ℒ1 Adaptive Control Design for SRS Robot Using Gaussian Process Regression

In this paper, a control scheme based on the combination of ℒ
₁
Adaptive Control (ℒ
₁
-AC) and Gaussian Process Regression (GPR) is presented so that in addition to maintaining the desired performance of the controller, be robustness to changing uncertainties at any time. In fact, ℒ
₁
-AC as the first part of the design, ensures transient performance and tradeoff between stability and robustness, while GPR as the second part, enables effective and safe learning of the dynamics of uncertainties. On the other hand, the determined dynamics of uncertainties can be easily applied to the ℒ
₁
-AC formulation, which is another reason for combining the two methods to improve performance. Therefore resulting dynamics can lead to a less conservative design for the tradeoff between robustness and stability. The performance of the proposed method is also evaluated on a Shoulder Rehabilitation System (SRS) with three degrees of freedom.