Optimal state feedback control for port-Hamiltonian systems : A shifted Hamiltonian approach integrating disturbance attenuation and adaptive parameter estimation

Abstract

This paper addresses the optimal control problem for Port-Hamiltonian (PH) systems, focusing to minimize state error and control energy, where the desired state is not necessarily at the origin. By leveraging the Hamilton-Jacobi-Bellman (HJB) equation, an improved optimal state feedback control law is derived to minimize a quadratic cost function. First, departing from conventional energy-shaping paradigms, this work develops a shifted Hamiltonian function that decouples stability analysis from optimality constraints, effectively resolving the conflict between asymptotic stabilization and performance metrics. Second, by incorporating disturbance $L_2$-gain attenuation, the proposed framework achieves asymptotic stability under external perturbations. Third, a parameter estimator with adaptive law is established for uncertain parameters. Simulation results verify that the proposed control scheme is feasible and effective.