Safety-Constrained Control with Tunable Performance Using Dual-Mode Method and Local Trajectory Adjustment

This paper presents a novel safety-constrained control framework for a class of uncertain high-order multi-input multi-output (MIMO) nonlinear systems, unifying trajectory correction strategies with tunable performance constraint designs. In contrast to existing methods that assume the desired trajectory is always safe and feasible, we introduce a localized trajectory correction mechanism based on a compact-support transition function. This mechanism achieves intended adjustments by superimposing local correction terms onto the reference trajectory. Additionally, we propose a new dual-mode tunable performance function that dynamically adapts to real-time tracking errors. Notably, this design allows users to predefine relaxation or tightening intervals to address potential perturbations or safety requirements. By constructing a barrier-inspired function through normalization mapping, the constrained system is transformed into an unconstrained one. Stabilizing this transformed system effectively solves the original constrained control problem. Simulation results demonstrate the applicability and effectiveness of the proposed framework, showcasing its advantages in handling system uncertainties and ensuring performance constraints.