User Preferences-Based Incompatible Multiobjective Iterative Learning Tracking Control

In multisensor systems, the output of each sensor is typically required to track a reference within a specified time frame. This situation exemplifies a multiobjective tracking problem (MOTP). By nature, MOTP involves multiple conflicting optimization objectives, precluding us from finding a single optimal solution. Instead, a set of solutions known as Pareto optimal solutions (POSs) exists, representing various trade-offs among the objectives. In practice, the goal is typically to identify an exact POS (EPOS) aligned with user preferences. Several methods have been proposed for approximately locating an EPOS. However, these methods transform the original problem into more tractable forms by introducing parameters, which inherently makes their convergence accuracy sensitive to parameter selection. Our primary approach entails utilizing the Chebyshev scalarization function (CSF) to characterize the EPOS and subsequently optimizing the CSF directly without introducing additional parameters. Initially, we formalize the MOTP incorporating user preferences. Subsequently, we design a novel index-set-based parallel multi-gradient descent algorithm (MGDA) to optimize the CSF. This method addresses the slow convergence issue of the traditional subgradient method by leveraging MGDA to determine a more appropriate descent direction and employing adaptive step sizes. Furthermore, in scenarios where parallel computing is not feasible, we propose a novel index-set-based serial MGDA to enhance computational efficiency. Both algorithms have been rigorously proven to converge to the EPOS. Illustrative simulations are provided to validate our theoretical findings.