New solver speeds up nonlinear control for complex systems
A Scalable Learned Iterative Solver for Nonlinear MPC via Temporal Decomposition
Machine Learning
Summary
Controlling complicated machines quickly and safely can be hard because solving the math problems needed takes too long. The authors developed a smarter way to break down these problems over time, letting their method handle longer time spans without becoming too big or slow. Their method learns through trial and error without needing lots of example solutions beforehand and keeps control decisions within safety limits. Tests showed it works faster than existing solvers while keeping the system running well.
What this means in practice
- •For industrial control engineers: Speed up real-time control of large nonlinear chemical plants by using the solver to handle complex constraints efficiently.
- •For robotics system designers: Deploy faster control algorithms on robots with many moving parts by applying the temporal decomposition solver to reduce computation time.
Authors
Lukas Lüken, Sergio Lucia
Abstract
Nonlinear model predictive control (NMPC) can be applied to large nonlinear systems with complex objectives while enforcing constraints, but the cost of solving the underlying optimization problems limits real-time application for systems with fast dynamics or many states. Neural networks can reduce this online cost by approximating the control law, but may violate constraints and typically require many precomputed optimizer solutions for training. The learning-based iterative solver for constrained optimization (LISCO) instead learns to predict primal-dual steps toward satisfaction of the Karush-Kuhn-Tucker (KKT) conditions through self-supervised training without precomputed solutions, but its dense, monolithic architecture grows with the prediction horizon. We remove this horizon dependence by exploiting the temporal structure of the problem in the solver architecture, which makes the network size independent of the horizon while leaving the training loss and the solver iteration unchanged. A closed-loop resampling strategy further aligns the training distribution with closed-loop operation at no additional sampling cost. On an economic NMPC benchmark of a CSTR cascade, the proposed solver scales to larger problems than monolithic LISCO and achieves median speedups of up to a factor of four over IPOPT. In closed loop, it achieves comparable control performance to IPOPT with no observed constraint violations.