Internal dissipation allocation in control Lyapunov function design

This letter studies how control Lyapunov function (CLF) structure affects CLF-based control under input constraints. In relaxed CLF-based quadratic programs (CLF–QPs), a mismatch between the prescribed dissipation and the CLF-induced input channel may cause excessive actuation demand, increased relaxation, and chattering-like behavior near the zero-channel set. A recursive backstepping representation exposes the internal dissipation and shows that uniformly increasing recursive dissipation strengthens zero-channel dissipation but also raises downstream actuation demand. To reshape this trade-off, a Lyapunov-level allocation mechanism redesigns the virtual controls, recursive coordinates, and dissipation profile. Simulations on a nonlinear spring–damper system illustrate the weak-channel effect and the dissipation–actuation trade-off, and show that the shaped CLF achieves convergence and disturbance attenuation comparable to high-gain uniform designs with lower control effort and a substantially smaller relaxation level.

Subjects

Backstepping

constrained control

Lyapunov methods

optimization

DDC Class

600: Technology

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Internal dissipation allocation in control Lyapunov function design