Deterministic near-optimal controls .2. Dynamic programming and viscosity solution approach

• 成果类型: Article
• 署名作者: Zhou, XY
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.21.3.655
• 发表日期: 1996
• 页码: 655-674
• 关键词: hamilton-jacobi equations; MAXIMUM PRINCIPLE

摘要

Near-optimization is as sensible and important as optimization for both theory and applications. This paper concerns dynamic near-optimization, or near-optimal controls, for systems governed by deterministic ordinary differential equations, and uses dynamic programming to study the near-optimality. Since nonsmoothness is inherent in this subject, the viscosity solution approach is employed to investigate the problem. The dynamic programming equation is derived in terms of epsilon-superdifferential/subdifferential. The relationships among the adjoint functions, the value functions, and the Hamiltonian along near-optimal trajectories are revealed. Verification theorems with which near-optimal feedback controls can be constructed are obtained.