A Comparison of LPV Gain Scheduling and Control Contraction Metrics for Nonlinear Control
For control engineers, this clarifies the relationship between two nonlinear control methods, but the comparison is primarily theoretical without empirical validation.
The paper compares LPV gain scheduling and Control Contraction Metrics (CCMs) for nonlinear control, showing that CCMs extend gain scheduling to achieve global reference-independent stability and performance by integrating local LPV controllers along a path between states.
Gain-scheduled control based on linear parameter-varying (LPV) models derived from local linearizations is a widespread nonlinear technique for tracking time-varying setpoints. Recently, a nonlinear control scheme based on Control Contraction Metrics (CCMs) has been developed to track arbitrary admissible trajectories. This paper presents a comparison study of these two approaches. We show that the CCM based approach is an extended gain-scheduled control scheme which achieves global reference-independent stability and performance through an exact control realization which integrates a series of local LPV controllers on a particular path between the current and reference states.