Composite Adaptive Control for Euler-Lagrange Systems with Additive Disturbances

In a typical adaptive update law, the rate of adaptation is generally a function of the state feedback error.

Ideally, the adaptive update law would also include some feedback of the parameter estimation error.

The desire to include some measurable form of the parameter estimation error in the adaptation law

resulted in the development of composite adaptive update laws that are functions of a prediction error

and the state feedback. In all previous composite adaptive controllers, the formulation of the prediction

error is predicated on the critical assumption that the system uncertainty is linear in the uncertain

parameters (LP uncertainty). The presence of additive disturbances that are not LP would destroy the

prediction error formulation and stability analysis arguments in previous results. In this paper, a new

prediction error formulation is constructed through the use of a recently developed Robust Integral of

the Sign of the Error (RISE) technique. The contribution of this design and associated stability analysis is

that the prediction error can be developed even with disturbances that do not satisfy the LP assumption

(e.g., additive bounded disturbances). A composite adaptive controller is developed for a general MIMO

Euler–Lagrange system with mixed structured (i.e., LP) and unstructured uncertainties. A Lyapunov-based

stability analysis is used to derive sufficient gain conditions under which the proposed controller yields

semi-global asymptotic tracking. Experimental results are presented to illustrate the approach.