She was given a problem, and she solved it.

Illinois professor Naira Hovakimyan can relate to this statement more than once regarding her career in mathematics and mechanical engineering so far. Recently, the L1 adaptive control solution developed by her and former postdoctoral fellow Chengyu Cao, assistant professor of mechanical engineering at University of Connecticut, has gained attention from numerous organizations who utilize control systems.

It is rare for one innovation to have potential applications in numerous industries. From airplanes to oil production, the L1 adaptive control theory accomplishes this extraordinary feat.

A control system is a device to regulate the behavior of other devices or systems usually within complex machinery. L1 Adaptive Control provides a systematic methodology for synthesizing control architectures that guarantee uniform desired performance for complex systems in the presence of uncertainties and environmental disturbances. The L1 Adaptive Control allows for fast adaptation without losing robustness, which was a problem acknowledged in the development of adaptive control. Because of L1’s performance, the amount of gain scheduling—a common approach to control of non-linear systems—can be significantly reduced, which in its turn provides significant savings for control system design and development.

Arguably the most recognized application of L1 Adaptive Control is its use on airplanes to stabilize the plane during adverse conditions. In addition to being used as a safety mechanism, L1 Adaptive Control expands the flight envelope and allows for exploration of departure-prone edges of the flight envelope long enough to collect flight data for modeling those departure conditions.

It is well known that pilot-induced-oscillations are one of the major causes of airplane crashes. These oscillations occur when the pilot attempts to stabilize the aircraft in the presence of turbulence, or other uncertainties. This can be compared to driver’s actions when the driver tries to brake on a slippery road and the car slides, which is an unpredictable response for the driver. An airplane, being a much faster system than the pilot, can get into large oscillations due to the pilot’s corrective actions, leading to catastrophic failures of the overall system. With L1 Adaptive Control, the system quickly adapts to the failure—without any need for a corrective action from the pilot—and guarantees accurate performance specifications to ensure the safety of the aircraft.

Hovakimyan and Cao started L1 Adaptive Control in 2005, and have had many proposals for its use since then. Some other applications of L1 Adaptive Control include managed pressure drilling in oil production and exploration, anesthesia, and fiber optics. Caterpillar Inc. has also expressed interest in the L1 adaptive control for its production line. A more immediate function of L1 adaptive control will be applied to disk drive control through Seagate, a manufacturer in hard drives.

“By expanding the flight envelope, L1 Adaptive Control enables collection of flight data from new territories that are not yet explored,” Hovakimyan says. Using this data, new models can be constructed to test adaptive control software in more realistic situations. Because of the risks involved with human lives, Hovakimyan expects that the airplane manufacturers will take much longer adopting this adaptive controller for commercial aviation. However, NASA Langley Research Center is currently considering it as a potential replacement to their existing baseline controller.

Hovakimyan credits Ph.D. student Enric Xargay from the Aerospace Engineering Department of the University of Illinois for the success in the flight testing of the L1 Adaptive Control at NASA: “You can have the most beautiful theory at hand, but you also need a young, energetic and talented student, who would not mind investing himself into every aspect of the problem, from abstract mathematics up to the pilot’s perception of the flight control system, including the hardware and software details of the experimental platform, to demonstrate that the theory can be applied correctly and can deliver the performance according to theoretical predictions.  Enric Xargay was that student for me.”

When asked why she focuses on the aircraft potential for adaptive control, Hovakimyan replied that airplanes provide the “most beautiful demonstration of a control theory.”

Hovakimyan received a Ph.D. in Physics and Mathematics in 1992 from the Institute of Applied Mathematics in Moscow, Russia, majoring in optimal control and differential games. Without an engineering background, she assumed a six month visiting position at Georgia Tech in 1998, where she was challenged to contribute to the field of engineering by developing stability analysis for adaptive flight control systems. She took the challenge seriously, and appreciated the opportunity of talking to practitioners from the Boeing Co. and researchers from Air Force Research Labs, who provided her with precise and good problem formulations to address, as well as supported her in applying for faculty positions in the U.S. Shortly after, she was part of the Department of Aerospace and Ocean Engineering at Virginia Tech until 2008, when she came to the University of Illinois Urbana Champaign. She especially credits Kevin Wise, a senior technical fellow from the Boeing Co. for the precise problem formulation that led to the development of L1 Adaptive Control and for sharing his feedback from the application of prior adaptive control methods. Hovakimyan is currently a professor in the department of mechanical science and engineering, as well as a Schaller faculty scholar and University scholar. She is the 2011 recipient of AIAA’s Mechanics and Control of Flight award, “for ground breaking work in L1 robust adaptive control, vision-based guidance, navigation and control, and cooperative path planning of UAVs.”

Visit Naira Hovakimyan's website.

*Update as of November 2011: CU Aerospace and its use of L1 Adaptive Control were awarded a SBIR award from NASA for the development of bio-assistive devices for human-robotic exploration in space.