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On a Class of General Hybrid Dynamical Systems
IFAC Proceedings Volumes, 1996
Complex systems typically possess a hierarchical structure. characterized by continuous-variable dynamics at the lowest level and logical decision-making at the highest. Virtually all control systems today perfonn computer-coded checks and issue logical as well as continuous-variable control commands. Such are "hybrid" systems. We introduce "general hybrid dynamical systems" as interacting collections of dynamical systems, evolving on continuous-variable state spaces, and subject to continuous controls and discrete phenomena. We discuss modeling issues, giving conditions for trajectories and providing a taxonomy for hybrid systems models. Wc review our hybrid systems analysis results, including topology, complexity/computation, stability tools, and examples. We summarize our hybrid control results. including optimal control theory, control algorithms, and examples.
Hybrid dynamical systems with controlled discrete transitions
Nonlinear Analysis: Hybrid Systems, 2007
This invited survey focuses on a new class of systems -hybrid dynamical systems with controlled discrete transitions. A type of system behavior referred to as the controlled infinitesimal dynamics is shown to arise in systems with widely divergent dynamic structures and application domains. This type of behavior is demonstrated to give rise to a new dynamic mode in hybrid system evolution -a controlled discrete transition. Conceptual and analytical frameworks for modeling of and controller synthesis for such transitions are detailed for two systems classes: one requiring bumpless switching among controllers with different properties, and the other -exhibiting single controlled impacts and controlled impact sequences under collision with constraints. The machinery developed for the latter systems is also shown to be capable of analysing the behavior of difficult to model systems characterized by accumulation points, or Zeno-type behavior, and unique system motion extensions beyond them in the form of sliding modes along the constraint boundary. The examples considered demonstrate that dynamical systems with controlled discrete transitions constitute a general class of hybrid systems.
Solution concepts for hybrid dynamical systems
2002
The recent interest in hybrid systems has given rise to a large variety of model classes and to many different notions of solution trajectories. In this paper we enumerate several solution concepts and compare them on the basis of some examples displaying Zeno behaviour. The relation to well-posedness is also discussed.
A Class of Hybrid Control Systems – Basic Problems and Trends
Revue Roumaine des Sciences Techniques - Serie Électrotechnique et Énergétique
In the hybrid control systems (HCSs) approach considered in this paper, a continuous system is controlled, through an interface, by a discrete event system (DES), representing the controller. Starting from a partition of the continuous state space into open cells, the continuous systemi.e. the plantcoupled to the interface is first abstracted to a discrete state, event driven model. The DES controller is built then within the DES control theory. This contribution emphasizes some specific problems and difficulties arising in this HCSs approach and proposes some extensions and future research directions. A simple and intuitive "toy" example accompanies the theoretical facts.
Towards an integrated conception of hybrid dynamical systems
Proceedings of the 15th IFAC World Congress, 2002, 2002
Hybrid dynamical systems are composed of continuous-time dynamical parts, mixed with event-driven parts. Most of the time, both parts are designed separately using specific techniques of each domain, and integrated a posteriori in an application-specific manner. This approach is restrictive in that it does not exhibit a hybrid global model of the designed system, that would though be required for analysis and behavior-checking to take place. In this paper, we discuss and illustrate our approach of hybrid systems modeling, that is based on the obvious statement that both domains (dynamical and event-driven) must be clearly considered in an integrated manner from the very beginning of the design. In our example, we exhibit a draft formal framework for hybrid system modeling, that would allow for verification techniques. For that purpose, we take advantage of the recently developed techniques and tools, in both areas. The numerical computation laboratorymatlabthat we chose for the dynamical system part design, fits perfectly with our goals. But the reactive synchronous language chosen-Esterel-, if it actually fits with the event-driven part specification, exhibits some weaknesses when dealing with data and values, that are needed when interfacing both parts together.
Towards Modelling of Hybrid Systems
Proceedings of the 45th IEEE Conference on Decision and Control, 2006
The article is an attempt to use methods of category theory and topology for analysis of hybrid systems. We use the notion of a directed topological space, c.f. [1]; it is a topological space together with a set of privileged paths. Dynamical systems are examples of directed topological spaces. A hybrid system consists of a number of dynamical systems that are glued together according to information encoded in the discrete part of the system. Motivated by [2] we develop a definition of a hybrid system as a functor from the category generated by a transition system to the category of directed topological spaces. Its directed homotopy colimit (geometric realization) is a single directed topological space. The behavior of hybrid systems can be then understood in terms of the behavior of dynamical systems through the directed homotopy colimit.
Advanced Textbooks in Control and Signal Processing, 2022
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Modeling and Analysis of Hybrid Systems Lecture Notes
This book deals with the modeling and analysis of hybrid systems from the view point of computer science. Hybrid systems are systems with mixed discrete-continuous behavior. Typical examples are physical systems controlled by a discrete controller. Whereas methods and tools for the modeling and simulation of the dynamic continuous behavior is hosted mainly in physics and control theory, the modeling and analysis of discrete systems is a subject of computer science.
Some Results in Stability Analysis of Hybrid Dynamical Systems
TEMA - Tendências em Matemática Aplicada e Computacional, 2011
In this paper we introduced a general model for the Hybrid Dynamical Systems and for such systems we introduced the usual concept of Lyapunov stability. Furthermore, we established two Principal Lyapunov Theorems and a converse theorem.