Quantum-Inspired Nonlinear Model PredictiveControl via Quantum Singular Value Transformationfor Autonomous Systems

The deployment of Nonlinear Model Predictive Con- trol (NMPC) in safety-critical autonomous systems is frequently constrained by the computational intractability of solving non- convex optimization problems within strict real-time deadlines. While quantum computing offers theoretical speedups, the lack of fault-tolerant hardware necessitates the development of quantum- inspired classical algorithms. This paper proposes a novel NMPC framework based on the Quantum Singular Value Transforma- tion (QSVT), which leverages polynomial approximation and ma- trix sketching to accelerate the solution of receding-horizon con- trol problems. We derive a comprehensive theoretical complexity analysis, demonstrating a reduction from the cubic complexity of classical Sequential Quadratic Programming (SQP) to a near- linear complexity dependent on sketch dimensions. The proposed QSVT-NMPC is benchmarked against classical NMPC, Sliding Mode Control (SMC), and a suite of quantum-inspired variants, including Simulated Quantum Annealing and Variational Quan- tum Circuits using an inverted pendulum system. Experimental results validate that the optimized QSVT-NMPC achieves a me- dian settling time of 3.0 seconds, outperforming other quantum- inspired methods and offering a superior trade-off between control stability and computational latency compared to classical approaches. The algorithm demonstrates significant robustness to parameter variations and reduced memory footprint, establishing it as a viable candidate for embedded implementation in next- generation autonomous systems