Dynamic Quantum-Assisted Co-Design of Controller and Lyapunov Candidate Parameters 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 candidate parameters are redesigned jointly at successive decision epochs. Unlike conventional nonlinear control designs that typically tune controller gains offline and perform stability analysis separately, the proposed method embeds performance improvement and sample-based Lyapunov verification 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 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 sampled forms of different Lyapunov decay specifications by modifying the corresponding penalty and is numerically evaluated 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}.
Related
- Koopman--Lyapunov and Koopman--Riccati Controller Synthesis
- Safe Controller Synthesis for Nonlinear Switched Systems via Probabilistic Abstractions
- Linear Lyapunov Functions for Nonlinear Compartmental Systems
- Learning Lyapunov Operators for Nonlinear Systems
- Parameters Robust Parallelizable Iterative Decoupled Algorithms for Thermo-Poroelasticity with Nonlinear Convective Transport
BibTeX
@misc{hasanzadeh2026dynamic,
title = {{Dynamic Quantum-Assisted Co-Design of Controller and Lyapunov Candidate Parameters for Nonlinear Systems}},
author = {Milad Hasanzadeh and Amin Kargarian and Mehdi Farasat},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.04296},
eprint = {2605.04296},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.04296},
}
RIS
TY - UNPB
TI - Dynamic Quantum-Assisted Co-Design of Controller and Lyapunov Candidate Parameters for Nonlinear Systems
AU - Milad Hasanzadeh
AU - Amin Kargarian
AU - Mehdi Farasat
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2605.04296
UR - https://arxiv.org/abs/2605.04296
AB - This paper proposes a dynamic quantum-assisted co-design framework for nonlinear closed-loop systems in which controller parameters and Lyapunov candidate parameters are redesigned jointly at successive decision epochs. Unlike conventional nonlinear control designs that typically tune controller gains offline and perform stability analysis separately, the proposed method embeds performance improvement and sample-based Lyapunov verification 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 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 sampled forms of different Lyapunov decay specifications by modifying the corresponding penalty and is numerically evaluated 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}.
ER -