Abstract
A model reference adaptive control scheme for multi-input multi-output discrete polynomic non-linear systems with input and output time delays and containing unknown parameters linearly is derived by using Lyapunov method.
To contain unknown parameters linearly in the plant model makes the adaptive law a very simple one in structure and an easy one to compute.
A predictor is constructed to estimate future output errors needed in the construction of control law for the presence of time delays. The estimation of a higher order output error is obtained from the estimation of the first order form of the output error by using a transformation matrix. This technique of the transformation is needed to treat with the polynomic non-linear systems.
It is shown that the output errors converge to zero if the input and the output of the closed loop system are bounded and that the parameter errors converge to zero if the plant is strictly identifiable.
Digital simulation of the Volterra's prey-predator system confirms that this discrete adaptive control scheme is useful even for continuous systems with input and output time delays as long as the sampling time is ade-quatly small.
