arXiv subjects

Herbert Werner

Publications and source records attributed to Herbert Werner.

15 recordsLinked to original sources

arXiv2025

Concave Comparison Functions for Accelerating Constrained Lyapunov Decay

What limits how fast a Lyapunov function can decay under input bounds? We address this question by showing how the shape of Lyapunov comparison functions governs guaranteed decay for control affine systems. Using a windowed nominal exponential rate together with the endpoint cap induced by actuator limits, we establish a strict ordering: concave comparison functions strictly outperform linear and convex ones, and strict concavity is necessary to improve the best achievable global exponential rate under a fixed endpoint cap. We derive a computable lower bound on the required actuation level for a target nominal rate and show that only concave shaping can reduce this level under the endpoint cap. We then establish a feasibility-preserving acceleration result: whenever a margin exists on a sublevel set, a feasible linear comparison can be replaced by a concave one that preserves feasibility while strictly increasing the guaranteed windowed decay. Finally, we give a tunable rational concave factor with controlled slope that yields a constructive design and integrates with CLF QP, as illustrated by examples.

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arXiv2024

Autoencoder-Based and Physically Motivated Koopman Lifted States for Wind Farm MPC: A Comparative Case Study

This paper explores the use of Autoencoder (AE) models to identify Koopman-based linear representations for designing model predictive control (MPC) for wind farms. Wake interactions in wind farms are challenging to model, previously addressed with Koopman lifted states. In this study we investigate the performance of two AE models: The first AE model estimates the wind speeds acting on the turbines these are affected by changes in turbine control inputs. The wind speeds estimated by this AE model are then used in a second step to calculate the power output via a simple turbine model based on physical equations. The second AE model directly estimates the wind farm output, i.e., both turbine and wake dynamics are modeled. The primary inquiry of this study addresses whether any of these two AE-based models can surpass previously identified Koopman models based on physically motivated lifted states. We find that the first AE model, which estimates the wind speed and hence includes the wake dynamics, but excludes the turbine dynamics outperforms the existing physically motivated Koopman model. However, the second AE model, which estimates the farm power directly, underperforms when the turbines' underlying physical assumptions are correct. We additionally investigate specific conditions under which the second, purely data-driven AE model can excel: Notably, when modeling assumptions, such as the wind turbine power coefficient, are erroneous and remain unchecked within the MPC controller. In such cases, the data-driven AE models, when updated with recent data reflecting changed system dynamics, can outperform physics-based models operating under outdated assumptions.

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arXiv2024

Robust Stability for Multiagent Systems with Spatio-Temporally Correlated Packet Loss

A problem with considering correlations in the analysis of multiagent system with stochastic packet loss is that they induce dependencies between agents that are otherwise decoupled, preventing the application of decomposition methods required for efficient evaluation. To circumvent that issue, this paper is proposing an approach based on analysing sets of networks with independent communication links, only considering the correlations in an implicit fashion. Combining ideas from the robust stabilization of Markov jump linear systems with recently proposed techniques for analysing packet loss in multiagent systems, we obtain a linear matrix inequality based stability condition which is independent of the number of agents. The main result is that the set of stabilized probability distributions has non-empty interior such that small correlations cannot lead to instability, even though only distributions of independent links were analysed. Moreover, two examples are provided to demonstrate the applicability of the results to practically relevant scenarios.

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arXiv2024

Transformation-Free Fixed-Structure Model Reduction for LPV Systems

In this paper, we propose a model reduction technique for linear parameter varying (LPV) systems based on available tools for fixed-structure controller synthesis. We start by transforming a model reduction problem into an equivalent controller synthesis problem by defining an appropriate generalized plant. The controller synthesis problem is then solved by using gradient-based tools available in the literature. Owing to the flexibility of the gradient-based synthesis tools, we are able to impose a desired structure on the obtained reduced model. Additionally, we obtain a bound on the approximation error as a direct output of the optimization problem. The proposed methods are applied on a benchmark mechanical system of interconnected masses, springs and dampers. To evaluate the effect of the proposed model-reduction approach on controller design, LPV controllers designed using the reduced models (with and without an imposed structure) are compared in closed-loop with the original model.

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arXiv2023

Structured IQC Synthesis of Robust $\mathcal{H}_2$ Controllers in the Frequency Domain

The problem of robust controller synthesis for plants affected by structured uncertainty, captured by integral quadratic constraints, is discussed. The solution is optimized towards a worst-case white noise rejection specification, which is a generalization of the standard $\mathcal{H}_2$-norm to the robust setting including possibly non-LTI uncertainty. Arbitrary structural constraints can be imposed on the control solution, making this method suitable for distributed systems. The nonsmooth optimization algorithm used to solve the robust synthesis problem operates directly in the frequency domain, eliminating scalability issues for complex systems and providing local optimality certificates. The method is evaluated using a literature example and a real-world system using a novel implementation of a robust $\mathcal{H}_2$-performance bound.

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arXiv2023

Convergence Properties of Fast quasi-LPV Model Predictive Control

In this paper, we study the convergence properties of an iterative algorithm for fast nonlinear model predictive control of quasi-linear parameter-varying systems without inequality constraints. Compared to previous works considering this algorithm, we contribute conditions under which the iterations are guaranteed to converge. Furthermore, we show that the algorithm converges to suboptimal solutions and propose an optimality-preserving variant with moderately increased computational complexity. Finally, we compare both variants in terms of quality of solution and computational performance with a state-of-the-art solver for nonlinear model predictive control in two simulation benchmarks.

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arXiv2023

A Distributed Linear Quadratic Discrete-Time Game Approach to Formation Control with Collision Avoidance

Formation control problems can be expressed as linear quadratic discrete-time games (LQDTG) for which Nash equilibrium solutions are sought. However, solving such problems requires solving coupled Riccati equations, which cannot be done in a distributed manner. A recent study showed that a distributed implementation is possible for a consensus problem when fictitious agents are associated with edges in the network graph rather than nodes. This paper proposes an extension of this approach to formation control with collision avoidance, where collision is precluded by including appropriate penalty terms on the edges. To address the problem, a state-dependent Riccati equation needs to be solved since the collision avoidance term in the cost function leads to a state-dependent weight matrix. This solution provides relative control inputs associated with the edges of the network graph. These relative inputs then need to be mapped to the physical control inputs applied at the nodes; this can be done in a distributed manner by iterating over a gradient descent search between neighbors in each sampling interval. Unlike inter-sample iteration frequently used in distributed MPC, only a matrix-vector multiplication is needed for each iteration step here, instead of an optimization problem to be solved. This approach can be implemented in a receding horizon manner, this is demonstrated through a numerical example.

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arXiv2023

A Scalable Approach for Analysing Multi-Agent Systems with Heterogeneous Stochastic Packet Loss

An important aspect in jointly analysing networked control systems and their communication is to model the networking in a sufficiently rich but at the same time mathematically tractable way. As such, this paper improves on a recently proposed scalable approach for analysing multi-agent systems with stochastic packet loss by allowing for heterogeneous transmission probabilities and temporal correlation in the communication model. The key idea is to consider the transmission probabilities as uncertain, which facilitates the use of tools from robust control. Due to being formulated in terms of linear matrix inequalities that grow linearly with the number of agents, the result is applicable to very large multi-agent systems, which is demonstrated by numerical simulations with up to 10000 agents.

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arXiv2023

Robust Performance Analysis of Cooperative Control Dynamics via Integral Quadratic Constraints

We study cooperative control dynamics with gradient based forcing terms. As a specific example, we focus on source-seeking dynamics with vehicles embedded in an unknown scalar field with a subset of agents having gradient information. As interaction mechanisms, formation control dynamics and flocking dynamics are considered. We leverage the framework of $α$-integral quadratic constraints to obtain convergence rate estimates whenever exponential stability can be achieved. The communication graph and the interaction potential are assumed to be time-invariant and uncertain. Sufficient conditions take the form of linear matrix inequalities independent of the size of network. A derivation (purely in time-domain) of the so-called \textit{hard} Zames-Falb $α$-IQCs involving general non-causal higher order multipliers is given along with a suitably adapted parameterization of the multipliers to the $α$-IQC setting. The time-domain arguments facilitate a straightforward extension to linear parameter varying systems. Numerical examples illustrate the application of the theoretical results.

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arXiv2023

A Decomposition Approach to Multi-Agent Systems with Bernoulli Packet Loss

In this paper, we extend the decomposable systems framework to multi-agent systems with Bernoulli distributed packet loss with uniform probability. The proposed sufficient analysis conditions for mean-square stability and $H_2$-performance -- which are expressed in the form of linear matrix inequalities -- scale linearly with increased network size and thus allow to analyse even very large-scale multi-agent systems. A numerical example demonstrates the potential of the approach by application to a first-order consensus problem.

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arXiv2023

Gradient-based Cooperative Control of quasi-Linear Parameter Varying Vehicles with Noisy Gradients

This paper extends recent results on the exponential performance analysis of gradient based cooperative control dynamics using the framework of exponential integral quadratic constraints ($α-$IQCs). A cooperative source-seeking problem is considered as a specific example where one or more vehicles are embedded in a strongly convex scalar field and are required to converge to a formation located at the minimum of a field. A subset of the agents are assumed to have the knowledge of the gradient of the field evaluated at their respective locations and the interaction graph is assumed to be uncertain. As a first contribution, we extend earlier results on linear time invariant (LTI) systems to non-linear systems by using quasi-linear parameter varying (qLPV) representations. Secondly, we remove the assumption on perfect gradient measurements and consider multiplicative noise in the analysis. Performance-robustness trade off curves are presented to illustrate the use of presented methods for tuning controller gains. The results are demonstrated on a non-linear second order vehicle model with a velocity-dependent non-linear damping and a local gain-scheduled tracking controller.

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arXiv2023

Robust Performance Analysis for Time-Varying Multi-Agent Systems with Stochastic Packet Loss

Recently, a scalable approach to system analysis and controller synthesis for homogeneous multi-agent systems with Bernoulli distributed packet loss has been proposed. As a key result of that line of work, it was shown how to obtain upper bounds on the $H_2$-norm that are robust with respect to uncertain interconnection topologies. The main contribution of the current paper is to show that the same upper bounds hold not only for uncertain but also time-varying topologies that are superimposed with the stochastic packet loss. Because the results are formulated in terms of linear matrix inequalities that are independent of the number of agents, multi-agent systems of any size can be analysed efficiently. The applicability of the approach is demonstrated on a numerical first-order consensus example, on which the obtained upper bounds are compared to estimates from Monte-Carlo simulations.

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arXiv2022

Event-Triggered l2-Optimal Formation Control with State-Estimation for Agents Modeled as LPV Systems

This paper proposes a distributed scheme with different estimators for the event-triggered formation control of polytopic homogeneously scheduled linear parameter-varying (LPV) multi-agent systems (MAS). Each agent consists of a time-triggered inner feedback loop and a larger event-triggered outer feedback loop to track a formation reference signal and reject input and output noise. If a local event-trigger condition is violated, the event-triggered outer feedback loop is closed through the communication network. The event-trigger condition is only based on locally available information. To design the controller, a synthesis problem is formulated as a linear matrix inequality of the size of a single agent under the assumption, that local estimators trigger intercommunication events with neighboring agents if the event-trigger condition is violated. The design procedure guarantees stability and bounded l2-performance. Furthermore, the estimators are interchangeable for a given controller. We compare in simulation zero-order hold, open-loop estimation, and closed-loop estimation strategies. Simulation trials are carried out with non-holonomic dynamic unicycles modeled as polytopic LPV systems.

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arXiv2022

Finite State Markov Modeling of C-V2X Erasure Links For Performance and Stability Analysis of Platooning Applications

Cooperative driving systems, such as platooning, rely on communication and information exchange to create situational awareness for each agent. Design and performance of control components are therefore tightly coupled with communication component performance. The information flow between vehicles can significantly affect the dynamics of a platoon. Therefore, both the performance and the stability of a platoon depend not only on the vehicle's controller but also on the information flow Topology (IFT). The IFT can cause limitations for certain platoon properties, i.e., stability and scalability. Cellular Vehicle-To-Everything (C-V2X) has emerged as one of the main communication technologies to support connected and automated vehicle applications. As a result of packet loss, wireless channels create random link interruption and changes in network topologies. In this paper, we model the communication links between vehicles with a first-order Markov model to capture the prevalent time correlations for each link. These models enable performance evaluation through better approximation of communication links during system design stages. Our approach is to use data from experiments to model the Inter-Packet Gap (IPG) using Markov chains and derive transition probability matrices for consecutive IPG states. Training data is collected from high fidelity simulations using models derived based on empirical data for a variety of different vehicle densities and communication rates. Utilizing the IPG models, we analyze the mean-square stability of a platoon of vehicles with the standard consensus protocol tuned for ideal communication and compare the degradation in performance for different scenarios.

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arXiv2021

Robust Performance Analysis of Source-Seeking Dynamics with Integral Quadratic Constraints

We analyze the performance of source-seeking dynamics involving either a single vehicle or multiple flocking-vehicles embedded in an underlying strongly convex scalar field with gradient based forcing terms. For multiple vehicles under flocking dynamics embedded in quadratic fields, we show that the dynamics of the center of mass are equivalent to the dynamics of a single agent. We leverage the recently developed framework of $α$-integral quadratic constraints (IQCs) to obtain convergence rate estimates. We first present a derivation of \textit{hard} Zames-Falb (ZF) $α$-IQCs involving general non-causal multipliers based on purely time-domain arguments and show that a parameterization of the ZF multiplier, suggested in the literature for the standard version of the ZF IQCs, can be adapted to the $α$-IQCs setting to obtain quasi-convex programs for estimating convergence rates. Owing to the time-domain arguments, we can seamlessly extend these results to linear parameter varying (LPV) vehicles possibly opening the doors to non-linear vehicle models with quasi-LPV representations. We illustrate the theoretical results on a linear time invariant (LTI) model of a quadrotor, a non-minimum phase LTI plant and two LPV examples which show a clear benefit of using general non-causal dynamic multipliers to drastically reduce conservatism.

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