Quantum-Assisted Barrier Sequential Quadratic Programming for Nonlinear Optimal Control
Nahid Binandeh Dehaghani, Rafał Wiśniewski, A. Pedro Aguiar · IEEE Control Systems Letters · 2025
We propose a quantum-assisted framework for solving constrained finite-horizon nonlinear optimal control problems using a barrier Sequential Quadratic Programming (SQP) approach. A quantum subroutine is incorporated to efficiently solve the Schur complement step using block-encoding and Quantum Singular Value Transformation techniques. We formally analyze the time complexity and convergence behavior under the cumulative effect of quantum errors, establishing local input-to-state stability and convergence to a neighborhood of the stationary point, with explicit error bounds in terms of the barrier parameter and quantum solver accuracy. The proposed framework enables computational complexity to scale polylogarithmically with the system dimension demonstrating the potential of quantum algorithms to enhance classical optimization routines in nonlinear control applications.