Koopman-based model predictive control for nonlinear systems with bounded model uncertainty

Tube MPC for Bilinear Koopman Models using Robust Control Contraction Metrics

A robust tube model predictive control framework for nonlinear systems represented by bilinear Koopman models identified from data, which establishes recursive feasibility, robust constraint satisfaction and input-to-state stability of the closed-loop system with respect to the mismatch between the Koopman model and the true dynamics.

Bilinear Koopman-Based Robust Model Predictive Control for Unknown Nonlinear Systems via Contraction Metrics

A RMPC framework for unknown nonlinear systems with general nonlinear constraints based on data-driven bilinear Koopman realizations is proposed and robust satisfaction of the original nonlinear constraints is proved by the true closed-loop trajectory, recursive feasibility, and convergence to a neighborhood of the target state.

Iterative State- and Control-Dependent Model Predictive Control: A Jacobian-Free Formulation for Constrained Nonlinear Systems

This paper presents an iterative model predictive control algorithm that stabilizes constrained nonlinear systems without evaluating a single plant derivative. By factoring the exact nonlinear dynamics into a pseudo-linear form using state- and control-dependent coefficients (SCDCs), we replace the standard nonconvex optimization with a sequence of constrained linear-quadratic programs. Refreezing the coefficient matrices along the previously predicted trajectory drives the iteration. Near the origin, we prove this sequence contracts to a unique fixed point. We explicitly bound the number of iterations required to reach any stopping tolerance, and we quantify the distance from the fixed point to a true Karush-Kuhn-Tucker point, showing this optimality gap vanishes quadratically as the state approaches the origin. Inflating the discrete algebraic Riccati equation generates terminal ingredients that guarantee recursive feasibility and asymptotic stability, even when the solver terminates early. We adapt the terminal penalty online, proving it remains uniformly bounded, and we secure output feedback through the block-observable canonical form, which extracts the exact system state directly from past inputs and outputs. Retaining the block-banded structure of the subproblem forces the computational cost to scale linearly with the horizon length $\ell$. This $O(\ell)$ complexity matches the iterative linear quadratic regulator (iLQR) but sharply undercuts the $O(\ell^3)$ scaling of dense sequential quadratic programming (SQP). Numerical studies on a saturated quadrotor, a nonholonomic integrator, and a nonminimum-phase plant illustrate the theoretical bounds and map how the algorithm compares with iLQR, SQP, and linear-parameter-varying MPC.

Data-Driven Koopman-Based Model Predictive Control for a Three-Tank Hydraulic System

This paper presents an applied study of data-driven Model Predictive Control (MPC) based on the Koopman operator framework for a three-tank hydraulic benchmark. The central contribution is a compact, physics-informed lifting strategy: observable functions are chosen directly from Torricelli’s law governing turbulent orifice flow, yielding a seven-dimensional Extended Dynamic Mode Decomposition (EDMD) model that captures the dominant nonlinearities with fewer basis functions than generic dictionaries. The resulting Koopman-MPC replaces the nonconvex optimization of nonlinear MPC (NMPC) with a convex quadratic program, achieving comparable tracking accuracy (0.65 cm vs. 0.64 cm mean error) while reducing the average per-step computation time by 36.7× (50 ms vs. 1807 ms in Python/SciPy). A Moving Horizon Estimator (MHE) operating on the full nonlinear model reconstructs the unmeasured tank level with accuracy comparable to the 2 mm measurement noise floor. These results provide a quantitative benchmark for Koopman-based predictive control on a nonlinear hydraulic system with bidirectional inter-tank coupling and regime-dependent flow transitions.

Inverse optimal control of general nonlinear systems based on adaptive dynamic programming

Robust Adaptive Koopman MPC Under Structured and Stochastic Uncertainty for Soft Continuum Robots

Soft continuum robots exhibit highly nonlinear and configuration-dependent dynamics, making accurate trajectory tracking challenging under model uncertainty and external disturbances. This paper presents an adaptive Koopman-based model predictive control (MPC) framework for a tendon-driven soft continuum robot and evaluates its performance through comprehensive closed-loop simulations. A lifted linear Koopman model is identified from experimentally collected robot data and incorporated into an MPC formulation to provide computationally efficient prediction while capturing dominant nonlinear behavior. To compensate for plant–model mismatch and time-varying uncertainties, an online Recursive Least Squares (RLS) adaptation mechanism is integrated into the Koopman–MPC framework, enabling continuous model refinement during closed-loop operation without repeated offline retraining. The proposed controller is evaluated through comprehensive closed-loop simulations on circular, triangular, helical, and figure-eight trajectories under stochastic disturbances and structured parametric bias conditions using a Koopman model identified from experimentally collected robot data. Results demonstrate consistent improvements in tracking performance compared with fixed Koopman MPC while maintaining real-time computational feasibility. Under structured parametric bias, the proposed controller reduces the mean tracking error from 9.30 mm to 1.36 mm during circular trajectory tracking and achieves sub-millimeter accuracy in several operating conditions. These findings highlight the potential of online Koopman model adaptation for predictive control of soft continuum robots operating under uncertainty.