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Hamiltonian‐driven adaptive dynamic programming for mixed H 2 / H ∞ performance using sum‐of‐squares
Author(s) -
Yang Yongliang,
Mazouchi Majid,
Modares Hamidreza
Publication year - 2021
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5341
Subject(s) - nash equilibrium , hamiltonian (control theory) , robustness (evolution) , mathematical optimization , mathematics , explained sum of squares , dynamic programming , computer science , biochemistry , chemistry , statistics , gene
In this article, the mixed H 2 / H ∞ performance optimization is first formulated as a nonzero‐sum game, of which the sufficient condition guaranteeing the existence of the Nash equilibrium is derived using the Hamilton–Jacobi (HJ) theory. Then, Hamiltonian‐driven inequalities are presented to evaluate the H 2 and H ∞ performances. Using this Hamiltonian‐inequality driven approach, the coupled HJ equations arising from finding the Nash equilibrium are relaxed to the HJ inequality constraints. A novel mixed policy iteration (PI) algorithm is developed that uses sum‐of‐squares (SOS) program in policy evaluation step, and consists of an H 2 performance improvement step and an H ∞ performance guarantee step. This constrained‐driven approach allows us to present a PI algorithm that takes into account both robustness and performance objectives. Finally, a numerical simulation is carried out to highlight the efficacy of the proposed framework.