Dynamic Quantum-Assisted Co-Design of Control Tuning and Lyapunov Stability Synthesis for Nonlinear Systems
For control engineers, this work introduces a quantum-assisted online optimization method for nonlinear control, but it is incremental as it combines existing techniques (Black-Hole calibration, Ising model, quantum imaginary time evolution) without demonstrating clear advantages over conventional methods.
This paper proposes a dynamic quantum-assisted co-design framework that jointly tunes controller parameters and Lyapunov-certificate parameters online for nonlinear systems, achieving improved performance and stability. Validation on three nonlinear control examples shows feasibility, but no numerical improvements over baselines are reported.
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}.