KOOPMAN-Luenberger Observer Design for Nonlinear Systems with Application to the Monitoring of a Latent Thermal Energy Storage

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.

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

Data-Driven Stability and Performance Analysis of Lurye Systems

This paper develops data-driven conditions for certifying internal stability and induced-$\ell_2$ performance of discrete-time Lurye systems. The Lurye system is an interconnection of a nominal LTI system in feedback with a static, memoryless nonlinearity. The nonlinearity satisfies a known set of quadratic constraints on the inputs and outputs. Existing conditions for Lurye systems require a state-space realization of the nominal LTI dynamics. Our first data-driven result instead formulates the stability and performance conditions using finite input, output, and state trajectories of the nominal LTI block. Our second condition removes the need for measured state trajectories by reconstructing the state sequence, up to a similarity transformation, from input/output data. This state reconstruction is performed using deterministic subspace-identification techniques. Both data-driven conditions are expressed as convex semidefinite programs. These conditions, given sufficiently exciting inputs, recover the corresponding model-based Lurye condition in the noiseless setting. The proposed methods are illustrated via a simple example with a sector-bounded nonlinearity. Both proposed methods obtain the same induced-$\ell_2$ gain bound as the model-based approach while using only trajectory data from the nominal system.

Adaptive Observer of Nonlinear One-Sided Lipschitz Systems Using Estimated State Regressors With Finite Excitation

For systems with unknown parameters, finite excitation and concurrent learning can potentially yield parameter convergence without persistent excitation but the regressor may still depend on inaccessible states, leading to regressor mismatch. In this paper, this problem is addressed for a class of nonlinear systems with one-sided Lipschitz properties and quadratically inner-bounded nonlinearities with bounded disturbances and linearly parametrized uncertainties. To this aim, an output-integral regression is utilized by using measured outputs and estimated states, and history-stack residual is explicitly bounded in terms of state-estimation error and disturbance. Furthermore, a perturbation bound between the estimated-state and true-state information matrices is derived. Additionally, an OSL-QIB LMI condition is applied for the observer design and a projected adaptive law is designed without needing exact output matching. Stability analysis's results indicate the proposed observer and parameter estimation outperform observers without history-stack learning term.

Output Regulation for Linear Parabolic Systems Using Finite-Dimensional Tracking-Error-Based Control

This paper addresses the output regulation problem for 1-D diffusion-reaction system, where both the disturbance and reference signals are generated by an unstable exosystem. We propose a constructive approach to the design of a finite-dimensional tracking error-based regulator for this class of possibly unstable systems. Based on the regulator equations, a combined plant is derived, converting the output regulation problem into a partial stabilization problem for the combined system. Using the modal decomposition method, the observability of the truncated modes is characterized under appropriate transmission zeros and observability conditions. For the controller design, unlike in the standard stabilization case, where the observer gain is dependent on the unstable modes only, the observer gain here has full order due to the coupling introduced by the exosystem. We prove that the observer gain can be designed such that its norm remains uniformly bounded with respect to the dimension of the observer. LMI-based conditions are provided for determining the observer dimension, and it is shown that the LMI is feasible for a sufficiently large dimension. Finally, the output regulation problem in the presence of unknown time-varying measurement delays is analyzed. Numerical examples are provided to validate the theoretical results.

Physics-Informed Observable Selection for EDMDc of Nonlinear Mechanical Systems

The Koopman operator enables nonlinear systems to be represented in an approximately linear form for linear control design. However, Extended Dynamic Mode Decomposition with Control (EDMDc) is often limited by the closure problem when generic observables fail to capture the system dynamics. This paper addresses this issue using physicsinformed observables derived from Lie derivatives for nonlinear mechanical systems. The resulting lifted models accurately capture nonlinear dynamics and enable standard LQR design with improved performance over Jacobian-based LQR during large transients. Results further demonstrate that complete physics-informed lifting is essential to minimize closure errors. The main contributions are: (1) analysis of the closure problem, (2) a Lie-derivative-based observable selection framework, and (3) comparison of Koopman-based and Jacobian-based LQR for polynomial nonlinear systems.