mathematics

I. Michael Ross

I. Michael Ross is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand I. Michael Ross rather than just read about it. In short: 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 and seminal papers in pseudospectral optimal control theory, energy-sink theory, the optimization and deflection of near-Earth asteroids and comets, robotics, attitude dynamics and control, orbital mech…

Key takeaways

I. Michael Ross belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect I. Michael Ross to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of I. Michael Ross from memory before moving on to harder problems.

Reference excerpt

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 and seminal papers in pseudospectral optimal control theory, energy-sink theory, the optimization and deflection of near-Earth asteroids and comets, robotics, attitude dynamics and control, orbital mechanics, real-time optimal control, unscented optimal control, continuous optimization and aeromaneuvering guidance and control. The Kang–Ross–Gong theorem, Ross' π lemma, Ross' time constant, the Ross–Fahroo lemma, and the Ross–Fahroo pseudospectral method are all named after him. 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, attitude dynamics and control and planetary defense, he is best known for work on pseudospectral optimal control. In 2001, Ross and Fahroo announced the covector mapping principle, first, as a special result in pseudospectral optimal control, and later as a general result in optimal control. This principle was based on the Ross–Fahroo lemma which proves 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. 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.

Software contributions In 2001, Ross created DIDO, a software package for solving optimal control 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. DIDO is used for solving optimal control problems in aerospace applications, search theory, 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.

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

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, IEEE Control Systems Magazine, IEEE Spectrum, and Space Daily.

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

External links Elissar Global

Worked examples

Example 1 — a first encounter with I. Michael Ross

Start with the simplest possible case. Write down what I. Michael Ross claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to I. Michael Ross before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about I. Michael Ross ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of I. Michael Ross

In research: I. Michael Ross appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses I. Michael Ross in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: I. Michael Ross is common in secondary-school and first-year university syllabi. It links to neighbouring topics 21st-century American mathematicians, American aerospace engineers, Living people, so understanding it makes those chapters shorter.
In everyday life: Look for I. Michael Ross outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study I. Michael Ross in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what I. Michael Ross means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain I. Michael Ross out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is I. Michael Ross in simple terms?

Why does I. Michael Ross matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study I. Michael Ross?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on I. Michael Ross.