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5 - Further switched systems
- from Part I - Theory
- Edited by Jan Lunze, Ruhr-Universität, Bochum, Germany, Françoise Lamnabhi-Lagarrigue, Centre National de la Recherche Scientifique (CNRS), Paris
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- Book:
- Handbook of Hybrid Systems Control
- Published online:
- 21 February 2011
- Print publication:
- 15 October 2009, pp 139-192
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Summary
Mixed logical dynamical systems and linear complementarity systems are representations of switched systems, which under the conditions described here are equivalent to the model used in Chapter 4. They are particularly useful for model-predictive control. The equivalences of several hybrid system models show that different models, which are suitable for specific analysis and design problems and have been investigated in detail, cover the same class of hybrid systems. The analysis of the well-posedness of the models leads to conditions on the model equations under which a unique solution exists.
Model-predictive control of hybrid systems
Model-predictive control (MPC) is a widely used technology in industry for control design of highly complex multivariable processes. The idea behind MPC is to start with a model of the open-loop process that explains the dynamical relations among system's variables (command inputs, internal states, and measured outputs). Then, constraint specifications on system variables are added, such as input limitations (typically due to actuator saturation) and desired ranges where states and outputs should remain. Desired performance specifications complete the control problem setup and are expressed through different weights on tracking errors and actuator efforts (as in classical linear quadratic regulation). At each sampling time, an open-loop optimal control problem based on the given model, constraints, weights, and with initial condition set at the current (measured or estimated) state, is repeatedly solved through numerical optimization.
2 - Survey of modeling, analysis, and control of hybrid systems
- from Part I - Theory
- Edited by Jan Lunze, Ruhr-Universität, Bochum, Germany, Françoise Lamnabhi-Lagarrigue, Centre National de la Recherche Scientifique (CNRS), Paris
-
- Book:
- Handbook of Hybrid Systems Control
- Published online:
- 21 February 2011
- Print publication:
- 15 October 2009, pp 31-56
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Summary
An overview of various modeling frameworks for hybrid systems is given followed by a comparison of the modeling power and the model complexity, which can serve as a guideline for choosing the right model for a given analysis or control problem with hybrid dynamics. Then, the main analysis and design tasks for hybrid systems are surveyed together with the methods for their solution, which will be discussed in more detail in subsequent chapters.
Models for hybrid systems
Overview
As models are the ultimate tools for obtaining and dealing with knowledge, not only in engineering, but also in philosophy, biology, sociology, and economics, a search has been undertaken for appropriate mathematical models for hybrid systems. This section gives an overview of the modeling formalisms that have been elaborated in hybrid systems theory in the past.
Structure of hybrid systems Many different models have been proposed in literature, as will be seen in following chapters. These models can be distinguished with respect to the phenomena that they are able to represent in an explicit form. Consequently, these models have different fields of applications. The main idea of these models is described by the block diagram shown in Fig. 2.1, which is often used in literature as a starting point of hybrid systems modeling and analysis, although not all models use this structure in a direct way.
1 - Introduction to hybrid systems
- from Part I - Theory
- Edited by Jan Lunze, Ruhr-Universität, Bochum, Germany, Françoise Lamnabhi-Lagarrigue, Centre National de la Recherche Scientifique (CNRS), Paris
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- Book:
- Handbook of Hybrid Systems Control
- Published online:
- 21 February 2011
- Print publication:
- 15 October 2009, pp 3-30
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Summary
This chapter gives an informal introduction to hybrid dynamical systems and illustrates by simple examples the main phenomena that are encountered due to the interaction of continuous and discrete dynamics. References to numerous applications show the practical importance of hybrid systems theory.
What is a hybrid system?
Wherever continuous and discrete dynamics interact, hybrid systems arise. This is especially profound in many technological systems, in which logic decision making and embedded control actions are combined with continuous physical processes. To capture the evolution of these systems, mathematical models are needed that combine in one way or another the dynamics of the continuous parts of the system with the dynamics of the logic and discrete parts. These mathematical models come in all kinds of variations, but basically consist of some form of differential or difference equations on the one hand and automata or other discrete-event models on the other hand. The collection of analysis and synthesis techniques based on these models forms the research area of hybrid systems theory, which plays an important role in the multi-disciplinary design of many technological systems that surround us.
Three reasons to study hybrid systems
The reasons to study hybrid systems can be quite diverse. Here we will provide three sources of motivation, which are related to (i) the design of technological systems, (ii) networked control systems, and (iii) physical processes exhibiting non-smooth behavior.