Optimization-based control by interconnection of nonlinear port-Hamiltonian systems

Abstract

In this paper, we develop a control-by-interconnection approach for the stabilization of nonlinear port-Hamiltonian systems. Motivated by model predictive control, the controller is realized as a continuous-time primal-dual gradient flow associated with a finite-horizon, control-constrained optimal control problem. By exploiting its port-Hamiltonian structure, the optimization dynamics are interconnected with the nonlinear plant. Introducing a time-scale parameter for the optimization dynamics reveals a singularly perturbed closed-loop system, whose reduced dynamics correspond to the optimal finite-horizon feedback, while the boundary-layer dynamics capture convergence of the primal-dual variables to the optimality system. Using a composite Lyapunov function and singular-perturbation arguments, we prove asymptotic stability of the coupled plant-controller dynamics, which is local for sufficiently fast optimization dynamics and becomes global under additional assumptions. Numerical experiments for a nonlinear port-Hamiltonian oscillator illustrate the results.