Adaptive controllers based on cost identification

Two adaptive control techniques based on cost function identification are presented. Both approaches do not make any use of a system model, and the control algorithm is calculated directly from the identified parameters. This approach avoids the intensive and recursive use of a system dynamics model typical of predictive strategies, and the possible error propagation generated by model inaccuracies. On the other hand, most optimal adaptive control implementations solve online the Riccati equation for the estimated system. This computationally intense task is also avoided by directly identifying the cost function. Both techniques use a linear model of the cost function so its parameters can be identified by recursive least squares. The regressor used in the identification is formed from the quadratic basis of inputs and states (or outputs). The controllers are designed based on a transformed state vector defined on incremental variables, to allow arbitrary set-points and constant disturbances. An example illustrates the performance of the controllers. The application to time varying systems is being investigated. Further work is currently in progress to extend these algorithms to nonlinear systems, where their simplicity and directness promise improved robustness over the conventional nonlinear predictive controllers based on system identification