arXiv subjects

Kai Wulff

Publications and source records attributed to Kai Wulff.

6 recordsLinked to original sources

arXiv2025

Stability of Lyapunov redesign trajectory tracking control with unbounded perturbations -- A tube-based stability analysis

Considering a nonlinear system in Byrnes-Isidori form that is subject to unbounded perturbations, we apply Lyapunov redesign via feedback linearisation for trajectory tracking. Leveraging the ideas of tube-based geometric characterisation of the invariance properties of the closed loop, we generalise the classical stability criterion from the~literature from constant to nonconstant reference trajectories. The proposed analysis is tailored to the Lyapunov redesign and the tracking problem insofar as we incorporate the reference trajectory and the transient decrease of the tracking error enforced by the controller. In particular, we exploit that the Lyapunov function of the tracking error satisfies a differential inequality, thereby guaranteeing that the solution of the closed loop remains in a contracting tube along the reference trajectory.

eess.SY↗

arXiv2025

High-gain model-following control for trajectory tracking

We consider trajectory tracking for minimum-phase nonlinear systems in Byrnes-Isidori form using the model-following control (MFC) architecture. The tracking problem is motivated by a hierarchical control concept where a higher-level instance provides the reference trajectory at run-time. We present a computational efficient implementation of the feedback linearisation MFC design, and apply high-gain feedback in the process control loop (PCL) to achieve practical tracking in presence of Lipschitz perturbations. Our main results establish ultimate boundedness of the tracking error and give a constructive bound for the high-gain scaling parameter to achieve arbitrary tracking precision. Further we establish that the peaking phenomenon can be attenuated using MFC. We demonstrate the results via an automotive case study considering advanced engine-based cruise control.

eess.SY↗

arXiv2025

Set-point control and local stability for flat nonlinear systems using model-following control

We consider the set-point control problem for nonlinear systems with flat output that are subject to perturbations. The nonlinear dynamics as well as the perturbations are locally Lipschitz. We apply the model-following control (MFC) approach which consists of a model control loop (MCL) for a feedforward generation and a process control loop (PCL) that compensates the perturbations using high-gain feedback. We analyse the resulting closed-loop system and discuss its relation to a standard flatness-based high-gain approach. In particular we analyse the estimated region of attraction provided by a quadratic Lyapunov function. A case study illustrates the approach and quantifies the region of attraction obtained for each control approach. Using the initial condition of the model control loop as tuning parameter for the MFC design, provides that a significantly larger region of attraction can be guaranteed compared to a conventional single-loop high-gain design.

eess.SY↗

arXiv2025

Trajectory tracking model-following control using Lyapunov redesign with output time-derivatives to compensate unmatched uncertainties

We study trajectory tracking for flat nonlinear systems with unmatched uncertainties using the model-following control (MFC) architecture. We apply state feedback linearisation control for the process and propose a simplified implementation of the model control loop which results in a simple model in Brunovsky-form that represents the nominal feedback linearised dynamics of the nonlinear process. To compensate possibly unmatched model uncertainties, we employ Lyapunov redesign with numeric derivatives of the output. It turns out that for a special initialisation of the model, the MFC reduces to a single-loop control design. We illustrate our results by a numerical example.

eess.SY↗

arXiv2024

Non-overshooting output shaping for switched linear systems under arbitrary switching using eigenstructure assignment

We consider the analytical control design for a pair of switched linear multiple-input multiple-output (MIMO) systems that are subject to arbitrary switching signals. A state feedback controller design method is proposed to obtain an eigenstructure assignment that ensures that the closed-loop switched system is globally asymptotically stable, and the outputs achieve the non-overshooting tracking of a step reference. Our analysis indicates whether non-overshooting or even monotonic tracking is achievable for the given system and considered outputs and provides a choice of possible eigenstructures to be assigned to the constituent subsystems. We derive a structural condition that verifies the feasibility of the chosen assignment. A constructive algorithm to obtain suitable feedback matrices is provided, and the method is illustrated with numerical examples.

eess.SY↗

arXiv2023

Feedback rectifiable pairs and stabilization of switched linear systems

We address the feedback design problem for switched linear systems. In particular we aim to design a switched state-feedback such that the resulting closed-loop subsystems share the same eigenstructure. To this effect we formulate and analyse the feedback rectification problem for pairs of matrices. We present necessary and sufficient conditions for the feedback rectifiability of pairs for two subsystems and give a constructive procedure to design stabilizing state-feedback for a class of switched systems. In particular the proposed algorithm provides sets of eigenvalues and corresponding eigenvectors for the closed-loop subsystems that guarantee stability for arbitrary switching. Several examples illustrate the characteristics of the problem considered and the application of the proposed design procedure.

math.OC↗