A dual adaptive control theory inspired by Hebbian associative learning

Hebbian associative learning is a common form of neuronal adaptation in the brain and is important for many physiological functions such as motor learning, classical conditioning and operant conditioning. Here we show that a Hebbian associative learning synapse is an ideal neuronal substrate for the simultaneous implementation of high-gain adaptive control (HGAC) and model-reference adaptive control (MRAC), two classical adaptive control paradigms. The resultant dual adaptive control (DAC) scheme is shown to achieve superior tracking performance compared to both HGAC and MRAC, with increased convergence speed and improved robustness against disturbances and adaptation instability. The relationships between convergence rate and adaptation gain/error feedback gain are demonstrated via numerical simulations. According to these relationships, a tradeoff between the convergence rate and overshoot exists with respect to the choice of adaptation gain and error feedback gain.