I. Michael Ross

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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] unscented optimal control [19] [20] [21] and continuous optimization [22] [23] [24] . The Kang–Ross–Gong theorem, [25] [26] Ross' π lemma, Ross' time constant, the Ross–Fahroo lemma, and the Ross–Fahroo pseudospectral method are all named after him. [27] [28] [29] [30] [31] According to a report published by Stanford University, [32] Ross is one of the world's top 2% of scientists.

Contents

Theoretical contributions

Although Ross has made contributions to energy-sink theory, attitude dynamics and control and planetary defense, he is best known [27] [28] [29] [31] [33] 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 [28] 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. [26] 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. [26]

Software contributions

In 2001, Ross created DIDO, a software package for solving optimal control problems. [34] [35] [36] 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. [37] DIDO is used for solving optimal control problems in aerospace applications, [38] [39] search theory, [40] 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. [41]

Flight contributions

In 2006, NASA used DIDO to implement zero propellant maneuvering [42] of the International Space Station. In 2007, SIAM News printed a page 1 article [41] announcing the use of Ross' theory. This led other researchers [37] 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. [25]

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, [41] IEEE Control Systems Magazine, [43] IEEE Spectrum , [30] and Space Daily. [44]

See also

Related Research Articles

<span class="mw-page-title-main">Optimal control</span> Mathematical way of attaining a desired output from a dynamic system

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 research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the Moon with minimum fuel expenditure. Or the dynamical system could be a nation's economy, with the objective to minimize unemployment; the controls in this case could be fiscal and monetary policy. A dynamical system may also be introduced to embed operations research problems within the framework of optimal control theory.

Trajectory optimization is the process of designing a trajectory that minimizes some measure of performance while satisfying a set of constraints. Generally speaking, trajectory optimization is a technique for computing an open-loop solution to an optimal control problem. It is often used for systems where computing the full closed-loop solution is not required, impractical or impossible. If a trajectory optimization problem can be solved at a rate given by the inverse of the Lipschitz constant, then it can be used iteratively to generate a closed-loop solution in the sense of Caratheodory. If only the first step of the trajectory is executed for an infinite-horizon problem, then this is known as Model Predictive Control (MPC).

The Gauss pseudospectral method (GPM), one of many topics named after Carl Friedrich Gauss, is a direct transcription method for discretizing a continuous optimal control problem into a nonlinear program (NLP). The Gauss pseudospectral method differs from several other pseudospectral methods in that the dynamics are not collocated at either endpoint of the time interval. This collocation, in conjunction with the proper approximation to the costate, leads to a set of KKT conditions that are identical to the discretized form of the first-order optimality conditions. This equivalence between the KKT conditions and the discretized first-order optimality conditions leads to an accurate costate estimate using the KKT multipliers of the NLP.

Pseudospectral optimal control is a joint theoretical-computational method for solving optimal control problems. It combines pseudospectral (PS) theory with optimal control theory to produce a PS optimal control theory. PS optimal control theory has been used in ground and flight systems in military and industrial applications. The techniques have been extensively used to solve a wide range of problems such as those arising in UAV trajectory generation, missile guidance, control of robotic arms, vibration damping, lunar guidance, magnetic control, swing-up and stabilization of an inverted pendulum, orbit transfers, tether libration control, ascent guidance and quantum control.

DIDO is a MATLAB optimal control toolbox for solving general-purpose optimal control problems. It is widely used in academia, industry, and NASA. Hailed as a breakthrough software, DIDO is based on the pseudospectral optimal control theory of Ross and Fahroo. The latest enhancements to DIDO are described in Ross.

In applied mathematics, the pseudospectral knotting method is a generalization and enhancement of a standard pseudospectral method for optimal control. The concept was introduced by I. Michael Ross and F. Fahroo in 2004, and forms part of the collection of the Ross–Fahroo pseudospectral methods.

The Legendre pseudospectral method for optimal control problems is based on Legendre polynomials. It is part of the larger theory of pseudospectral optimal control, a term coined by Ross. A basic version of the Legendre pseudospectral was originally proposed by Elnagar and his coworkers in 1995. Since then, Ross, Fahroo and their coworkers have extended, generalized and applied the method for a large range of problems. An application that has received wide publicity is the use of their method for generating real time trajectories for the International Space Station.

The Chebyshev pseudospectral method for optimal control problems is based on Chebyshev polynomials of the first kind. It is part of the larger theory of pseudospectral optimal control, a term coined by Ross. Unlike the Legendre pseudospectral method, the Chebyshev pseudospectral (PS) method does not immediately offer high-accuracy quadrature solutions. Consequently, two different versions of the method have been proposed: one by Elnagar et al., and another by Fahroo and Ross. The two versions differ in their quadrature techniques. The Fahroo–Ross method is more commonly used today due to the ease in implementation of the Clenshaw–Curtis quadrature technique. In 2008, Trefethen showed that the Clenshaw–Curtis method was nearly as accurate as Gauss quadrature. This breakthrough result opened the door for a covector mapping theorem for Chebyshev PS methods. A complete mathematical theory for Chebyshev PS methods was finally developed in 2009 by Gong, Ross and Fahroo.

<span class="mw-page-title-main">Dragoslav D. Šiljak</span>

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Introduced by I. Michael Ross and F. Fahroo, the Ross–Fahroo pseudospectral methods are a broad collection of pseudospectral methods for optimal control. Examples of the Ross–Fahroo pseudospectral methods are the pseudospectral knotting method, the flat pseudospectral method, the Legendre-Gauss-Radau pseudospectral method and pseudospectral methods for infinite-horizon optimal control.

<span class="mw-page-title-main">Zero-propellant maneuver</span>

A zero-propellant maneuver (ZPM) is an optimal attitude trajectory used to perform spacecraft rotational control without the need to use thrusters. ZPMs are designed for spacecraft that use momentum storage actuators. Spacecraft ZPMs are used to perform large angle rotations or rate damping (detumbling) without saturating momentum actuators, and momentum dumping without thrusters.

Named after I. Michael Ross and F. Fahroo, the Ross–Fahroo lemma is a fundamental result in optimal control theory.

The Bellman pseudospectral method is a pseudospectral method for optimal control based on Bellman's principle of optimality. It is part of the larger theory of pseudospectral optimal control, a term coined by Ross. The method is named after Richard E. Bellman. It was introduced by Ross et al. first as a means to solve multiscale optimal control problems, and later expanded to obtain suboptimal solutions for general optimal control problems.

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, It provides conditions under which dualization can be commuted with discretization in the case of computational optimal control.

Ross' π lemma, named after I. Michael Ross, is a result in computational optimal control. Based on generating Carathéodory-π solutions for feedback control, Ross' π-lemma states that there is fundamental time constant within which a control solution must be computed for controllability and stability. This time constant, known as Ross' time constant, is proportional to the inverse of the Lipschitz constant of the vector field that governs the dynamics of a nonlinear control system.

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 optimal control theory. The Ross–Fahroo lemma and the Ross–Fahroo pseudospectral method are named after her. In 2010, she received, the AIAA Mechanics and Control of Flight Award for fundamental contributions to flight mechanics.

The flat pseudospectral method is part of the family of the Ross–Fahroo pseudospectral methods introduced by Ross and Fahroo. The method combines the concept of differential flatness with pseudospectral optimal control to generate outputs in the so-called flat space.

A Carathéodory-π solution is a generalized solution to an ordinary differential equation. The concept is due to I. Michael Ross and named in honor of Constantin Carathéodory. Its practicality was demonstrated in 2008 by Ross et al. in a laboratory implementation of the concept. The concept is most useful for implementing feedback controls, particularly those generated by an application of Ross' pseudospectral optimal control theory.

GPOPS-II is a general-purpose MATLAB software for solving continuous optimal control problems using hp-adaptive Gaussian quadrature collocation and sparse nonlinear programming. The acronym GPOPS stands for "General Purpose OPtimal Control Software", and the Roman numeral "II" refers to the fact that GPOPS-II is the second software of its type.

In mathematics, unscented optimal control combines the notion of the unscented transform with deterministic optimal control to address a class of uncertain optimal control problems. It is a specific application of Riemmann-Stieltjes optimal control theory, a concept introduced by Ross and his coworkers.

References

  1. ↑ I. M. Ross, A Primer on Pontryagin’s Principle in Optimal Control, Second Edition, Collegiate Publishers, San Francisco, CA, 2015.
  2. 1 2 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.
  3. ↑ 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.
  4. ↑ 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.
  5. 1 2 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.
  6. ↑ 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. hdl:10945/29675. S2CID   7106469.
  7. ↑ Ross, I. M. (1996). "Formulation of Stability Conditions for Systems Containing Driven Rotors". Journal of Guidance, Control and Dynamics. 19 (2): 305–308. Bibcode:1996JGCD...19..305R. doi:10.2514/3.21619. hdl:10945/30326. S2CID   121987998.
  8. ↑ Ross, I. M. (1993). "Nutational Stability and Core Energy of a Quasi-rigid Gyrostat". Journal of Guidance, Control and Dynamics. 16 (4): 641–647. Bibcode:1993JGCD...16..641R. doi:10.2514/3.21062. hdl:10945/30324. S2CID   122480792.
  9. ↑ 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. S2CID   123431410.
  10. ↑ 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. Bibcode:1999JGCD...22..415P. doi:10.2514/2.4413.
  11. ↑ 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.
  12. ↑ 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. Bibcode:2009JGCD...32.1039G. doi:10.2514/1.39697.
  13. ↑ 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. Bibcode:2010JGCD...33..160F. doi:10.2514/1.43549. S2CID   120117410.
  14. ↑ 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. Bibcode:2003JGCD...26..657R. doi:10.2514/2.5095.
  15. ↑ 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. Bibcode:2002JGCD...25..818R. doi:10.2514/2.4951.
  16. ↑ 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
  17. ↑ 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.
  18. ↑ 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. Bibcode:2008JGCD...31..307R. CiteSeerX   10.1.1.301.1423 . doi:10.2514/1.29532.
  19. ↑ 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.
  20. ↑ 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.
  21. ↑ 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. ↑ Ross, I.M. (July 2019). "An optimal control theory for nonlinear optimization". Journal of Computational and Applied Mathematics. 354: 39–51. doi:10.1016/j.cam.2018.12.044. ISSN   0377-0427.
  23. ↑ Ross, Isaac M. (2023-03-31). "Derivation of Coordinate Descent Algorithms from Optimal Control Theory". Operations Research Forum. 4 (2). doi:10.1007/s43069-023-00215-6. ISSN   2662-2556.
  24. ↑ Ross, I.M. (May 2023). "Generating Nesterov's accelerated gradient algorithm by using optimal control theory for optimization". Journal of Computational and Applied Mathematics. 423: 114968. doi:10.1016/j.cam.2022.114968. ISSN   0377-0427.
  25. 1 2 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.
  26. 1 2 3 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.
  27. 1 2 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.
  28. 1 2 3 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.
  29. 1 2 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. Bibcode:2011PNAS..108.1879L. doi: 10.1073/pnas.1009797108 . PMC   3033291 . PMID   21245345.
  30. 1 2 N. Bedrossian, M. Karpenko, and S. Bhatt, "Overclock My Satellite: Sophisticated Algorithms Boost Satellite Performance on the Cheap", IEEE Spectrum , November 2012.
  31. 1 2 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. Bibcode:2008JGCD...31.1716S. doi:10.2514/1.34897.
  32. ↑ Ioannidis, John P. A. (2023-10-04). ""October 2023 data-update for "Updated science-wide author databases of standardized citation indicators""". Elsevier Data Repository, V6, doi: 10.17632/btchxktzyw.6. 6. doi:10.17632/btchxktzyw.6.
  33. ↑ P. Williams, "Application of Pseudospectral Methods for Receding Horizon Control," Journal of Guidance, Control and Dynamics, Vol.27, No.2, pp.310-314, 2004.
  34. ↑ 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. S2CID   10469414.
  35. ↑ 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 Archived 2016-03-04 at the Wayback Machine .
  36. ↑ Ross, Isaac (2020). "Enhancements to the DIDO Optimal Control Toolbox". arXiv: 2004.13112 [math.OC].
  37. 1 2 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.
  38. ↑ 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
  39. ↑ 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
  40. ↑ Stone, Lawrence; Royset, Johannes; Washburn, Alan (2016). Optimal Search for Moving Targets. Switzerland: Springer. pp. 155–188. ISBN   978-3-319-26897-2.
  41. 1 2 3 W. Kang and N. Bedrossian, "Pseudospectral Optimal Control Theory Makes Debut Flight", SIAM News, Vol. 40, Page 1, 2007.
  42. ↑ "International Space Station Zero-Propellant Maneuver (ZPM) Demonstration (ZPM) - 07.29.14". NASA.
  43. ↑ 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.
  44. ↑ TRACE Spacecraft's New Slewing Procedure, Space Daily, December 28, 2010
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