A fuzzy logic approach to LQG design with variance constraints

One of the well-known deficiencies of most modern control methods [i.e., 2, , and 1 (or 1) design] is that they attempt to represent multiple criteria with scalar cost functions. Hence, in practice the (static or dynamic) weights in the scalar cost function must be determined by an iterative process in order to satisfy the multiple objectives. It is of great time and cost benefit to automate this iterative process, but these problems tend to be highly nonlinear and extremely difficult to model analytically. However, a good designer can often observe trends and develop effective weight selection methodologies. The designer’s logic is inherently “fuzzy” and it is hence natural to use fuzzy logic for algorithm implementation. This paper develops a fuzzy algorithm for selecting the weights in a linear quadratic Gaussian (LQG) cost functional such that constraints on the variances of the system are satisfied. This problem is denoted the variance constrained LQG (VCLQG) problem. Variations of this problem are considered in the existing literature using crisp logic. Numerical experiments show that when both the input and output variances are constrained, the fuzzy algorithm converges faster and tends to be much more robust to new systems or constraints than the crisp algorithms.