Optimal supervisory control of nonlinear process systems via lifted Carleman representations
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Date
2026-07-12
Authors
Κατσαμπάνης, Αθανάσιος
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Abstract
Nonlinear control systems often operate in regimes where classical linear models provide only limited guidance, yet fully nonlinear optimization methods remain too computationally demanding for fast real-time implementation. This thesis develops a control framework that addresses this gap by combining operator-based embeddings, spatial partitioning, and multi-rate supervision into a unified architecture suitable for nonlinear systems with tight timing constraints.
The approach begins by representing the dynamics through a polynomial embedding that cap- tures nonlinear behavior in a structured bilinear form. Instead of relying on a single expansion point, the state space is covered by a set of locally valid embedded models generated offline through a geometric criterion. Each region of this atlas is associated with a reduced representation that retains only the algebraically essential terms, ensuring both numerical stability and compact storage.
To make practical use of this atlas, the thesis introduces a two-layer control strategy. At the fast time scale, control inputs are obtained by smoothly combining the precomputed local controllers associated with each region, enabling rapid response without online matrix computations. At the slower time scale, a predictive correction mechanism evaluates the system’s evolution, compensates for the effects not captured by the local models, and selectively expands the atlas when the trajectory approaches areas insufficiently represented by the offline seeds. This selective refinement avoids excessive memory usage while preserving global coverage.
The framework is evaluated on two benchmarks, the Lorenz oscillator and third-order polynomial system. Across both cases, the method achieves stable regulation, smooth transitions between regions, and computational performance compatible with real-time execution. The results demonstrate that combining embedded representations with geometry-aware discretization and targeted predictive refinement offers a practical and efficient alternative to traditional nonlinear control approaches.
Overall, the thesis presents a structured methodology for constructing a global control strategy from locally accurate models, balancing offline preparation with minimal online computation. The resulting architecture provides a scalable and computationally efficient pathway for controlling nonlinear systems without relying on heavy real-time optimization.
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Keywords
Process control, Nonlinear systems, Nonlinear model predictive control (NMPC), Robust control