Learning feedback Nash strategies for nonlinear port-Hamiltonian systems

Abstract

This paper presents an adaptive control strategy for solving multi-player noncooperative differential games with dynamics modelled as general nonlinear input-state-output port-Hamiltonian systems. The proposed controller is obtained by extending an existing single-player feedback Nash strategy to N players and by using the Hamiltonian of the port-Hamiltonian system as an admissible control-Lyapunov function for each player. Necessary and sufficient conditions for the stability of the resulting controlled system are provided by employing Lyapunov stability theory. Furthermore, the N player feedback strategy is extended by adaptively weighting the individual value functions to ensure convergence to the Nash solution. Finally, numerical simulations demonstrate the effectiveness of the proposed explicit control laws.

Keywords:

• Port-Hamiltonian systems
• noncooperative differential game
• Hamilton–Jacobi–Bellman equation
• feedback Nash equilibrium

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Deutsche Forschungsgemeinschaft [grant number HO 4738/3-1; project number 360464149].