Hybrid Modelling in System Simulation

In times of increasing power and capacity in computer simulation mathematical models are getting more and more important. For different technical applications and in natural science but also in economic systems and management processes appropriate mathematical model descriptions are necessary. Hybrid modelling is a special technique for more complex model descriptions in order to reduce the degree of complexity. In different fields of interest the behavior of a model is dependent on the active state. When the model description is changing from one state to another a so-called state event takes place. State event modelling is the overall term to describe this modelling approach. One state is defined by one dynamic system description and another state is described by the next description. The mathematical environment of the model allows finding the description which is the best matching one in each state. In this sense it is possible to find the most efficient model description for each state and it is not necessary to build up a complicated model structure to cover all cases in one model. Beside the principle effect of the basic structure it is also possible to combine different mathematical modelling techniques for realizing a hybrid model for a certain complex system. In each case a certain mathematical model of the mathematical method can be provided. This is the formal mathematical definition of a multi method approach. In different states different models are simulated and a certain master algorithm is managing the overall administration of the discrimination. The mentioned issues are covered under the overall term hybrid modelling and will be introduced in the corresponding paper

Hybrid Modelling in System Simulation

In times of increasing power and capacity in computer, simulation mathematical models are getting more and more important. For different technical applications and in natural science but also in economic systems and management processes appropriate mathematical model descriptions are necessary. Hybrid modelling is a special technique for more complex model descriptions in order to reduce the degree of complexity. In different fields of interest, the behavior of a model is dependent on the active state. When the model description is changing from one state to another, a so-called state event takes place. State event modelling is the overall term to describe this modelling approach. One state is defined by one dynamic system description and another state is described by the next description. The mathematical environment of the model allows finding the description which is the best matching one in each state. In this sense it is possible to find the most efficient model description for each state and it is not necessary to build up a complicated model structure to cover all cases in one model. Beside the principle effect of the basic structure it is also possible to combine different mathematical modelling techniques for realizing a hybrid model for a certain complex system. In each case a certain mathematical model of the mathematical method can be provided. This is the formal mathematical definition of a multi method approach. In different states different models are simulated and a certain master algorithm is managing the overall administration of the discrimination. The mentioned issues are covered under the overall term hybrid modelling and will be introduced in the corresponding paper

Integration of an object formalism within a hybrid dynamic simulation environment

PrODHyS is a general object-oriented environment which provides common and reusable components designed for the development and the management of dynamic simulation of systems engineering. Its major characteristic is its ability to simulate processes described by a hybrid model. In this framework, this paper focuses on the "Object Differential Petri Net" (ODPN) formalism integrated within PrODHyS. The use of this formalism is illustrated through a didactic example relating to the field of Chemical Process System Engineering (PSE)

A Complete Axiomatization of Quantified Differential Dynamic Logic for Distributed Hybrid Systems

We address a fundamental mismatch between the combinations of dynamics that occur in cyber-physical systems and the limited kinds of dynamics supported in analysis. Modern applications combine communication, computation, and control. They may even form dynamic distributed networks, where neither structure nor dimension stay the same while the system follows hybrid dynamics, i.e., mixed discrete and continuous dynamics. We provide the logical foundations for closing this analytic gap. We develop a formal model for distributed hybrid systems. It combines quantified differential equations with quantified assignments and dynamic dimensionality-changes. We introduce a dynamic logic for verifying distributed hybrid systems and present a proof calculus for this logic. This is the first formal verification approach for distributed hybrid systems. We prove that our calculus is a sound and complete axiomatization of the behavior of distributed hybrid systems relative to quantified differential equations. In our calculus we have proven collision freedom in distributed car control even when an unbounded number of new cars may appear dynamically on the road

On the convergence of autonomous agent communities

This is the post-print version of the final published paper that is available from the link below. Copyright @ 2010 IOS Press and the authors.Community is a common phenomenon in natural ecosystems, human societies as well as artificial multi-agent systems such as those in web and Internet based applications. In many self-organizing systems, communities are formed evolutionarily in a decentralized way through agents' autonomous behavior. This paper systematically investigates the properties of a variety of the self-organizing agent community systems by a formal qualitative approach and a quantitative experimental approach. The qualitative formal study by applying formal specification in SLABS and Scenario Calculus has proven that mature and optimal communities always form and become stable when agents behave based on the collective knowledge of the communities, whereas community formation does not always reach maturity and optimality if agents behave solely based on individual knowledge, and the communities are not always stable even if such a formation is achieved. The quantitative experimental study by simulation has shown that the convergence time of agent communities depends on several parameters of the system in certain complicated patterns, including the number of agents, the number of community organizers, the number of knowledge categories, and the size of the knowledge in each category

Collaborative Verification-Driven Engineering of Hybrid Systems

Hybrid systems with both discrete and continuous dynamics are an important model for real-world cyber-physical systems. The key challenge is to ensure their correct functioning w.r.t. safety requirements. Promising techniques to ensure safety seem to be model-driven engineering to develop hybrid systems in a well-defined and traceable manner, and formal verification to prove their correctness. Their combination forms the vision of verification-driven engineering. Often, hybrid systems are rather complex in that they require expertise from many domains (e.g., robotics, control systems, computer science, software engineering, and mechanical engineering). Moreover, despite the remarkable progress in automating formal verification of hybrid systems, the construction of proofs of complex systems often requires nontrivial human guidance, since hybrid systems verification tools solve undecidable problems. It is, thus, not uncommon for development and verification teams to consist of many players with diverse expertise. This paper introduces a verification-driven engineering toolset that extends our previous work on hybrid and arithmetic verification with tools for (i) graphical (UML) and textual modeling of hybrid systems, (ii) exchanging and comparing models and proofs, and (iii) managing verification tasks. This toolset makes it easier to tackle large-scale verification tasks

Multi-level agent-based modeling - A literature survey

During last decade, multi-level agent-based modeling has received significant and dramatically increasing interest. In this article we present a comprehensive and structured review of literature on the subject. We present the main theoretical contributions and application domains of this concept, with an emphasis on social, flow, biological and biomedical models.Comment: v2. Ref 102 added. v3-4 Many refs and text added v5-6 bibliographic statistics updated. v7 Change of the name of the paper to reflect what it became, many refs and text added, bibliographic statistics update