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Modelling, analysis and design of hybrid systems. (English) Zbl 1003.93001

Lecture Notes in Control and Information Sciences. 279. Berlin: Springer. xiii, 504 p. (2002).
The book summarizes the results of a priority research program called KONDISK-Dynamics and Control of Systems with Mixed Continuous and Discrete Dynamics launched by the DFG in Germany. It consists of Preface, 4 Parts (24 contributions), References, and Applications.
Part I.-Modeling starts with the paper by Lunze that challenges hybrid systems theory for only truly hybrid systems. A system is considered as a hybrid system (HS) if both the continuous states and the state jumps are important for the control task to be solved. Drath combines the classical discrete Petri Net (PN) approach and the concept of continuous PNs in resulting Hybrid Dynamical Nets (HDN). The HDN approach is combined with the concepts of token attributes resulting in Attributed Hybrid Dynamic Nets allowing a more effective modelling by an object-oriented encapsulation of subnets. Bender et al. give an overview of a hybrid extension to the real time object-oriented methodology (ROOM) for the model-based development of HSs including its application in simulation and test case generation. Münnemann et al. define encapsulations and templates for a function block in a way similar to ROOM to create reusable standardized components. Lunze et al. examine the properties of discrete abstractions of continuous systems including the implications of the resulting non-determinism of discrete-event models.
Part II.-Simulation begins with the paper by Remelhe et al. which presents the requirements for modelling of HSs and introduces a software environment for the integration of complex hierarchical discrete-event models in MODELICA, a powerful object-oriented language for continuous systems. Pawletta et al. present a modelling and simulation approach for modular-hierarchically structured systems with hybrid behaviour and complex structural changes. It supports time-varying structures of coupled systems to avoid overhead arising in the coordination of subsystems. Nordwig applies the software engineering concepts of restricted genericity and structural dynamics to the modelling of HSs. The graphical tool zooed based on the object-oriented specification language ZimOO is presented.
Part III.-Analysis and Verification is opened with the survey paper by Kowalewski introducing the formal analysis of HSs. It highlights different directions from which hybrid models and their analysis are approached in computer science and control theory. Nenninger et al. present the net-state-model, a combination of a continuous system (ODE) and a Petri Net. Reachability analysis for a class of HSs is given. The method is explained for HSs with piecewise affine dynamics. It includes an example of a two-tank system. Wolter et al. discuss the analysis of fluid stochastic PNs. An improved numerical solution for nets with two continuous dimensions provides an algorithm based on the ADI discretization. An illustrative example is supplied. Simon et al. describe a method to deal with time critical problems in automatic control of manufacturing systems using timestep PNs. It enables to prevent the net from getting blocked because of timing conditions by solving a linear optimization problem. Huuck et al. present several options how to tackle the complexity arising in the formal verification of HSs. The model checking approach is combined with abstraction and decomposition techniques such as the assumption/commitment method as well as deductive methods.
Part IV.-Controller Synthesis begins with the paper by Moor et al. It deals with the abstraction monotone continuous systems with discrete external signal (as described in Part I by Lunze et al.) to synthesize a discrete-event controller. Lunze et al. present a two-level approach for controller reconfiguration for systems modelled by a timed stochastic automaton. First, a discrete-event model of the faulty system is used to design a discrete controller, bringing the system into a new equilibrium. Then, a linear controller is designed to stabilize the system around the new equilibrium. Wegele et al. examine a robust controller design for HSs. To prove robustness of the control design, a verification technique based on optimization is used. Müller et al. propose a discrete controller design for a continuous system. The Petri-Net-State-Model involves modules of PNs for the discrete partial modes and extended state space models describing continuous parts, coupled via binary interfaces to synthesize controller corrections. Undesired transitions are detected in the condensation of the evolution graph and excluded by modifications of the PN and the firing conditions. Buss et al. define the hybrid optimal control problem for hybrid nonlinear systems. Two solution techniques are given to get suboptimal solutions, i.e fixed interior point constraints on a grid and branch-and-bound. An example is supplied. Stursberg et al. describe a linear mixed-integer discrete-time approximation of a HS for a linear cost function.
Part V.-Applications starts with the paper by Decknatel et al. defining hybrid high-level nets based on Colored PNs. This concept is applied to the performance analysis of a train protection system. Mosterman et al. deal with a modelling and simulation approach for analysis of aircraft elevator feedback with incorporated redundancy management system. Manz et al. present an online monitoring method based on a combination of qualitative and dynamic models. An online state space reduction, an online analysis for failure detection and hazard prediction are carried out. They are applied to the three-tank-system example. Czogalla et al. describe a method efficiently combining different modelling approaches, such as mesoscopic, cellular, and microscopic, to simulate controlled road traffic. Schlegl et al. present a hybrid controller for a robotic hand. The controller architecture comprises a complex planning scheme and a formal method to compensate discrete contact state error.
The volume essentially contributes to a more comprehensive understanding of hybrid systems both in the computer science and the control engineering communities. The book is an excellent up-to-date resource of working knowledge with long-term evidence in the field. Both theoretical and practical aspects of continuous-discrete systems are covered. The proceedings can serve also as a useful reference book about this challenging research topic. The book is intended for all professionals, researchers, practitioners, and graduate students in control, electrical, and mechanical engineering as well as in computer science interested in the subject.

MSC:

93-06 Proceedings, conferences, collections, etc. pertaining to systems and control theory
00B15 Collections of articles of miscellaneous specific interest
93A30 Mathematical modelling of systems (MSC2010)
93C99 Model systems in control theory
68N30 Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)
68U20 Simulation (MSC2010)
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