A Reachable Set Analysis Method for Generating Near-Optimal Trajectories of Constrained Multiphase Systems

Christian M. Chilan () and Bruce A. Conway ()
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Christian M. Chilan: University of Illinois, 306 Talbot Laboratory, MC-236
Bruce A. Conway: University of Illinois, 306 Talbot Laboratory, MC-236

Journal of Optimization Theory and Applications, 2015, vol. 167, issue 1, No 9, 194 pages

Abstract: Abstract Few sophisticated problems in the optimal control of a dynamical system can be solved analytically. There are many numerical solution methods, but most, especially those with the most potential accuracy, work iteratively and must be initialized with a guess of the solution. Satisfactory guesses may be very difficult to generate. In this work, a “Reachable Set Analysis” (RSA) method is developed to find near-optimal trajectories for multiphase systems with no a priori knowledge. A multiphase system is a generalization of a dynamical system that includes possible changes on the governing equations throughout the trajectory; the traditional dynamical system where the governing equations do not change is included in the formulation as a special case. The RSA method is based on a combination of metaheuristic algorithms and nonlinear programming. A particularly beneficial aspect of the solution found using RSA is that it satisfies the system governing equations and comes arbitrarily close (to a degree chosen by the planner) to satisfying given terminal conditions. Three qualitatively different multiphase problems, such as a low-thrust transfer from Earth to Mars, a system with chattering arcs in the optimal control, and a motion planning problem with obstacles, are solved using the near-optimal trajectories found by RSA as initial guesses to show the effectiveness of the new method.

Keywords: Trajectory optimization; Obstacle avoidance; Evolutionary algorithms; Nonlinear programming; Reachable sets; 49M37; 65C35 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-014-0651-2

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