Discrete-Time Model Reference Adaptive Control of Uncertain Dynamical Systems in the Presence of Coupled Dynamics

An uncertain system with coupled dynamics can lead to poor tracking performance or even unstability when using control techniques that are classified as discrete-time or continuous-time. It should be noted that achieving the Lyapunov stability of the uncertain systems in the presence of coupled dynamics with discrete-time model reference adaptive control techniques typically result in unavoidable complexity. This makes it difficult to generalize successful continuous-time adaptive control results to discrete-time environments. Thus, this work proposes a model reference adaptive control architecture based on a discrete-time setting to deal with systems in the presence of uncertainties and coupled dynamics. This is achieved by using observer dynamics, where the tracking error between the system state and the reference model is shown to be asymptotically stable using a Lyapunov function composed of logarithmic and quadratic functions. An illustrative example is also presented to show the efficacy of the discrete-time model reference adaptive control architecture over the standard counterpart.