Performance assessment and benchmarking LQG predictive optimal controllers for discrete-time state-space systems

Abstract

The performance assessment and benchmarking of discrete-time multivariable LQG predictive optimal control problems is considered for systems represented in state equation form. The class of predictive controllers represents the most popular multivariable design methods for the process industries. It is claimed that these methods provide improved performance but the question addressed is how this performance should be judged. A multistep LQGPC optimal control cost-function is minimized where future set-point or reference knowledge is assumed. The predictive control cost-function includes the future tracking error and control signal components. The state-equation system description can be written in terms of these future inputs, so that the model includes the outputs for time t and a vector of future outputs. The benchmark cost values are obtained from the solution of appropriate Riccati and Lyapunov equations. The results throw new light on the relationship between predictive, LQ and LQG control laws and more importantly into the way the performance of predictive controls should be assessed.