An SLP Filter Algorithm for Probabilistic Analytical Target Cascading

Decision-making under uncertainty is particularly challenging in the case of multidisciplinary, multilevel system optimization problems. Subsystem interactions cause strong couplings, which may be amplified by uncertainty. Thus, effective coordination strategies can be particularly beneficial. Analytical target cascading (ATC) is a deterministic optimization method for multilevel hierarchical systems, which was recently extended to probabilistic formulations in the so-called probabilistic design. Solving the optimization problem requires propagation of uncertainty, namely, evaluating or estimating the output distributions. This uncertainty propagation can be a very challenging and computationally expensive task for highly nonlinear functions. In order to overcome the general difficulty in uncertainty propagation, this article extends the use of the SLP algorithm to the probabilistic ATC formulation. By linearizing and solving a problem successively, the algorithm takes advantage of the simplicity and ease of uncertainty propagation for a linear system. A suspension strategy, developed for a deterministic SLP-based ATC strategy, is applied to reduce computational cost by suspending the analyses of subsystems that do not need considerable redesigns. The accuracy and effectiveness of the proposed SLP-based PATC strategy is demonstrated with several numerical examples.