Dynamic Optimization for Reachability Problems

A. B. Kurzhanski and P. Varaiya

Journal of Optimization Theory and Applications, 2001, vol. 108, issue 2, No 1, 227-251

Abstract: 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.

Keywords: reachability; target sets; Hamiltonians; dynamic programming; Hamilton–Jacobi–Bellman equations; nonlinear systems; convex analysis (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (1)

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DOI: 10.1023/A:1026497115405

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