#### Control Seminar

# Duality for Convexification of Autonomous Control Problems

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Many future engineering applications will require dramatic increases in our existing Autonomous Control capabilities. These include robotic sample return missions to planets, comets, and asteroids, formation flying spacecraft applications, applications utilizing swarms of autonomous agents, unmanned aerial, ground, and underwater vehicles, and autonomous commercial robotic applications. A key control challenge for many autonomous systems is to achieve the performance goals safely with minimal resource use in the presence of mission constraints and uncertainties. In principle these problems can be formulated and solved as optimization problems. The challenge is solving them reliably onboard the autonomous system in real time.

Our research has provided new analytical results that enabled the formulation of many autonomous control problems in a convex optimization framework, i.e., convexification of the control problem. The main mathematical theory used in achieving convexication is the duality theory of optimization. Duality theory manifests itself as Pontryagin's Maximum Principle in infinite dimensional optimization problems and as KKT conditions infinite dimensional parameter optimization problems. Both theories were instrumental in our developments. Our analytical framework also allowed the computation of the precise bounds of performance for a control system, e.g., the bounds of agility for a vehicle, so that we can make accurate quantification of the capabilities enabled. This proved to be an important step in rigorous V&V of the resulting control decision making algorithms.

This presentation introduces several real-world examples where this approach either produced dramatically improved performance over the heritage technology or enabled a new technology. A particularly important application is the fuel optimal control for planetary soft landing, whose complete solution has been an open problem since the Apollo Moon landings of 1960s. We developed a novel "lossless convexication" method of solution, which will enable the next generation planetary missions, such as Mars robotic sample return and manned missions. Another interesting example is Markov chain synthesis with temporal and spatial safety constraints.

Behcet Acikmese is an Assistant Professor in the Department of Aerospace Engineering and Engineering Mechanics at the University of Texas at Austin. He received his Ph.D. in Aerospace Engineering from Purdue University. He joined NASA Jet Propulsion Lab·oratory (JPL) in 2003. He was a senior technologist at JPL and a lecturer in GALCIT at Caltech. At JPL, Dr. Acikmese developed control algorithms for planetary landing, formation flying spacecraft, and asteroid and comet sample return missions. He was the developer of the flyaway control algorithms in Mars Science Laboratory, which successfully landed on Mars in August 2012, and the reaction control system (RCS) control algorithms for NASA SMAP mission, which will be ? own in 2014. Dr. Acikmese developed a novel real-time convex optimization based planetary landing guidance algorithm that was flight tested by NASA JPL, which is a first demonstration of a real-time optimization algorithm for onboard guidance of a rocket, showing dramatic performance improvements over the existing state-of-the-art techniques. Dr. Acikmese is an Associate Fellow of AIAA and a senior member of IEEE.