arXiv subjects

Martin Horn

Publications and source records attributed to Martin Horn.

At least 19 recordsLinked to original sources

arXiv2024

Safety Metric Aware Trajectory Repairing for Automated Driving

Recent analyses highlight challenges in autonomous vehicle technologies, particularly failures in decision-making under dynamic or emergency conditions. Traditional automated driving systems recalculate the entire trajectory in a changing environment. Instead, a novel approach retains valid trajectory segments, minimizing the need for complete replanning and reducing changes to the original plan. This work introduces a trajectory repairing framework that calculates a feasible evasive trajectory while computing the Feasible Time-to-React (F-TTR), balancing the maintenance of the original plan with safety assurance. The framework employs a binary search algorithm to iteratively create repaired trajectories, guaranteeing both the safety and feasibility of the trajectory repairing result. In contrast to earlier approaches that separated the calculation of safety metrics from trajectory repairing, which resulted in unsuccessful plans for evasive maneuvers, our work has the anytime capability to provide both a Feasible Time-to-React and an evasive trajectory for further execution.

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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.

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arXiv2023

Stochastic Model Predictive Control for Networked Systems with Random Delays and Packet Losses in All Channels

A stochastic Model Predictive Control strategy for control systems with communication networks between the sensor node and the controller and between the controller and the actuator node is proposed. Data packets are subject to random delays and packet loss is possible; acknowledgments for received packets are not provided. The expected value of a quadratic cost is minimized subject to linear constraints; the set of all initial states for which the resulting optimization problem is guaranteed to be feasible is provided. The state vector of the controlled plant is shown to converge to zero with probability one.

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arXiv2023

Control-oriented modeling of a LiBr/H2O absorption heat pumping device and experimental validation

Absorption heat pumping devices (AHPDs, comprising absorption heat pumps and chillers) are devices that use thermal energy instead of electricity to generate heating and cooling, thereby facilitating the use of waste heat and renewable energy sources such as solar or geothermal energy. Despite this benefit, widespread use of AHPDs is still limited. One reason for this is partly unsatisfactory control performance under varying operating conditions, which can result in poor modulation and part load capability. A promising approach to tackle this issue is using dynamic, model-based control strategies, whose effectiveness, however, strongly depend on the model being used. This paper therefore focuses on the derivation of a viable dynamic model to be used for such model-based control strategies for AHPDs such as state feedback or model-predictive control. The derived model is experimentally validated, showing good modeling accuracy. Its modeling accuracy is also compared to alternative model versions, that contain other heat transfer correlations, as a benchmark. Although the derived model is mathematically simple, it does have the structure of a nonlinear differential-algebraic system of equations. To obtain an even simpler model structure, linearization at an operating point is discussed to derive a model in linear state space representation. The experimental validation shows that the linear model does have slightly worse steady-state accuracy, but that the dynamic accuracy seems to be almost unaffected by the linearization. The presented new modeling approach is considered suitable to be used as a basis for the design of advanced, model-based control strategies, ultimately aiming to improve the modulation and part load capability of AHPDs.

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arXiv2023

Switched Lyapunov Function based Controller Synthesis for Networked Control Systems: A Computationally Inexpensive Approach

This paper presents a Lyapunov function based control strategy for networked control systems (NCS) affected by variable time delays and data loss. A special focus is put on the reduction of the computational complexity. A specific buffering mechanism is defined first, such that it adds an additional delay up to one sampling period. The resulting buffered NCS can then be formulated as a switched system which leads to the significant simplification of the NCS model and subsequent controller synthesis. The novel approach does not only circumvent the need for any over-approximation technique, since the switched NCS model can be used for stability analysis directly, but also reduces the infinite set of allowable values of the dynamic matrix to a small finite set. The proposed strategy leads hereby to a strongly decreased number of optimization variables and linear matrix inequalities (LMIs) which allows greater flexibility with respect to additional degrees of freedom affecting the transient behavior. The performance and computational efficiency of the control strategy are demonstrated by means of simulation example.

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arXiv2023

Search-Based Task and Motion Planning for Hybrid Systems: Agile Autonomous Vehicles

To achieve optimal robot behavior in dynamic scenarios we need to consider complex dynamics in a predictive manner. In the vehicle dynamics community, it is well know that to achieve time-optimal driving on low surface, the vehicle should utilize drifting. Hence many authors have devised rules to split circuits and employ drifting on some segments. These rules are suboptimal and do not generalize to arbitrary circuit shapes (e.g., S-like curves). So, the question "When to go into which mode and how to drive in it?" remains unanswered. To choose the suitable mode (discrete decision), the algorithm needs information about the feasibility of the continuous motion in that mode. This makes it a class of Task and Motion Planning (TAMP) problems, which are known to be hard to solve optimally in real-time. In the AI planning community, search methods are commonly used. However, they cannot be directly applied to TAMP problems due to the continuous component. Here, we present a search-based method that effectively solves this problem and efficiently searches in a highly dimensional state space with nonlinear and unstable dynamics. The space of the possible trajectories is explored by sampling different combinations of motion primitives guided by the search. Our approach allows to use multiple locally approximated models to generate motion primitives (e.g., learned models of drifting) and effectively simplify the problem without losing accuracy. The algorithm performance is evaluated in simulated driving on a mixed-track with segments of different curvatures (right and left). Our code is available at https://git.io/JenvB

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arXiv2022

Detectability Conditions and State Estimation for Linear Time-Varying and Nonlinear Systems

This work proposes a detectability condition for linear time-varying systems based on the exponential dichotomy spectrum. The condition guarantees the existence of an observer, whose gain is determined only by the unstable modes of the system. This allows for an observer design with low computational complexity compared to classical estimation approaches. An extension of this observer design to a class of nonlinear systems is proposed and local convergence of the corresponding estimation error dynamics is proven. Numerical results show the efficacy of the proposed observer design technique.

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arXiv2021

Unknown Input Observer Design for Linear Time-Invariant Systems -- A Unifying Framework

This paper presents a new observer design approach for linear time invariant multivariable systems subject to unknown inputs. The design is based on a transformation to the so-called special coordinate basis. This form reveals important system properties like invertability or the finite and infinite zero structure. Depending on the system's strong observability properties, the special coordinate basis allows for a straightforward unknown input observer design utilizing linear or nonlinear observers design techniques. The chosen observer design technique does not only depend on the system properties, but also on the desired convergence behavior of the observer. Hence, the proposed design procedure can be seen as a unifying framework for unknown input observer design.

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arXiv2021

Robust exact differentiators with predefined convergence time

The problem of exactly differentiating a signal with bounded second derivative is considered. A class of differentiators is proposed, which converge to the derivative of such a signal within a fixed, i.e., a finite and uniformly bounded convergence time. A tuning procedure is derived that allows to assign an arbitrary, predefined upper bound for this convergence time. It is furthermore shown that this bound can be made arbitrarily tight by appropriate tuning. The usefulness of the procedure is demonstrated by applying it to the well-known uniform robust exact differentiator, which is included in the considered class of differentiators as a special case.

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arXiv2021

A Non-Conservative Stability Criterion for Networked Control Systems with time-varying Packet Delays

A networked output feedback loop subject to packetized transmissions of the output signal is considered. Based on the small gain theorem, an easy-to-use stability criterion covering two important cases is presented. In the first case a packet numbering mechanism is employed whereas in the second case neither packet numbering nor synchronization between sender and receiver is assumed. The analysis makes use of acausal subsystems and deduces the optimal constant time delay that should be used in a nominal controller design such that additional packet delay variations introduced by the network are maximized. A simulation example of a networked control system with a filtered Smith predictor illustrates the application of the proposed criterion and compares the results to different approaches from literature.

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arXiv2021

Strong Detectability and Observers for Linear Time Varying Systems

This work presents a notion of strong detectability for linear time varying systems affected by unknown inputs. It is shown that this notion is equivalent to detectability of an auxiliary system without unknown inputs. This allows a straightforward observer design for dependable state estimation in the presence of unknown inputs. The design reduces to a deterministic Kalman filter design problem, where the observer gains can be obtained from the solution of a differential Riccati equation. The efficacy of the proposed approach is demonstrated by means of a numerical example.

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arXiv2020

From classical to Networked Control: Retrofitting the Concept of Smith Predictors

Filtered Smith predictors are well established for controlling linear plants with constant time delays. Apart from this classical application scenario, they are also employed within networked control loops, where the measurements are sent in separate packets over a transmission channel that is subject to time-varying delays. However, no stability guarantees can be given in this case. The present paper illustrates that the time-varying delays as well as the packetized character of the transmissions have to be taken into account for stability analysis. Hence, three network protocols, which use different packet selection and hold mechanisms, are considered. Criteria for robust stability of the networked feedback loop are given. They are based on the small gain theorem and allow a computationally inexpensive way to check stability for the case with bounded packet delays. Simulation examples provide insight into the presented approach and show why the inclusion of the time-varying packetized character of the network transmissions is vital for stability analysis.

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arXiv2020

Finite-horizon Linear Quadratic Control for Networked Control Systems with non-distributed plants

An optimal control law for networked control systems with a discrete-time linear time-invariant (LTI) system as plant and networks between sensor and controller as well as between controller and actuator is proposed. This controller is designed by solving an optimization problem that is a generalization of the optimization problem used to obtain the Linear Quadratic Regulator (LQR) for deterministic discrete-time LTI systems. The networks are represented by random delays and drop outs of transmitted data packets.

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arXiv2020

Uniform Detectability of Linear Time Varying Systems with Exponential Dichotomy

Exponential dichotomies play a central role in stability theory for dynamical systems. They allow to split the state space into two subspaces, where all trajectories in one subspace decay whereas all trajectories in the other subspace grow, uniformly and exponentially. This paper studies uniform detectability and observability notions for linear time varying systems, which admit an exponential dichotomy. The main contributions are necessary and sufficient detectability conditions for this class of systems.

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arXiv2019

Pipe Roughness Identification of Water Distribution Networks: The Full Turbulent Case

This paper proposes a technique to identify individual pipe roughness parameters in a water distribution network by means of the inversion of the steady-state hydraulic network equations. By enabling the reconstruction of these hydraulic friction parameters to be reliable, this technique improves the conventional model's accuracy and thereby promises to enhance model-based leakage detection and localization. As it is the case in so-called fireflow tests, this methodology is founded on the premise to measure the pressure distributed at a subset of nodes in the network's graph while assuming the nodal consumption to be known. Beside of the proposed problem formulation, which is restricted to only allow turbulent flow in each of the network's pipes initially, developed algorithms are presented and evaluated using simulation examples.

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arXiv2019

Pipe Roughness Identification of Water Distribution Networks: A Tensor Method

The identification of pipe roughnesses in a water distribution network is formulated as nonlinear system of algebraic equations which turns out to be demanding to solve under real-world circumstances. This paper proposes an enhanced technique to numerically solve this identification problem, extending the conventional Newton-Raphson approach with second-order derivatives in the determination of the search direction. Enabled through some interesting mathematical findings, the resulting formulation can be represented compactly and thus facilitates the development of an efficient and more robust solving-technique. Algorithms on the basis of this more enhanced solving method are then compared to a customized Newton-Raphson approach in simulation examples.

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arXiv2019

Search-Based Motion Planning for Performance Autonomous Driving

Driving on the limits of vehicle dynamics requires predictive planning of future vehicle states. In this work, a search-based motion planning is used to generate suitable reference trajectories of dynamic vehicle states with the goal to achieve the minimum lap time on slippery roads. The search-based approach enables to explicitly consider a nonlinear vehicle dynamics model as well as constraints on states and inputs so that even challenging scenarios can be achieved in a safe and optimal way. The algorithm performance is evaluated in simulated driving on a track with segments of different curvatures.

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arXiv2019

Learning a Behavior Model of Hybrid Systems Through Combining Model-Based Testing and Machine Learning (Full Version)

Models play an essential role in the design process of cyber-physical systems. They form the basis for simulation and analysis and help in identifying design problems as early as possible. However, the construction of models that comprise physical and digital behavior is challenging. Therefore, there is considerable interest in learning such hybrid behavior by means of machine learning which requires sufficient and representative training data covering the behavior of the physical system adequately. In this work, we exploit a combination of automata learning and model-based testing to generate sufficient training data fully automatically. Experimental results on a platooning scenario show that recurrent neural networks learned with this data achieved significantly better results compared to models learned from randomly generated data. In particular, the classification error for crash detection is reduced by a factor of five and a similar F1-score is obtained with up to three orders of magnitude fewer training samples.

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