On Adaptive Control of Unactuated Dynamical Systems through Interconnections with Stability and Performance Guarantees

Experimental Results of a Model Reference Adaptive Control Approach on an Interconnected Uncertain Dynamical System

“…This thesis demonstrates the experimental validation of a recently proposed adaptive control architecture in [1] on a benchmark mechanical system setup composed of two carts connected by a spring to show the efficacy of this architecture in practice, to appear in [3]. It has been shown that through enforcing performance guarantees individually on the actuated and unactuated portions of the interconnected dynamical system, the respective system error trajectories are restricted to user-defined compact sets.…”

“…In (2.3) and (2.4), H 0 ∈ R q×n and J 0 ∈ R m×p are known parts of the physical interconnection while H ∆ ∈ R q×n and J ∆ ∈ R m×p are their unknown parts. Note that the objective of [1] is to design a control signal for the actuated dynamics given by (2.2) such that the trajectories of the actuated dynamics follow the trajectories of a desired reference model, the trajectories of the unactuated dynamics given by (2.1) follow the trajectories of a desired reference model, and the respective system error trajectories of the actuated and unactuated dynamics are restricted to a-priori, user-defined compact sets enforcing performance guarantees. To begin, the following necessary definition from [4] (also used in [1]) is provided.…”

“…We start with outlining the key aspects of the proposed adaptive control architecture in [1], in which the control and performance enforcement of the unactuated dynamics is accomplished through the physical interconnection with the actuated dynamics. Specifically, the previously proposed control is applied to stabilize the overall interconnected system in the presence of unknown physical interconnections as well as uncertainties in both the actuated and unactuated dynamics.…”

“…In this thesis, an experimental study is provided on a benchmark mechanical system setup. In particular, this platform is composed of an actuated cart coupled with an unactuated cart through a spring, and is used to experimentally demonstrate the proposed adaptive control approach of [1]. We are now ready to state the notation used throughout this thesis.…”

Adaptive control of unactuated dynamical systems through interconnections: Stability and performance guarantees

“…Finally, we note here that a preliminary conference version of this article appeared in Reference . The present article significantly goes beyond this preliminary conference article in the sense that (i) a more extensive literature review is included, (ii) additional remarks are included to discuss and further motivate the proposed control architecture, (iii) detailed proofs of all results are included, and (iv) additional simulation studies are provided.…”