Consensus-based control for a network of diffusion PDEs with boundary local interaction

In this paper the problem of driving the state of a network of identical agents, modeled by boundary-controlled heat equations, towards a common steady-state profile is addressed. Decentralized consensus protocols are proposed to address two distinct problems. The first problem is that of steering the states of all agents towards the same constant steady-state profile which corresponds to the spatial average of the agents initial condition. A linear local interaction rule addressing this requirement is given. The second problem deals with the case where the controlled boundaries of the agents dynamics are corrupted by additive persistent disturbances. To achieve synchronization between agents, while completely rejecting the effect of the boundary disturbances, a nonlinear sliding-mode based consensus protocol is proposed. Performance of the proposed local interaction rules are analyzed by applying a Lyapunov-based approach. Simulation results are presented to support the effectiveness of the proposed algorithms

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

Principles and Concepts of Agent-Based Modelling for Developing Geospatial Simulations

The aim of this paper is to outline fundamental concepts and principles of the Agent-Based Modelling (ABM) paradigm, with particular reference to the development of geospatial simulations. The paper begins with a brief definition of modelling, followed by a classification of model types, and a comment regarding a shift (in certain circumstances) towards modelling systems at the individual-level. In particular, automata approaches (e.g. Cellular Automata, CA, and ABM) have been particularly popular, with ABM moving to the fore. A definition of agents and agent-based models is given; identifying their advantages and disadvantages, especially in relation to geospatial modelling. The potential use of agent-based models is discussed, and how-to instructions for developing an agent-based model are provided. Types of simulation / modelling systems available for ABM are defined, supplemented with criteria to consider before choosing a particular system for a modelling endeavour. Information pertaining to a selection of simulation / modelling systems (Swarm, MASON, Repast, StarLogo, NetLogo, OBEUS, AgentSheets and AnyLogic) is provided, categorised by their licensing policy (open source, shareware / freeware and proprietary systems). The evaluation (i.e. verification, calibration, validation and analysis) of agent-based models and their output is examined, and noteworthy applications are discussed.Geographical Information Systems (GIS) are a particularly useful medium for representing model input and output of a geospatial nature. However, GIS are not well suited to dynamic modelling (e.g. ABM). In particular, problems of representing time and change within GIS are highlighted. Consequently, this paper explores the opportunity of linking (through coupling or integration / embedding) a GIS with a simulation / modelling system purposely built, and therefore better suited to supporting the requirements of ABM. This paper concludes with a synthesis of the discussion that has proceeded. The aim of this paper is to outline fundamental concepts and principles of the Agent-Based Modelling (ABM) paradigm, with particular reference to the development of geospatial simulations. The paper begins with a brief definition of modelling, followed by a classification of model types, and a comment regarding a shift (in certain circumstances) towards modelling systems at the individual-level. In particular, automata approaches (e.g. Cellular Automata, CA, and ABM) have been particularly popular, with ABM moving to the fore. A definition of agents and agent-based models is given; identifying their advantages and disadvantages, especially in relation to geospatial modelling. The potential use of agent-based models is discussed, and how-to instructions for developing an agent-based model are provided. Types of simulation / modelling systems available for ABM are defined, supplemented with criteria to consider before choosing a particular system for a modelling endeavour. Information pertaining to a selection of simulation / modelling systems (Swarm, MASON, Repast, StarLogo, NetLogo, OBEUS, AgentSheets and AnyLogic) is provided, categorised by their licensing policy (open source, shareware / freeware and proprietary systems). The evaluation (i.e. verification, calibration, validation and analysis) of agent-based models and their output is examined, and noteworthy applications are discussed.Geographical Information Systems (GIS) are a particularly useful medium for representing model input and output of a geospatial nature. However, GIS are not well suited to dynamic modelling (e.g. ABM). In particular, problems of representing time and change within GIS are highlighted. Consequently, this paper explores the opportunity of linking (through coupling or integration / embedding) a GIS with a simulation / modelling system purposely built, and therefore better suited to supporting the requirements of ABM. This paper concludes with a synthesis of the discussion that has proceeded

Using Hybrid Agent-Based Systems to Model Spatially-Influenced Retail Markets

One emerging area of agent-based modelling is retail markets; however, there are problems with modelling such systems. The vast size of such markets makes individual-level modelling, for example of customers, difficult and this is particularly true where the markets are spatially complex. There is an emerging recognition that the power of agent-based systems is enhanced when integrated with other AI-based and conventional approaches. The resulting hybrid models are powerful tools that combine the flexibility of the agent-based methodology with the strengths of more traditional modelling. Such combinations allow us to consider agent-based modelling of such large-scale and complex retail markets. In particular, this paper examines the application of a hybrid agent-based model to a retail petrol market. An agent model was constructed and experiments were conducted to determine whether the trends and patterns of the retail petrol market could be replicated. Consumer behaviour was incorporated by the inclusion of a spatial interaction (SI) model and a network component. The model is shown to reproduce the spatial patterns seen in the real market, as well as well known behaviours of the market such as the "rocket and feathers" effect. In addition the model was successful at predicting the long term profitability of individual retailers. The results show that agent-based modelling has the ability to improve on existing approaches to modelling retail markets.Agents, Spatial Interaction Model, Retail Markets, Networks

Shocks in coupled socio-ecological systems: what are they and how can we model them?

Coupled socio-ecological systems (SES) are complex systems characterized by self-organization, non-linearities, interactions among heterogeneous elements within each subsystem, and feedbacks across scales and among subsystems. When such a system experiences a shock or a crisis, the consequences are difficult to predict. In this paper we first define what a shock or a crisis means for SES. Depending on where the system boundary is drawn, shocks can be seen as exogenous or endogenous. For example, human intervention in environmental systems could be seen as exogenous, but endogenous in a socio-environmental system. This difference in the origin and nature of shocks has certain consequences for coupled SES and for policies to ameliorate negative consequences of shocks. Having defined shocks, the paper then focuses on modelling challenges when studying shocks in coupled SES. If we are to explore, study and predict the responses of coupled SES to shocks, the models used need to be able to accommodate (exogenous) or produce (endogenous) a shock event. Various modelling choices need to be made. Specifically, the ‘sudden’ aspect of a shock suggests the time period over which an event claimed to be a shock occurred might be ‘quick’. What does that mean for a discrete event model? Turning to magnitude, what degree of change (in a variable or set of variables) is required for the event to be considered a shock? The ‘surprising’ nature of a shock means that none of the agents in the model should expect the shock to happen, but may need rules enabling them to generate behaviour in exceptional circumstances. This requires a certain design of the agents’ decision-making algorithms, their perception of a shock, memory of past events and formation of expectations, and the information available to them during the time the shock occurred

Control limitations from distributed sensing: theory and Extremely Large Telescope application

We investigate performance bounds for feedback control of distributed plants where the controller can be centralized (i.e. it has access to measurements from the whole plant), but sensors only measure differences between neighboring subsystem outputs. Such "distributed sensing" can be a technological necessity in applications where system size exceeds accuracy requirements by many orders of magnitude. We formulate how distributed sensing generally limits feedback performance robust to measurement noise and to model uncertainty, without assuming any controller restrictions (among others, no "distributed control" restriction). A major practical consequence is the necessity to cut down integral action on some modes. We particularize the results to spatially invariant systems and finally illustrate implications of our developments for stabilizing the segmented primary mirror of the European Extremely Large Telescope.Comment: submitted to Automatic