Some Applications of Optimal Control Theory

Prof. Yossi Ben-Asher
Department of Aerospace Engineering
Technion – Israel Institute of Technology

Some applications of optimal control theory are presented for Aircraft, Maneuvering Rockets and Racing Cars.

  1. Aircraft: This study explores the effectiveness of applying optimal control techniques to the flight control law clearance problem. The main idea is to search for the worst-case combination of pilot commands and wind disturbances. The main criteria chosen were the angle-of-attack limit exceeding criterion in the longitudinal plane, and the angle-of-sideslip limit exceeding criterion in the lateral plane. Other criteria, such as load factor and side-force were also considered. The flight control system developed for this aircraft by the Institute of Flight System Dynamics (FSD) of Technische Universität München has been used for the clearance task.
  2. Maneuvering Rockets: The problem of optimizing the trajectories of aerodynamically maneuvering rockets is considered. The optimization objectives are the maximal range or the minimal control effort for a given range. Both terminal and path constraints are studied. The gradient method in function space is applied to solve the problem. It is shown to provide an easily implementable fast approximation for the solution. An extension to rockets maneuvering with pulse motors around a ballistic course is also provided.
  3. Racing Cars: A racing car controlling its acceleration and turn rate is considered, with a limitation on its maximal turning radius due to limited friction between the wheels and the ground.  The research extends Dubins’ seminal work for constant speed minimum-time trajectory. By applying optimal control theory, it determines six types of path primitives that the optimal path may comprise.

For all problems the optimal control theory is applied using Pontryagin’s Minimum Principle and, when applicable, employing Kelley’s Condition for singular arcs. All studied cases are supported and demonstrated by numerical optimization results based on both Pseudo-Spectral and Collocation methods.

The talk will be given in English

Wed, 16-12-2015, 16:30 (Gathering at 16:00)

Classroom 165, ground floor, Library, Aerospace Eng.

Light refreshments will be served before the lecture

Some Applications of Optimal Control Theory