Lp-optimality for regression designs under correlations

The input energy constraints in a linear dynamic system considered in this paper are of the form that the Euclidean norm of each column of its design matrix is bounded above by a constant. An exact L-p-optimal design is obtained in closed form which is easily computable. Interestingly, the L-p-optimal designs for the generalized and the ordinary least squares estimators coincide. An example is given to demonstrate how the results can be used to find a design that performs well under all L-p criteria.