Recursive Optimal State and Input Observer for Discrete Time-Variant Systems

One of the important challenges facing control engineers in developing automated machineryis to be able to monitor the machines using remote sensors. Observrs are often used to reconstruct the machine variables of interest. However, conventional observers are unalbe to observe the machine variables when the machine models, upon which the observers are based, have inputs that cannot be measured. Since this is often the case, the authors previsously developed a steady-state optimal state and input observer for time-invariant systems [1], this paper extends that work to time-variant systems. A recursive observer, similar to a Kalman-Bucy filter, is developed . This optimal observer minimizes the trace of the error variance for discrete , linear , time-variant, stochastic systems with unknown inputs.