A. Kurzhanski, P. Varaiya
Feb 1, 2001
Citations
6
Influential Citations
164
Citations
Quality indicators
Journal
Journal of Optimization Theory and Applications
Abstract
This paper uses dynamic programming techniques to describe reach sets andrelated problems of forward and backward reachability. The original problemsdo not involve optimization criteria and are reformulated in terms ofoptimization problems solved through the Hamilton–Jacobi–Bellmanequations. The reach sets are the level sets of the value function solutionsto these equations. Explicit solutions for linear systems with hard boundsare obtained. Approximate solutions are introduced and illustrated forlinear systems and for a nonlinear system similar to that of theLotka–Volterra type.