Hamiltonian‐driven adaptive dynamic programming for mixedH₂/H∞performance using sum‐of‐squares

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.