Peter Wieland

Brief paper: An internal model principle is necessary and sufficient for linear output synchronization

Output synchronization of a network of heterogeneous linear state-space models under time-varying and directed interconnection structures is investigated. It is shown that, assuming stabilizability and detectability of the individual systems and imposing very mild connectedness assumptions on the interconnection structure, an internal model requirement is necessary and sufficient for synchronizability of the network to polynomially bounded trajectories. The resulting dynamic feedback couplings can be interpreted as a generalization of existing methods for identical linear systems.

On consensus in multi-agent systems with linear high-order agents

Abstract Consensus of a group of agents in a multi-agent system is considered. All agents are modeled by identical linear n th order dynamical systems and the interconnection topology between the agents is modeled as a directed weighted graph. We provide answers to the questions whether the group converges to consensus and what consensus value it eventually reaches. Furthermore, we give a necessary and sufficient condition for convergence to consensus in the double integrator case and propose an LMI-based design for group consensus in the general case. An example is used to illustrate the results.

On topology and dynamics of consensus among linear high-order agents

Consensus of a group of agents in a multi-agent system with and without a leader is considered. All agents are modelled by identical linear n-th order dynamical systems while the leader, when it exists, may evolve according to a different linear model of the same order. The interconnection topology between the agents is modelled as a directed weighted graph. We provide answers to the questions of whether the group converges to consensus and what consensus value the group eventually reaches. To that end, we give a detailed analysis of relevant algebraic properties of the graph Laplacian. Furthermore, we propose an LMI-based design for group consensus in the general case.

Constructive safety using control barrier functions

Abstract This paper presents a new safety feedback design for nonlinear systems based on barrier certificates and the idea of control Lyapunov functions. In contrast to existing methods, this approach ensures safety independently of abstract high-level tasks that might be unknown or change over time. Leaving as much freedom as possible to the safe system, the authors believe that the flexibility of this approach is very promising. The design is validated using an illustrative example.

An Internal Model Principle for Consensus in Heterogeneous Linear Multi-Agent Systems

Abstract The problem of reaching consensus in a heterogeneous multi-agent system is considered. The agents are modeled as linear time-invariant systems with potentially different state dimension and different dynamics. The interconnection topology between the agents is modeled as a directed and weighted graph. We propose an internal model principle for consensus translating in necessary conditions for existence of solutions to the output and state consensus problem.

On Synchronous Steady States and Internal Models of Diffusively Coupled Systems

We investigate the problem of synchronizing nonidentical nonlinear dynamical systems by means of generalized diffusive couplings. The focus is not on the actual solution to the problem but on the derivation of necessary conditions for the existence of such a solution despite the systems possessing nonidentical models. We show that for the problem to be solvable a synchronous steady state needs to exist. This condition leads to the requirement that all individual system models need to embed an internal model of some common endosystem. The latter condition is expressed in terms of nonlinear partial differential equations. The conditions derived in this paper are related to those known from the theory of output regulation.

Parameterization models for pesticide exposure via crop consumption.

An approach for estimating human exposure to pesticides via consumption of six important food crops is presented that can be used to extend multimedia models applied in health risk and life cycle impact assessment. We first assessed the variation of model output (pesticide residues per kg applied) as a function of model input variables (substance, crop, and environmental properties) including their possible correlations using matrix algebra. We identified five key parameters responsible for between 80% and 93% of the variation in pesticide residues, namely time between substance application and crop harvest, degradation half-lives in crops and on crop surfaces, overall residence times in soil, and substance molecular weight. Partition coefficients also play an important role for fruit trees and tomato (Kow), potato (Koc), and lettuce (Kaw, Kow). Focusing on these parameters, we develop crop-specific models by parametrizing a complex fate and exposure assessment framework. The parametric models thereby reflect the frameworks physical and chemical mechanisms and predict pesticide residues in harvest using linear combinations of crop, crop surface, and soil compartments. Parametric model results correspond well with results from the complex framework for 1540 substance-crop combinations with total deviations between a factor 4 (potato) and a factor 66 (lettuce). Predicted residues also correspond well with experimental data previously used to evaluate the complex framework. Pesticide mass in harvest can finally be combined with reduction factors accounting for food processing to estimate human exposure from crop consumption. All parametric models can be easily implemented into existing assessment frameworks.

Dynamics of pesticide uptake into plants

Dynamic plant uptake models are suitable for assessing environmental fate and behavior of toxic chemicals in food crops. However, existing tools mostly lack in-depth analysis of system dynamics. Furthermore, no existing model is available as parameterized version that is easily applicable for use in spatially resolved frameworks for comparative assessment. In the present paper, we thus analyze the dynamics of substance masses in a multi-compartment plant-environment system by applying mathematical decomposition techniques. We thereby focus on the evolution of pesticide residues in crop components harvested for human consumption by taking wheat grains as example. Results show that grains, grain surface and soil are the compartments predominantly influencing the mass evolution of most pesticides in the plant-environment system as a function of substance degradation in plant components and overall residence time in soil. Additional influences are associated with substance molecular weight and time span between pesticide application and crop harvest. Building on these findings, we provide an accurate and yet simple linear approximation of the dynamical system to predict masses in harvested crop components relative to the total applied pesticide, defined as harvest fractions. Parameterized predictions correspond well with results from the full dynamic model, with an overall deviation of a factor 22 for harvest fractions in the relevant range between 1 and 10-10 in wheat. The in-depth analysis of model dynamics provides additional information of the evolution of pesticides in food crops, which is important for regulators and practitioners. In addition, the parametric representation of system dynamics allows for drastically reducing input data requirements and for comparing harvest fractions of a wide range of substances without using a complex dynamic model. Highlights? We analytically decompose a complex model to simulate pesticides uptake into plants. ? We assess initial mass, substance & crop properties influencing the system dynamics. ? High variability in degradation half-lives and residence times is emphasized. ? The full dynamic model is summarized in a parametric representation for wheat. ? Key compartments are fruit, plant surface and soil for cereals.

An internal model principle for synchronization

The problem of achieving synchrony in a group of heterogeneous systems is considered. By synchrony, we understand the fact of temporal coincidence of output trajectories of the individual systems. The individual systems are modeled as general time-invariant nonlinear systems which are coupled through relative error measures. The question is addressed, what properties the individual systems need to possess if there exists a solution to the synchronization problem. An answer to that question is given in the form of an internal model principle for synchronization representing a necessary condition for synchronization.

On consensus among identical linear systems using input-decoupled functional observers

The consensus problem among identical linear systems under relative sensing is considered. We propose a method to design dynamic feedback laws depending on relative output measures between the individual systems, that ensure temporal coincidence of the output trajectory of all members of the group. Our method is based on functional input-decoupled observers and a static feedback. The two design steps can be performed independently with independent robustness features.