From Hybrid Automata to DAE-Based Modeling

The use of formal methods, techniques and tools may generally guarantee a systems' safe operation. Such a process includes system modeling with a mathematical model, which is an approximation of the physical system, and is used to make easier the next step of analysis. Formal analysis of hybrid systems, which involve mixed continuous-valued and discrete dynamics, is concerned with verifying whether a hybrid system satisfies a desired specification, like avoiding an unsafe region of the state space. In this paper, we examine the general impact of hybrid automata on modeling and analyzing hybrid systems and we discuss in particular some advantages that arise when exploiting them in the context of particular methods for verifying the reachability of states in common paradigms that have already being investigated with other classical methods. Finally, we use two case studies concerning different classes of hybrid automata to demonstrate the applicability and the efficiency of explo...

HAL (Le Centre pour la Communication Scientifique Directe), 2022

Since its 3.3 release, Modelica offers the possibility to specify models of dynamical systems with multiple modes having different DAE-based dynamics. However, the handling of such models by the current Modelica tools is not satisfactory, with mathematically sound models yielding exceptions at runtime. In this report, we illustrate this behavior on several small-sized examples, shedding light on the shortcomings of the approximate structural analysis implemented in current Modelica tools. To address part of these issues, we propose a systematic transformation process for multimode Modelica models, based on the results of an already implemented multimode structural analysis, that guarantees that the output Modelica model is correctly compiled by state-of-the-art Modelica tools. Still, this transformation is limited to models that do not exhibit impulsive behaviors at mode changes: the remaining issues illustrated by our introductory examples can only be solved by a structural analysis of mode changes, coupled with a specific handling of impulsive variables. We address these points in this report by proposing, first, a structural analysis method able to handle modes and mode changes in a unified framework, and second, a compile-time identification and characterization of impulsive variables. Implementations of both methods, based on efficient symbolic representations and algorithms, are in the works.

Formal analysis of Simulink/Statefow (SLSF) diagrams requires association of semantics to these diagrams. In this thesis, we present a technique and the related tool called HyLink for translating a useful subclass of SLSF diagrams to hybrid automata. In the absence of ocial semantics, there are two possible interpretations of these diagrams: one is based on the ideal mathematical interpretation obtained from the syntax of the building blocks and the other is based on the simulation traces generated by the simulation engine. These two interpretations lead to two di erent kinds of hybrid automata-the former gives an automaton with state-dependent transitions and the latter gives a time-triggered automaton. We show that under certain assumptions, the semantics of the latter converge to the former as the simulation step size decreases. We illustrate HyLink's translation scheme, the assumptions, and the convergence result through several case studies.

SIMULATION SERIES, 1997

Non linear behaviors of real-world physical systems are often abstracted into piecewise linear models by simplifying component parameters or coarsening the time scale of behavior analysis. The net result is often abrupt, discontinuous changes in system behavior, which typically violate the principles of continuity of power and conservation of energy. We have developed a hybrid modeling paradigm that combines energetic bond graph models with nite state automata for discrete meta-level control of model con ...

Physical systems are by nature continuous, but often nonlinear. This increases model complexity and causes numerical sti ness in simulation. By modeling these nonlinearities as discontinuities, the models can be linearized and operate in multiple modes. This paper discusses a hybrid modeling methodology that combines continuous energy ow m o deling using bond graphs and discrete signal ow modeling using controlled junctions with associated nite state automata to generate complex, multi-mode behavior. When threshold values are crossed, multiple discontinuous changes may occur before a new continuous mode of operation is reached. An analysis method is presented to establish physically inconsistent areas based on the energy distribution in the system at the time of switching. Time complexity o f the method is constrained by a model partitioning approach based on identifying areas of instantaneous change.

Frequently, systems showing time-continuous as well as time-discrete behavior arise in multi-physics problems. Simulators supporting the dynamic simulation of hybrid systems often can deal with simple model variations only. A fundamental change of the model structure such as adding or removing differential or algebraic equations (structural variability) is not possible with most simulators. Unlike presently available Modelica simulators, Mosilab can be used to describe systems with inherent dynamics of the model structure, i.e. systems whose mathematical structure can change during simulation. Within Mosilab, the modeling language Mosila is used which is essentially Modelica with an extension based on statecharts for the mapping of state dependent changes of the model structure. Several numerical solvers can be used for simulation. Because events changing the state of the system may appear, the solvers have to fulfil certain requirements such as calculating consistent initial condit...

Proceedings of the 20th International Conference on Hybrid Systems: Computation and Control

Differential Algebraic Equation (DAE) systems constitute the mathematical model supporting physical modeling languages such as Modelica, VHDL-AMS, or Simscape. Unlike ODEs, they exhibit subtle issues because of their implicit latent equations and related differentiation index. Multi-mode DAE (mDAE) systems are much harder to deal with, not only because of their mode-dependent dynamics, but essentially because of the events and resets occurring at mode transitions. Unfortunately, the large literature devoted to the numerical analysis of DAEs does not cover the multi-mode case. It typically says nothing about mode changes. This lack of foundations cause numerous difficulties to the existing modeling tools. Some models are well handled, others are not, with no clear boundary between the two classes. In this paper we develop a comprehensive mathematical approach to the structural analysis of mDAE systems which properly extends the usual analysis of DAE systems. We define a constructive semantics based on nonstandard analysis and show how to produce execution schemes in a systematic way. This report is an extended version of the publication [2].

International Joint Conference on Artificial Intelligence, 1997

Modeling abstractions in physical systems result in hybrid models which encompass continuous behaviors with discrete changes, causing discontinuities in system behavior generation which violate the physical laws of conservation of energy and continuity of power. This paper develops a formal specification for handling discrete model configuration changes at welldefined points in time, and a consistent transfer of the continuous system state from a previous model configuration to a new one based on the ...

A rigorous means for modeling and evaluating hybrid systems is needed for the efficient and cost-effective development of embedded real-time software for a wide variety of applications (weapons, manufacturing, intelligent vehicles, process control). The development of a standard hybrid systems modeling language (SHSML) and corresponding rigorous simulation environments represent important contributions to fulfilling this requirement