Identification of a Multistep-Ahead Observer and Its Application to Predictive Control

State observation is a fundamental component of modern control theory. In discrete-time format, the standard observer is one-step ahead. It estimates of the system state at the next time step k + based on information available at the current time step k. For multi-step ahead prediction (to estimate the state at time step k + a, for some o t>l ) , one can repeatedly propagate the one-step estimation a times into the future, but this process tends to accumulate errors from one propagation to the next. This paper introduces the notion of an observer which directly predicts the state of the system at a some specified time step in the future based on current information. More importantly, this multiple-step ahead observer, which involves the system controllability matrix, is identified directly from input-output data. Hence, there is no need for a model of the system before hand. One possible application of a multi-step ahead observer is in receding-horizon predictive control, which bases its control action at the present time on a prediction of the system response at some time step in the future. If desired, it is possible to recover the usual one-step ahead state-space model of the system from the identified multiple-step ahead observer as well, although a stabilizing feedback controller can be designed from the identified observer directly. Numerical examples will be used to illustrate the key identification and control aspects of this formulation.