Co-Chair | Jonathan Sprinkle
Department of Electrical Engineering and Computer Science University of California, Berkeley Berkeley, CA |
Co-Chair | Pieter J.
Mosterman Real-time and Simulation Technologies The MathWorks, Inc. USA |

Over the last decades engineered systems have reached a tremendous level of complexity, involving expertise from many disciplines and entailing a variety of implementation technologies (e.g., embedded software, microelectromechanical systems, analog circuits, and digital circuits).

Paper 1 [Bert van Beek] presents the hybrid Chi language, a formalism for modeling, simulation and verification of hybrid systems. The formal semantics of hybrid Chi allows the definition of provably correct implementations for simulation, verification and real-time control. This paper discusses the principles of deriving an implementation for simulation and verification directly from the semantics, and presents an implementation based on a symbolic solver. The simulator is illustrated by means of a case study.

Paper 2 [Gabor Karsai] presents Model-Integrated Computing as a development approach that advocates the use of Domain-Specific Modeling throughout the system development process and lifecycle. This paper describes and summarizes the generic and reusable software tools that support MIC and which can be tailored to solve a wide variety of modeling, analysis, and generation problems in an engineering process.

Paper 3 [Madhukar Anand] discusses the use of dimensional analysis in scientific applications. Dimensional analysis forms a basis for catching errors as it introduces a type discipline into the equations and formulae. Dimensions in physical quantities are measured via their standard units. However, many programming and modeling tools provide limited support for incorporating these units into the variables. Thus, it is quite difficult for a programmer to ensure dimensional consistency in the code. Different existing standards for units further complicates this problem and an incautious use could cause inconsistencies, often with catastrophic results. In this paper, we propose an extension of the basic type system in CHARON, a language for modeling of hybrid systems, to include Unit and Dynamic data types. Through a combination of indirect user-guided annotations and type inference, we address the problem of ensuring both dimensional consistency, and consistency with respect to different unitsystems. Further, we also introduce dynamic data typing, that allows programmers to specify entities that bind at runtime. Such abstractions are particularly useful to program controllers for dynamic environments. We illustrate these benefits with an example on mobile robots.

Paper 4 [T. John Koo] proposes a computational approach for estimating the stability region of an asymptotically stable equilibrium point. The stability region is estimated through an iterative process specified as an algorithm. Reachable sets are used in the estimation algorithm for checking the invariant property of the initial estimate of a stability region and for representing the enlarged stability regions. The convergence of the estimation algorithm can be shown by considering the sequence properties of the reachable sets. Level set methods are used for representing reachable sets and tracking the evolution of the boundary of a reachable set since they can be used to effectively represent complex continuous sets and, furthermore, there exist efficient computation methods for computing the evolution of reachable sets for nonlinear systems. The proposed approach allows natural extension to higher dimensional systems and enables the computation to be carried out in a parallel manner. ReachLab, a model-based tool, is developed to enable rapid prototyping of the algorithm, and to allow the use of various computation methods for implementing the algorithm on a cluster of parallel computing machines. The accuracy of the proposed approach is compared with another accurate approach. The computation results for three nonlinear systems are presented.

Paper 5 [Sagar Sen] presents a methodology that enables the specification and synthesis of software tools to aid in plant and controller modeling for multi-domain (electrical, mechanical, ...) physical systems. The methodology is based on meta-modeling and graph rewriting. The plant is modeled in a domain-specific formalism called the Real World Visual Model (RWVM). Such a model is successively transformed to an Idealized Physical Model (IPM), to an Acausal Bond Graph (ABG), and finally to a Causal Bond Graph (CBG). A Modelica model, consisting of a Causal (algebraic and differential equation) Block Diagram (CBD), is generated from the CBG. All transformations are explicitly modeled using Graph Grammars. A PID controller model, specified in Modelica as a CBD is subsequently integrated with the plant model. AToM^3, A Tool for Multi-formalism and Meta Modeling is used to meta-model and synthesize visual modeling environments for the RWVM, IPM, ABG, and CBG formalisms as well as for transformations between them. The entire process of modeling, transformation, and simulation is demonstrated by means of a hoisting device example. Our methodology drastically reduces development time (of the modeling tool an indirectly of the domain-specific models), integrates model checking via Bond Graph causal analysis, and facilitates management and reuse of meta-knowledge by explicitly modeling formalisms and transformations.

Paper
6 [Pieter Collins] presents the software package ConPAHS, that
facilitates control design of continuous-time piecewise-affine hybrid
systems on polytopes. For the control objective of reaching a
particular state from a specified initial state, the output of the
package is a piecewise-affine control law. After a short review of the
control theory for this problem, the paper presents the functional
specification of ConPAHS, the objected oriented software principles
used, the program structure, and the design choices. Three examples
including simulations are provided to illustrate the use of ConPAHS.

- D.A. Van Beek, K.L. Man, M.A. Reniers, J.E. Rooda, and R.R.H. Schiffelers,
*Eindhoven University of Technology*, Eindhoven, Netherlands**"The Model-Integrated Computing Toolsuite: Metaprogrammable Tools for Embedded Control System Design"**, slides- Gabor Karsai, Akos Ledeczi, Sandeep Neema, and Janos Sztipanovits
- Department of Electrical and Computer Engineering,
*Vanderbilt University*, Nashville, TN **"Unit & Dynamic Typing in Hybrid Systems Modeling with CHARON"**, slides- Madhukar Anand, Insup Lee, George J. Pappas, and Oleg Sokolsky,
- Department of Electrical and Systems Engineering,
*University of Pennsylvania*, Philadelphia, PA **"A Computational Approach for Estimating Stability Regions"**, slides- T. John Koo and Hang Su
- Department of Electrical and Computer Engineering,
*Vanderbilt University*, Nashville, TN **"Multi-Domain Physical System Modeling and Control Based on Meta-Modeling and Graph Rewriting"**, slides- Sagar Sen and Hans Vangheluwe
- Department of Computer Science,
*McGill University*, Montreal, Canada **"ConPAHS - a Software Package for Control of Piecewise-Affine Hybrid Systems"**, slides- Pieter Collins, Luc C.G.J.M Habets, Anton Kuut, Margreet Nool, Mihaly Petreczky, and Jan H. van Schuppen
*Center for Mathematics and Computer Science*, Amsterdam, Netherlands