Continuous-Time Generalized Predictive Adaptive Control

Abstract

The paper describes an approach to the continuous time adaptive control systems, which are based on the continuous time generalized predictive (GP) control. An alternative procedure for GP controller design is represented, which is based on a state observer - Kalman filter. First the design procedure is shown for discrete time systems. In the first step the discrete time Kalman filter for processes disturbed by noise which is usually used at the GPC design is developed. The second step is to solve a time variant Riccate type equation which is obtained if the standard optimal state controller cost function is made equal to the GPC cost function by introducing time variant costing coefficients. It is shown that using the proposed procedure GPC for any costing and control horizon can be designed and that GPC is an optimal state controller with a special representation of the Kalman filter what extends previous results showing that the linear quadratic Gaussian (LQG) control is a special case of the GPC. The idea of GPC design as a state controller with an Kalman filter can be carried over to the continuous time domain. The continuous time GPC criterion function for regulation can be made equal to the standard criterion function of the continuous time state controller by an appropriate choice of the standard quadratic performance criterion matrices in the same way as with discrete time systems. The control law which is believed to be an equivalent of the continuous time GPC is then given by standard state controller feedback law and can be combined with an continuous time identification procedure to yield adaptive control system. Simulation results with the nonminimum phase proces illustrate the proposed adaptive controll system design procedure.