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Structure-Preserving Koopman Model Predictive Control for Closed-Loop Stabilisation of Memristive Neural Dynamics

Researchers introduced a Koopman operator‑based model predictive control (MPC) framework for a four‑state memristive Hindmarsh‑Rose neuron, a biophysical model that captures chaotic bursting and electromagnetic induction. By constructing a physics‑informed dictionary from iterated Lie derivatives, they reduced the lifted observable space to 13 dimensions while providing formal truncation‑error and stability guarantees. The resulting linear predictor, identified via extended dynamic mode decomposition with control, feeds a constrained receding‑horizon controller that outperforms traditional PID, LQR, sliding‑mode, neural‑network MPC and data‑enabled predictive control. Benchmarks show the lowest tracking error (RMSE 0.091), fastest settling time (0.47 s), and 100 % stabilization under input saturation, remaining robust to 20 % parameter variations.