The hybrid χ (Chi) formalism integrates concepts from dynamics and control theory with concepts from computer science, in particular from process algebra and hybrid automata. It integrates ease of modeling with a straightforward, structured operational semantics. Its 'consistent equation semantics' enforces state changes to be consistent with invariants as in most hybrid automata. Ease of modeling is ensured by means of the following concepts: 1) different classes of variables: discrete and continuous, of subclass jumping or non-jumping, and algebraic; 2) strong time determinism of alternative composition in combination with delayable guards; 3) integration of urgent and non-urgent actions; 4) differential algebraic equations as a process term as in mathematics; 5) steady-state initialization; and 6) several user-friendly modeling extensions. Furthermore, the Chi language incorporates several concepts for complex system specification: 1) process terms for scoping that integrate abstraction, local variables, local channels and recursion definitions; 2) process definition and instantiation that enable process re-use, encapsulation, hierarchical and/or modular composition of processes; and 3) different interaction mechanisms: handshake synchronization and synchronous communication for discreteevent processes that do not share variables, and shared variables for continuous-time processes. The syntax and semantics are illustrated using many different examples. Furthermore, general translations from hybrid automata and PWA systems to χ are given. Chapter 2 Syntax and informal semantics of the Chi language This section presents a concise definition of the syntax and informal semantics of hybrid χ. The syntax definition is incomplete in the sense that the syntax of predicates, expressions, etc, is not defined.

The increasing complexity of systems and the increasing market pressure necessitate the need for methods to maximize reuse and to minimize the effort to develop new systems. Modelbased engineering is one of these methods. It uses models and model-based techniques in the development process to analyze and synthesize systems and components.

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Tasks executing on general purpose multiprocessor platforms exhibit variations in their execution times. As such, there is a need to explicitly consider robustness, i.e., tolerance to these fluctuations. This work aims to quantify the robustness of schedules of directed acyclic graphs (DAGs) on multiprocessors by defining probabilistic robustness metrics and to present a new approach to perform robustness analysis to obtain these metrics. Stochastic execution times of tasks are used to compute completion time distributions which are then used to compute the metrics. To overcome the difficulties involved with the max operation on distributions, a new curve fitting approach is presented using which we can derive a distribution from a combination of analytical and limited simulation based results. The approach has been validated on schedules of time-critical applications in ASML wafer scanners.

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van der Sanden, L.J.; Nogueira Bastos, J.P.; Voeten, J.P.M.; Geilen, M.C.W.; Reniers, M.A.; Basten, T.; Jacobs, J.; Schiffelers, R.R.H. Published in:Proceedings of the 2016 Forum on specification and Design Languages, FDL 2016, Bremen, Germany, September 14-16, 2016 Published: 01/09/2016 Document VersionPublisher's PDF, also known as Version of Record (includes final page, issue and volume numbers)Please check the document version of this publication:• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication Citation for published version (APA):van der Sanden, L. J., Nogueira Bastos, J. P., Voeten, J. P. M., Geilen, M. C. W., Reniers, M. A., Basten, T., ... Schiffelers, R. R. H. (2016). Compositional specification of functionality and timing of manufacturing systems. In Proceedings of the 2016 Forum on specification and Design Languages, FDL 2016, Bremen, Germany, September 14-16, 2016 General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Abstract-This paper introduces a formal modeling approach for compositional specification of both functionality and timing of manufacturing systems. Functionality aspects can be considered orthogonally to timing aspects. The functional aspects are specified using two abstraction levels; high-level activities and lower level actions. Design of a functionally correct controller is possible by looking only at the activity level, abstracting from the different execution orders of actions and their timing. As a result, controller design can be performed on a much smaller state space compared to an explicit model where timing and actions are present. The performance of the controller can be analyzed and optimized by taking into account the timing characteristics. Since formal semantics are given in terms of a (max, +) sta...

Abstract-Latest trends in embedded platform architectures show a steady shift from high frequency single core platforms to lower-frequency but highly-parallel execution platforms. Scheduling applications with stringent latency requirements on such multiprocessor platforms is challenging. Our work is motivated by the scheduling challenges faced by ASML, the world's leading provider of wafer scanners. A wafer scanner is a complex cyber-physical system that manipulates silicon wafers with extreme accuracy at high throughput. Typical control applications of the wafer scanner consist of thousands of precedence-constrained tasks with latency requirements. Machines are customized so that precise characteristics of the control applications to be scheduled and the execution platform are only known during machine start-up. This results in large-scale scheduling problems that need to be solved during start-up of the machine under a strict timing constraint on the schedule delivery time. This paper introduces a fast and scalable static-order scheduling approach for applications with stringent latency requirements and a fixed binding on multiprocessor platforms. It uses a heuristic that makes scheduling decisions based on a new metric to find feasible schedules that meet timing requirements as quickly as possible and it is shown to be scalable to very large task graphs. The computation of this metric exploits the binding information of the application. The approach will be incorporated into the ASML's latest generation of wafer scanners.