LQG optimal control design for uncertain systems

The modelling and control of systems with uncertain parameters which can be represented by random variables are considered. The model structure is chosen so that high-frequency lag terms may be introduced whose parameters have zero expected value. Similarly uncertain zeros may be considered. An LQG controller is obtained which stabilises the nominal plant model and also provides a degree of robustness to the uncertain poles or zeros. The LQG cost function to be minimised includes an expectation over the parameters, as well as on the stochastic signals. The design procedure introduced enables the cost function weighting terms to be parameterised in terms of the variances of the unknown parameters and a design scalar.