Model Reduction in the Presence of Parameter Uncertainty

Covariance equivalent realizations have been used recently to produce reduced-order models that match a specified number of output covariances and Markov parameters of the original model. This paper extends this theory to models with uncertain parameters. The approach is to take an nth order nominal system with h uncertain parameters, form its (n+nh) sensitivity model, then reduce the sensitivity model to size (n+γlh), where l is the number of outputs and γ is an integer chosen by the designer. The reduced-order model then matches (γ+l) output covariances and γ Markov parameters of the original sensitivity system. This method leaves the nominal system unchanged, and hence 1) retains all dynamical information of the nominal system, 2) maintains the correct cross-correlation between nominal outputs and sensitivity outputs, and 3) preserves the distinction between plant and sensitivity states in the reduced model. This last property enables one to use the reduced model to generate a controller which minimizes a cost function that includes output (trajectory) sensitivity and input (control) sensitivity terms.