Dynamic Quantum-Assisted Co-Design of Control Tuning and Lyapunov Stability Synthesis for Nonlinear Systems

Abstract

This paper proposes a dynamic quantum-assisted co-design framework for nonlinear closed-loop systems in which controller parameters and Lyapunov-certificate parameters are redesigned jointly at successive decision epochs. Unlike conventional nonlinear control designs that typically tune controller gains offline and verify stability separately, the proposed method embeds performance improvement and Lyapunov-based stability synthesis within a unified online optimization loop. The main novelty is a two-step computational structure that first contracts the continuous admissible search region around the current operating condition using a Black-Hole-based calibration procedure and then constructs a finite binary representation only over this calibrated region. The encoded objective is obtained from sampled nonlinear closed-loop evaluations and approximated by a local quadratic pseudo-Boolean surrogate, enabling an Ising-type Hamiltonian representation suitable for quantum-assisted optimization. Quantum imaginary time evolution is then used to explore the encoded Hamiltonian, and the resulting candidate bitstrings are decoded into continuous controller and Lyapunov parameters. To reduce dependence on the surrogate model, the decoded candidates are re-evaluated using the original nonlinear closed-loop cost and Lyapunov penalties before the final update is applied. The framework can accommodate different Lyapunov decay specifications by modifying the stability penalty and is validated on first-order nonlinear consensus, second-order nonlinear consensus, and induction-motor drive control examples. The implementation code used to generate the reported results is available at \href{https://github.com/LSU-RAISE-LAB/DQCLS-NS}{GitHub}.