arXiv subjects

Johann Reger

Publications and source records attributed to Johann Reger.

18 recordsLinked to original sources

arXiv2026

Chattering Reduction for a Second-Order Actuator via Dynamic Sliding Manifolds

We analyze actuator chattering in a scalar integrator system subject to second-order actuator dynamics with an unknown time constant and first-order sliding-mode control, using both a conventional static sliding manifold and a dynamic sliding manifold. Using the harmonic balance method, we prove that it is possible to adjust the parameters of the dynamic sliding manifold for the specified system class so as to reduce the amplitude of the chattering in comparison to the static manifold. We illustrate our results with a simulation example. This contribution serves as a proof of concept to motivate further investigations in chattering reduction via dynamic sliding manifolds.

eess.SY↗

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

On robotic manipulators with time-dependent inertial parameters: From physical consistency to boundedness of the mass matrix

We generalize the robotics equation describing the dynamics of open kinematic chains by including the effect of time-dependent change of inertial parameters as well as the effects of causative mass-density redistribution, triggered by internal movement of mass-carrying particles relative to their body-fixed frames. Time dependency of inertial parameters that results from the sole addition of mass to the robot prominently occurs during the loading of end-effectors--a scenario covered by our model without restriction from the restraint that kinematic parameters of the robot must remain constant. Further, our model also includes internal mass-density redistributions that adhere to this kinematic restraint such as trolleys attached to the robot or the movement of passengers. To accompany the generalized robotics equation with some theoretical infrastructure, we then introduce the concepts of uniform physical consistency and upper boundedness of inertial parameters under which desirable, structural properties regarding the existence of finite, positive uniform bounds of the mass matrix can be shown to carry over to the more involved case of time-dependent inertial parameters. These findings have implications for adaptive control, as they facilitate more realistic testing for robustness against unforeseen time dependencies. Moreover, the results in this paper also provide a pathway to ensuring the desirable existence of finite, positive uniform bounds of the estimated mass matrix under upper bounded, uniformly physically consistent estimation regimes.

math.OC↗

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

Indirect Adaptive Control Using a Static Update Law

The update law in the indirect adaptive control scheme can be extended to include feedthrough of an error term. This reduces undesired oscillations of the calculated weights. When the ${\sigma}$-modification is used for achieving robustness against unstructured uncertainties, the gain of the feedthrough in the update law cannot be chosen arbitrarily. Compared to our previous result, we show stability of the closed loop for a larger parameter-range for the gain of the feedthrough in the update law. This parameter-range includes a configuration for which the influence of the integration in the update law diminishes over time, i.e. for which the adaptation for large times is governed solely by the feedthrough in the update law. By initializing at zero, this allows for removing the integration from the update law, resulting in a static update law. For the purely linear case, the adaptation acts like a disturbance observer. Frequency-domain analysis of the closed loop with a second order plant shows that removing the integration from the update law with ${\sigma}$-modification and feedthrough affects how precisely disturbances in the low-frequency band are observed. If the damping injected into the adaptation process by the ${\sigma}$-modification exceeds certain bounds, then the precision is increased by using the static update law.

math.OC↗

arXiv2024

The modulating function method for state estimation and feedback of infinite-dimensional systems

We investigate state feedback and observation for infinite-dimensional linear systems, including a variety of partial differential equations with boundary control and observation. We extend the modulating function approach to infinite-dimensional systems. This approach, simply put, involves reconstructing part of the state by convolving with null controls of the adjoint system. We show how this method aids in state reconstruction, and we also examine distributional solutions of the adjoint system, showing their ability to handle unbounded feedback operators. This enables us to use feedback from spatial point evaluations in partial differential equations.

math.OC↗

arXiv2024

Sensitivity analysis and experimental evaluation of PID-like continuous sliding mode control

Continuous higher order sliding mode (CHOSM) controllers represent an efficient tool for disturbance rejection. For the systems with relative degree r, CHOSM approaches provide theoretically exact compensation of the matched Lipschitz perturbation, ensuring the finite-time convergence to the (r+1)-th sliding-mode set, by using only information on the sliding output and its derivatives up to the order (r-1). In this paper, we investigate the disturbance rejection properties of a PID-like CHOSM controller, as the simplest and intuitively clear example which incorporates nonlinear actions on the output error, its derivative, and integration of its sign. We use the harmonic balance approach and develop an analysis of propagation of the matched Lipschitz perturbation through the control loop in frequency domain. The resulted solution appears in form of the Bode-like loci which depend also on the amplitude of harmonic disturbances. Such amplitude-frequency characteristics allow certain comparability with standard disturbance sensitivity functions of a linear PID-controlled system in frequency domain. Also a simple and straightforward design procedure for the robust linear PID controller targeting the second-order system plants under investigation is provided for benchmarking. Additional (parasitic) actuator dynamics, which can lead to self-induced steady oscillations, i.e. chattering, is ditto respected. A detailed experimental case study, accomplished on an electro-mechanical actuator in the laboratory setting, highlight and make the pros and cons of both PID and CHOSM controllers well comparable for a broadband disturbance rejection.

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↗

arXiv2024

Modulating function based algebraic observer coupled with stable output predictor for LTV and sampled-data systems

This paper proposes an algebraic observer-based modulating function approach for linear time-variant systems and a class of nonlinear systems with discrete measurements. The underlying idea lies in constructing an observability transformation that infers some properties of the modulating function approach for designing such algebraic observers. First, we investigate the algebraic observer design for linear time-variant systems under an observable canonical form for continuous-time measurements. Then, we provide the convergence of the observation error in an L2-gain stability sense. Next, we develop an exponentially stable sampled-data observer which relies on the design of the algebraic observer and an output predictor to achieve state estimation from available measurements and under small inter-sampling periods. Using a trajectory-based approach, we prove the convergence of the observation error within a convergence rate that can be adjusted through the fixed time-horizon length of the modulating function and the upper bound of the sampling period. Furthermore, robustness of the sampled-data algebraic observer, which yields input-to-state stability, is inherited by the modulating kernel and the closed-loop output predictor design. Finally, we discuss the implementation procedure of the MF-based observer realization, demonstrate the applicability of the algebraic observer, and illustrate its performance through two examples given by linear time-invariant and linear time-variant systems with nonlinear input-output injection terms.

eess.SY↗

arXiv2023

Minimizing the Homogeneous $\mathcal{L}_2$-Gain of Homogeneous Differentiators

The differentiation of noisy signals using the family of homogeneous differentiators is considered. It includes the high-gain (linear) as well as robust exact (discontinuous) differentiator. To characterize the effect of noise and disturbance on the differentiation estimation error, the generalized, homogeneous $\mathcal{L}_2$-gain is utilized. Analog to the classical $\mathcal{L}_p$-gain, it is not defined for the discontinuous case w.r.t. disturbances acting on the last channel. Thus, only continuous differentiators are addressed. The gain is estimated using a differential dissipation inequality, where a scaled Lyapunov function acts as storage function for the homogeneous $\mathcal{L}_2$ supply rate. The fixed differentiator gains are scaled with a gain-scaling parameter similar to the high-gain differentiator. This paper shows the existence of an optimal scaling which (locally) minimizes the homogeneous $\mathcal{L}_2$-gain estimate and provides a procedure to obtain it. Differentiators of dimension two are considered and the results are illustrated via numerical evaluation and a simulation example.

eess.SY↗

arXiv2023

Modified Implicit Discretization of the Super-Twisting Controller

In this paper a novel discrete-time realization of the super-twisting controller is proposed. The closed-loop system is proven to converge to an invariant set around the origin in finite time. Furthermore, the steady-state error is shown to be independent of the controller gains. It only depends on the sampling time and the unknown disturbance. The proposed discrete-time controller is evaluated comparative to previously published discrete-time super-twisting controllers by means of the controller structure and in extensive simulation studies. The continuous-time super-twisting controller is capable of rejecting any unknown Lipschitz-continuous perturbation and converges in finite time. Furthermore, the convergence time decreases, if any of the gains is increased. The simulations demonstrate that the closed-loop systems with each of the known controllers lose one of these properties, introduce discretization-chattering, or do not yield the same accuracy level as with the proposed controller. The proposed controller, in contrast, is beneficial in terms of the above described properties.

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↗

arXiv2022

Accelerating Extremum Seeking Convergence by Richardson Extrapolation Methods

In this paper, we propose the concept of accelerated convergence that has originally been developed to speed up the convergence of numerical methods for extremum seeking (ES) loops. We demonstrate how the dynamics of ES loops may be analyzed to extract structural information about the generated output of the loop. This information is then used to distil the limit of the loop without having to wait for the system to converge to it.

eess.SY↗

arXiv2022

Comparison of Fractional-Order and Integer-Order H-infinty Control of a Non-Collocated Two-Mass Oscillator

We consider the robust control of a two-mass oscillator with a dominant input delay. Our aim is to compare a fractional-order tuning approach including the partial compensation of non-minimum phase zeros with a classical H-infinity loop-shaping design, since both these designs lead to a relatively high controller order. First of all a detailed physical model is derived and validated using measurement data. Based on the linearized model both controllers are designed to be comparable, i.e. they show a similar crossover frequency in the open loop and the final controller order is reduced to the same range for both designs. The major differences between both are the different methods how the feed-forward action is included. The loop-shaping approach with fractional-order elements relies on the plant inverse using a flat output, whereas the H-infinty design incorporates a two-degree of freedom control, i.e. the reference signal is included into the known inputs of the generalized plant. Each controller is tested in simulation and experiment. As both open-loops are nearly identical in the frequency range of interest, the results from an input disturbance experiment show no major difference. The different design approaches of the feed-forward path are clearly visible in the tracking experiment.

eess.SY↗

arXiv2022

Fractional-Order Partial Cancellation of Integer-Order Poles and Zeros

The key idea of this contribution is the partial compensation of non-minimum phase zeros or unstable poles. Therefore the integer-order zero/pole is split into a product of fractional-order pseudo zeros/poles. The amplitude and phase response of these fractional-order terms is derived to include these compensators into the loop-shaping design. Such compensators can be generalized to conjugate complex zeros/poles, and also implicit fractional-order terms can be applied. In the case of the non-minimum phase zero, its compensation leads to a higher phase margin and a steeper open-loop amplitude response around the crossover frequency resulting in a reduced undershooting in the step-response, as illustrated in the numerical example.

eess.SY↗

arXiv2018

On algebraic time-derivative estimation and deadbeat state reconstruction

This note places into perspective the so-called algebraic time-derivative estimation method recently introduced by Fliess and co-authors with standard results from linear state-space theory for control systems. In particular, it is shown that the algebraic method can in a sense be seen as a special case of deadbeat state estimation based on the reconstructibility Gramian of the considered system.

math.OC↗