Dissipation analysis and H∞ control of stochastic nonlinear systems based on Hamiltonian realization

This paper proposes a novel dissipation analysis and a constructive H∞ control method for stochastic nonlinear systems. First, we put forward a sufficient condition for the dissipation of stochastic nonlinear systems by completing their Hamiltonian realization. The internal structure and energy property of the system is explored as well. Then, we show that the dissipation property is preserved for parallel and feedback interconnected dissipative stochastic Hamiltonian systems. Moreover, based on the dissipation property of the subsystems, a feedback dissipation controller is proposed for series interacted dissipative stochastic Hamiltonian systems. Finally, we propose an H∞ controller based on the stochastic dissipative Hamiltonian realization of uncertain stochastic nonlinear systems and show that the Hamiltonian function can be chosen to construct a solution of Hamiltonian- Jacobi inequality. Numerical simulation results illustrate the effectiveness of the proposed method.