Leveraging second-order information for tuning of inverse optimal controllers

TL;DR

This paper introduces a second-order information-based method for tuning inverse optimal controllers in nonlinear systems, achieving quadratic convergence and improved stability performance.

Contribution

It proposes a novel approach linking second-order methods with inverse optimal control tuning, enabling faster convergence and better stability in nonlinear systems.

Findings

Achieves quadratic convergence in controller tuning.

Validated on power inverter network simulations.

Demonstrates improved closed-loop stability and decay rates.

Abstract

We leverage second-order information for tuning of inverse optimal controllers for a class of discrete-time nonlinear input-affine systems. For this, we select the input penalty matrix, representing a tuning knob, to yield the Hessian of the Lyapunov function of the closed-loop dynamics. This draws a link between second-order methods known for their high speed of convergence and the tuning of inverse optimal stabilizing controllers to achieve a fast decay of the closed-loop trajectories towards a steady state. In particular, we ensure quadratic convergence, a feat that is otherwise not achieved with a constant input penalty matrix. To balance trade-offs, we suggest a practical implementation of the Hessian and validate this numerically on a network of phase-coupled oscillators that represent voltage source controlled power inverters.