Minimax optimal control of uncertain quasi-integrable Hamiltonian systems with time-delayed bounded feedback

A minimax optimal control strategy for uncertain quasi-integrable Hamiltonian systems with time-delayed bounded feedback control is proposed. First, a quasi-integrable Hamiltonian system with time-delayed bounded control forces and uncertain excitation and system parameters is converted into a set of Itô stochastic differential equations without time delay. Then, the partially averaged Itô stochastic differential equations for the energy processes are derived by using the stochastic averaging method for quasi-integrable Hamiltonian systems. For these equations together with an appropriate performance index, a worst-case optimal control strategy is derived via solving a stochastic differential game problem. The worst-case disturbances and the optimal bounded controls are obtained by solving a Hamilton–Jacobi–Isaacs (HJI) equation. Finally, two examples are worked out in detail to illustrate the application and effectiveness of the proposed method.