SystemsIn the course, we will develop adaptive control methods for three types of systems: ARX, ARMAX, and state space models. ARX and ARMAX models provide a direct relation between the system inputs and outputs whereas in state space models, they are related through a state variable. ARX modelsWe will consider auto-regressive models with exogenous (i.e., manipulated) inputs (ARX). They are in the form ![]() where ![]() Furthermore, we can introduce the polynomials ![]() Finally, it is convenient to write the ARX model in the form ![]() where ![]() ARMAX modelsWe will also consider auto-regressive moving average models with exogenous inputs (ARMAX): ![]() It can also be written in the form ![]() State space modelsFinally, we will consider state space models in the form ![]() ![]() where |