Supervised Learning in Model Reference Adaptive Sliding Mode Control

The well known back-propagation algorithm has revolutionized machine learning and artificial intelligence, particularly in neural network applications. Although gradient descent-based algorithms are utilized in control applications, they are not as prevalent as in neural network applications. This discrepancy can be attributed to the successful development of various adaptation laws which ensure system stability while meeting the required design criteria. Many of these laws can be found in model reference adaptive control (MRAC) and adaptive sliding mode control (ASMC). This paper investigates the applicability of the Brandt-Lin (B-L) learning algorithm, mathematically equivalent to the back-propagation algorithm, in adaptive control applications. We find that combining the B-L learning algorithm with SMC yields a robust controller suitable for model reference adaptive sliding mode control (MRA-SMC). The controller is applicable to linear and a class of nonlinear dynamic systems and is suitable for efficient implementation. We derive the stability criteria for this controller and conduct simulations to study the adaptation’s impact on chattering. Our work exemplifies one approach to adopt the back-propagation algorithm in control applications.