Idempotent Methods for Control and Games
Abstract
Research into application of max-plus (and mode general idempotent) algebra based methods for solution of nonlinear control and estimation problems was undertaken. Such problems are typically solved via the method of dynamic programming, which converts the problems into partial differential equations (PDEs). However that approach is subject to the well-known curse-of-dimensionality when classical grid-based methods are applied to solve the PDEs. The term "curse-of-dimensionality" refers to the fact that the computational complexity grows exponentially fast as the dimension of the state space increases, and has typically forbidden the use of such approaches to real-world applications for well over a half-century. The methods developed in this effort are not subject to the that tremendous computational complexity growth. They are subject to a certain curse-of -complexity; however that is addressed via optimal idempotent projections, which may be instantiated as pruning operations. Specific research topics addressed include extension of these methods to nonlinear stochastic control problems, nonlinear robust estimation problems, quantum-spin control, certain classes of dynamic games, and solution of classes of linear, infinite-dimensional control problems.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 10, 2013
- Accession Number
- ADA590145
Entities
People
- William M. McEneaney
Organizations
- University of California, San Diego