Energy‐based output regulation for stochastic port‐Hamiltonian systems

Abstract

This article investigates the output regulation for stochastic port‐Hamiltonian systems (SPHSs) subject to sinusoidal disturbances. An energy‐based regulation scheme with an internal model unit is proposed by exploiting the stochastic Hamiltonian structure, which drives the tracking error to the origin while maintaining asymptotical stability in probability of the closed‐loop system. An energy‐based robust regulation scheme as well as an alternative condition is then developed without solving Hamilton–Jacobi–Issacs inequalities. The proposed regulators preserve the stochastic Hamiltonian structure of the disturbed SPHS by coordinate transformation. Hence the output regulation problems fall into the stabilization framework for SPHSs and there is no need to solve regulator equations. These results cover the stabilization of SPHSs and the output regulation of deterministic port‐Hamiltonian systems. Simulations on an inverted pendulum show the effectiveness of the proposed methods.

Adaptive interconnection and damping assignment passivity‐based control for an underactuated cable‐driven robot

“…In contrast to the classical passivity method, where the storage function does not represent necessarily the closed-loop energy, 5 IDA-PBC may be applied to a widespread class of systems by shaping total energy such that the closed-loop system has a port Hamiltonian representation. 6,7 For this purpose, the desired equations of the closed-loop system are considered and all corresponding Hamiltonian functions are obtained from the solution of some partial differential equations (PDEs) which are called matching equations. 8 See Reference 9 and its references for some of the applications of this method.…”