This paper presents improved new adaptive laws in the design of Model Reference Adaptive Control (MRAC) systems, based on Lyapunov stability theory.It focuses on the standard adaptive laws which were developed based on a Positive Definite Quadratic Lyapunov functions; these standard laws make the derivative of the Lyapunov function only negative semi-definite; this feature was observed for the past three decades (1970s, 80s and 90s). However, it is noted that the transient response of the system error converging to zero has been significantly oscillatory. It is in this context, this paper presents new improved adaptive laws using a new Lyapunov function that employs the integral of square of error signal. The new adaptive laws offer improved transient response of the system error converging to zeroin particular, in a less oscillatory fashion. In addition, these new adaptive laws lead the derivative of the new Lyapunov function to become negative definite, along as the system error is not zero. The paper presents first mathematical development for 1st order and 2nd order systems, having relative degree as unity; then, it later presents simulation study, using the MATLAB package. The simulation results support the mathematical arguments.
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Last date updated on November, 2020