Relaxation and Customization Techniques for Optimal Control and Dynamic Games
Abstract
APPROVED FOR PUBLIC RELEASE Many practical problems arising in logistics and engineering can be expressed as optimization problems., For example, ship scheduling and routing problems can be formulated as mixed integer linear programs. Precision landing of aircraft, on deck and trajectory planning for underwater vehicles can be modeled as nonlinear optimal control problems. Combat can be modeled, as games where each agent is solving an optimization problem. Because of non-convexity, each of these problems is challenging to so,lve. The solution process can be aided by relaxation techniques and algorithmic customization. While progress has been made in both,since the 1980s, a significant gap remains -- particularly in the area of real-time optimization where algorithms must be fast and p,rovably convergent. The pervasive trend toward autonomy necessitates that this gap be closed. The proposed project objective is to,enable real-time optimization for broader classes of problems through relaxation and algorithmic customization. The research focus i,s infinite-dimensional optimization problems arising from optimal control and game theory. This focus is directly aligned with that,of the ``Computational Methods for Decision Making -- Resource Optimization" program at ONR, which is interested in the construction, of new mathematical theories for problems such as command and control, mission planning, and interdiction. The proposed research pl,an is built upon a strong foundation of preliminary research, and it consists of three thrusts. 1. Expand applicability of relaxati,on techniques to broader classes of problems 2. Customize algorithms for efficient numerical solution 3. Develop new computational m,ethods for Nash equilibria and swarm problems Anticipated outcomes of this work include mathematical theories and numerical algorit,hms for efficient solution of optimization problems. Motivating problems include precision aircraft landings, mission planning of mu,lti-agent systems such as underwater vehicles, game-theoretic problems such as interdiction, and others of the operations research t,ype.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 08, 2022
- Source ID
- N000142212131
Entities
People
- Matthew W. Harris
Organizations
- Office of Naval Research
- United States Navy
- Utah State University