4. Iterative Optimization

In many practical cases the theoretical conditions required by the “one-shot” solutions are not met. Moreover, operational constraints of the process often require that only small adjustments to existing parameter settings can be made, which precludes the application of VRFT in these situations. In such cases the data-driven control design must be performed through iterative procedures in which each iteration requires collecting more data, each time with a different controller in the loop. In Chap. 4 a general review of basic optimization theory is given, setting the stage for the chapters to follow. The basic convergence properties of the basic optimization algorithms—steepest descent and Newton-Raphson in particular—are analyzed. Some robustness properties, that is, convergence under imprecise information, of these algorithms are also demonstrated.