Fuzzy quadratic weights for variance constrained LQG design

One of the well known deficiencies of most modern control methods is that they attempt to represent multiple criteria using scalar cost functions. Hence, in practice the cost function weights (static or dynamic) must be chosen by trial and error in order to satisfy the multiple objectives. This paper develops a fuzzy algorithm for selecting the weights in an linear quadratic Gaussian (LQG) cost functional such that variance constraints on the system inputs and outputs are satisfied. This problem is denoted the variance constrained LQG problem. Variations of this problem are considered in the existing literature using crisp logic. It is seen that the fuzzy algorithm converges faster and tends to be much more numerically robust than the crisp algorithms