician, a program manager at the Air Force Office of Scientific Research, and a former program manager at the Defense Sciences Office. Along with I. M. Ross, she has published papers in pseudospectral op ...

), the

AIAA The American Institute of Aeronautics and Astronautics (AIAA) is a professional society for the field of aerospace engineering. The AIAA is the U.S. representative on the International Astronautical Federation and the International Council of ...

Mechanics and Control of Flight Award for "fundamentally changing the landscape of flight mechanics". His research has made headlines in ''SIAM News'', ''

IEEE The Institute of Electrical and Electronics Engineers (IEEE) is an American 501(c)(3) organization, 501(c)(3) public charity professional organization for electrical engineering, electronics engineering, and other related disciplines. The IEEE ...

Control Systems Magazine'',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. ''

'', and ''Space Daily''.TRACE Spacecraft's New Slewing Procedure, ''Space Daily'', December 28, 2010

References

External links