A family of adaptive H controllers for switched dissipative Hamiltonian systems

This paper investigates adaptive H control problem for switched dissipative Hamiltonian systems (SDHSs). Firstly, using the dissipative Hamiltonian structural properties, such systems generated an augmented SDHS, with which some results on the controller design are then obtained. When there are external disturbances and parameter perturbations in such systems, a family of adaptive H controller is designed using the multiple Lyapunov functions (MLFs). Secondly, an algorithm for solving parameters of controllers is proposed with symbolic computation. The proposed method avoids solving Hamilton-Jacobi-Issacs inequalities (equations), and the obtained controllers are relatively simple in form and easy in operation. Finally, a numerical example is studied by using the new results proposed in this paper to SDHSs with external disturbances and parameter perturbations, and some numerical simulations are carried out to support our new results.