Predefined-Time Gradient Flows for Generalized Time-Varying Optimization and Application to WMR System

This article introduces the predefined-time gradient flow-based method (PT-GF), a novel optimization algorithm developed within the prediction-correction framework to address time-varying convex continuous optimization problems. The PT-GF algorithm is applicable to both unconstrained and constrained problems, including those with time-varying equality and inequality constraints. It is distinguished by its superlinear convergence rate and its ability to provide precise estimates of settling time bounds. To ensure feasibility in problems with inequality constraints, PT-GF is integrated with barrier interior point methods, introducing novel predefined-time slack variables. This integration not only achieves predefined-time convergence but also enables a controlled transition of decision variables from an initial infeasible state to a feasible one within a specified time frame. Furthermore, PT-GF is applied to practical scenarios involving target tracking for wheeled mobile robots (WMRs) with state constraints. The effectiveness of the PT-GF approach is demonstrated through extensive simulation studies and real-world experiments.