arXiv subjects

Lukas Lanza

Publications and source records attributed to Lukas Lanza.

At least 19 recordsLinked to original sources

arXiv2026

A model-free approach to control barrier functions for higher-order systems

Control barrier functions (CBFs) are a widely applied modular tool to ensure safe operation of nonlinear dynamical control systems. However, for their construction accurate knowledge of the system dynamics is typically needed. This requirement was recently alleviated for relative-degree-one systems using techniques from prescribed performance control (PPC) or funnel control (FC). This article extends the model-free CBF design to nonlinear systems of arbitrary relative degree. Moreover, we show with a simple example that a straightforward extension of existing results for relative-degree-one systems fails. Instead, we utilize novel techniques from funnel control to characterize a subset of the controls satisfying a CBF condition without requiring a dynamic model or state measurement. Finally, we demonstrate the applicability of our results on a seven degrees of freedom robotic manipulator with relative degree two.

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arXiv2025

On Model Predictive Funnel Control with Equilibrium Endpoint Constraints

We propose model predictive funnel control, a novel model predictive control (MPC) scheme building upon recent results in funnel control. The latter is a high-gain feedback methodology that achieves evolution of the measured output within predefined error margins. The proposed method dynamically optimizes a parameter-dependent error boundary in a receding-horizon manner, thereby combining prescribed error guarantees from funnel control with the predictive advantages of MPC. On the one hand, this approach promises faster optimization times due to a reduced number of decision variables, whose number does not depend on the horizon length. On the other hand, the continuous feedback law improves the robustness and also explicitly takes care of the inter-sampling behavior. We focus on proving stability by leveraging results from MPC stability theory with terminal equality constraints. Moreover, we rigorously show initial and recursive feasibility.

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arXiv2025

Two-component controller design to safeguard data-driven predictive control

We design a two-component controller to achieve reference tracking with output constraints - exemplified on systems of relative degree two. One component is a data-driven or learning-based predictive controller, which uses data samples to learn a model and predict the future behavior of the system. We exemplify this component concisely by data-enabled predictive control (DeePC) and by model predictive control based on extended dynamic mode decomposition (EDMD). The second component is a model-free high-gain feedback controller, which ensures satisfaction of the output constraints if that cannot be guaranteed by the predictive controller. This may be the case, for example, if too little data has been collected for learning or no (sufficient) guarantees on the approximation accuracy derived. In particular, the reactive/adaptive feedback controller can be used to support the learning process by leading safely through the state space to collect suitable data, e.g., to ensure a sufficiently-small fill distance. Numerical examples are provided to illustrate the combination of EDMD-based model predictive control and a safeguarding feedback for the set-point transitions including the transition between the set points within prescribed bounds.

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arXiv2025

A model-free approach to control barrier functions using funnel control

Control barrier functions (CBFs) are a popular approach to design feedback laws that achieve safety guarantees for nonlinear systems. The CBF-based controller design relies on the availability of a model to select feasible inputs from the set of CBF-based controls. In this paper, we develop a model-free approach to design CBF-based control laws, eliminating the need for knowledge of system dynamics or parameters. Specifically, we address safety requirements characterized by a time-varying distance to a reference trajectory in the output space and construct a CBF that depends only on the measured output. Utilizing this particular CBF, we determine a subset of CBF-based controls without relying on a model of the dynamics by using techniques from funnel control. The latter is a model-free high-gain adaptive control methodology, which achieves tracking guarantees via reactive feedback. In this paper, we discover and establish a connection between the modular controller synthesis via zeroing CBFs and model-free reactive feedback. The theoretical results are illustrated by a numerical simulation.

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arXiv2024

Lyapunov based dynamic controller designs for reach-and-avoid problems

Safe obstacle avoidance and target set stabilization for nonlinear systems using reactive feedback control is under consideration. Based only on local information and by considering virtual dynamics, a safe path is generated online. The control law for the virtual dynamics is combined with a feedback controller for the dynamics of interest, where Lyapunov arguments and forward invariance are used to ensure that the state of the system remains in a vicinity of the path. To allow for discrete decisions in the avoidance controller design, the closed-loop dynamics are formulated using the hybrid systems framework. The results are illustrated by a numerical example for unicycle dynamics.

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arXiv2024

Exact output tracking in prescribed finite time via funnel control

Output reference tracking of unknown nonlinear systems is considered. The control objective is exact tracking in predefined finite time, while in the transient phase the tracking error evolves within a prescribed boundary. To achieve this, a novel high-gain feedback controller is developed that is similar to, but extends, existing high-gain feedback controllers. Feasibility and functioning of the proposed controller is proven rigorously. Examples for the particular control objective under consideration are, for instance, linking up two train sections, or docking of spaceships.

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arXiv2024

On derivative-free sample-and-hold control with prescribed performance

A feedback controller is proposed to perform output reference tracking with prescribed performance for nonlinear continuous-time systems of relative degree two. The controller is of sampled-data type, i.e., measurements are available only at sampling times - a typical situation in real systems when sensors are involved. Furthermore, only output information is available, i.e., neither the full state nor derivatives can be used for feedback. A sufficient uniform sampling rate is derived and the control consists of piecewise constant signals on the sampling intervals, i.e., zero-order hold. Feasibility of the controller and satisfaction of the control objective are rigorously proven. The controller is illustrated by a numerical example.

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arXiv2024

Reinforcement Learning for Docking Maneuvers with Prescribed Performance

We propose a two-component data-driven controller to safely perform docking maneuvers for satellites. Reinforcement Learning is used to deduce an optimal control policy based on measurement data. To safeguard the learning phase, an additional feedback law is implemented in the control unit, which guarantees the evolution of the system within predefined performance bounds. We define safe and safety-critical areas to train the feedback controller based on actual measurements. To avoid chattering, a dwell-time activation scheme is implemented. We provide numerical evidence for the performance of the proposed controller for a satellite docking maneuver with collision avoidance.

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arXiv2024

Distributed Optimization for Energy Grids: A Tutorial on ADMM and ALADIN

The ongoing transition towards energy and power systems dominated by a large number of renewable power injections to the distribution grid poses substantial challenges for system operation, coordination, and control. Optimization-based methods for coordination and control are of substantial research interest in this context. Hence, this chapter provides a tutorial introduction of distributed optimization algorithms for energy systems with a large share of renewables. Specifically, we focus on the Alternating Direction Method of Multipliers (ADMM) and on the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) method as both algorithms are frequently considered for coordination and control of power and energy systems. We discuss the application of ALADIN and ADMM to AC optimal power flow problems and to energy management problems. Moreover, we give an outlook on open problems.

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arXiv2024

On model predictive control with sampled-data input for output tracking with prescribed performance

We propose a model predictive control (MPC) scheme with sampled-data input which ensures output-reference tracking within prescribed error bounds for relative-degree-one systems. Hereby, we explicitly deduce bounds on the required maximal control input and sampling frequency such that the MPC scheme is both initially and recursively feasible. A key feature of the proposed approach is that neither terminal conditions nor a sufficiently-large prediction horizon are imposed, rendering the MPC scheme computationally efficient. We illustrate the MPC algorithm via a numerical example of a torsional oscillator.

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arXiv2023

Safe data-driven reference tracking with prescribed performance

We study output reference tracking for unknown continuous-time systems with arbitrary relative degree. The control objective is to keep the tracking error within predefined time-varying bounds while measurement data is only available at discrete sampling times. To achieve the control objective, we propose a two-component controller. One part is a recently developed sampled-data zero-order hold controller, which achieves reference tracking within prescribed error bounds. To further improve the control signal, we explore the system dynamics via input-output data, and include as the second component a data-driven MPC scheme based on Willems et al.'s fundamental lemma. This combination yields significantly improved input signals as illustrated by a numerical example.

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arXiv2023

Robust Funnel Model Predictive Control for output tracking with prescribed performance

We propose a novel robust Model Predictive Control (MPC) scheme for nonlinear multi-input multi-output systems of relative degree one with stable internal dynamics. The proposed algorithm is a combination of funnel MPC, i.e., MPC with a particular stage cost, and the model-free adaptive funnel controller. The new robust funnel MPC scheme guarantees output tracking of reference signals within prescribed performance bounds -- even in the presence of unknown disturbances and a structural model-plant mismatch. We show initial and recursive feasibility of the proposed control scheme without imposing terminal conditions or any requirements on the prediction horizon. Moreover, we allow for model updates at runtime. To this end, we propose a proper initialization strategy, which ensures that recursive feasibility is preserved. Finally, we validate the performance of the proposed robust MPC scheme by simulations.

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arXiv2023

Experimental validation for the combination of funnel control with a feedforward control strategy

Current engineering design trends, such as light-weight machines and humanmachine-interaction, often lead to underactuated systems. Output trajectory tracking of such systems is a challenging control problem. Here, we use a twodesign-degree of freedom control approach by combining funnel feedback control with feedforward control based on servo-constraints. We present experimental results to verify the approach and demonstrate that the addition of a feedforward controller mitigates drawbacks of the funnel controller. We also present new experimental results for the real-time implementation of a feedforward controller based on servo-constraints on a minimum phase system.

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arXiv2023

Funnel control of linear systems with arbitrary relative degree under output measurement losses

We consider tracking control of linear minimum phase systems with known arbitrary relative degree which are subject to possible output measurement losses. We provide a control law which guarantees the evolution of the tracking error within a (shifted) prescribed performance funnel whenever the output signal is available. The result requires a maximal duration of measurement losses and a minimal time of measurement availability, which both strongly depend on the internal dynamics of the system, and are derived explicitly. The controller is illustrated by a simulation of a mass-on-car system.

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arXiv2023

Safe continual learning in model predictive control with prescribed bounds on the tracking error

We develop a three-component Model Predictive Control (MPC) algorithm to achieve output-reference tracking with prescribed performance for continuous-time nonlinear systems. One component is so-called funnel MPC, which achieves reference tracking with prescribed performance for the model output for suitable models. Recently, this MPC algorithm has been combined with a model-free reactive feedback controller (second component) to account for model-plant mismatches, bounded disturbances, and uncertainties. By construction, this two-component controller defines a robust funnel MPC algorithm. It achieves output-reference tracking within prescribed bounds on the tracking error for a class of unknown nonlinear systems. In this paper, we extend the robust funnel MPC by a machine learning component to adapt the underlying model to the system data and, thus, improve the contribution of MPC. We derive sufficient structural conditions to define a class of models for funnel MPC, and provide a characterization of suitable learning schemes. Since robust funnel MPC is inherently robust and the evolution of the tracking error in the prescribed performance funnel is guaranteed, the additional learning component is able to perform the learning task online -- even without an initial model or offline training.

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arXiv2023

Sampled-data funnel control and its use for safe continual learning

We propose a novel sampled-data output-feedback controller for nonlinear systems of arbitrary relative degree that ensures reference tracking within prescribed error bounds. We provide explicit bounds on the maximum input signal and the required uniform sampling time. A key strength of this approach is its capability to serve as a safety filter for various learning-based controller designs, enabling the use of learning techniques in safety-critical applications. We illustrate its versatility by integrating it with two different controllers: a reinforcement learning controller and a non-parametric predictive controller based on Willems et al.'s fundamental lemma. Numerical simulations illustrate effectiveness of the combined controller design.

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arXiv2022

Output feedback control with prescribed performance via funnel pre-compensator

We study output reference tracking of systems with high relative degree via output feedback only; this is, tracking where the output derivatives are unknown. To this end, we prove that the conjunction of the funnel pre-compensator with a minimum phase system of arbitrary relative degree yields a system of the same relative degree which is minimum phase as well. The error between the original system's output and the pre-compensator's output evolves within a prescribed performance funnel; and moreover, the derivatives of the funnel pre-compensator's output are known explicitly. Therefore, output reference tracking with prescribed transient behaviour of the tracking error is possible without knowledge of the derivatives of the original system's output; via funnel control schemes for instance.

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arXiv2021

Output tracking for a non-minimum phase robotic manipulator

We exploit a recently developed funnel control methodology for linear non-minimum phase systems to design an output error feedback controller for a nonlinear robotic manipulator, which is not minimum phase. We illustrate the novel control design by a numerical case study, where we simulate end-effector output tracking of the robotic manipulator.

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