James A. Stiver

Supervisory control of hybrid systems

In this paper, the supervisory control of hybrid systems is introduced and discussed at length. Such control systems typically arise in the computer control of continuous processes, for example, in manufacturing and chemical processes, in transportation systems, and in communication networks. A functional architecture of hybrid control systems consisting of a continuous plant, a discrete-event controller, and an interface is used to introduce and describe analysis and synthesis concepts and approaches. Our approach highlights the interaction between the continuous and discrete dynamics, which is the cornerstone of any hybrid system study. Discrete abstractions are used to approximate the continuous plant. Properties of the discrete abstractions to be appropriate representations of the continuous plant are presented, and important concepts such as determinism and controllability are discussed. Supervisory control design methodologies are presented to satisfy control specifications described by formal languages. Several examples are used throughout the paper to illustrate our approach.

Hybrid System Modeling and Autonomous Control Systems

Hybrid control systems contain two distinct types of systems, continuous state and discrete-state, that interact with each other. Their study is essential in designing sequential supervisory controllers for continuous-state systems, and it is central in designing control systems with high degree of autonomy.

A logical DES approach to the design of hybrid control systems

Hybrid control systems, that is, systems which contain both continuous dynamics and discrete event dynamics are studied in this paper. First, a model is introduced that describes the continuous plant and discrete event controller along with an interface which connects them. A Discrete Event System (DES) automaton description is employed to describe the plant together with the interface and it is used to analyze the hybrid control system. Controllability is defined for hybrid control systems, enhancing existing DES control concepts. It is then used to obtain a controller design method for hybrid control systems.

Modeling and analysis of hybrid control systems

A hybrid control system is a continuous-time system modeled by differential equations, and the controller is a discrete event system modeled by an automaton. A framework for modeling hybrid control systems, including the necessary interface between the plant and controller is presented. A method to represent the entire system as a discrete event system is shown. The concept of determinism is used to analyze hybrid control system behavior and guide in hybrid control system design.<<ETX>>

Interface and Controller Design for Hybrid Control Systems

The hybrid control systems considered here consist of a continuous-time plant under the control of a discrete event system. Communication between the plant and controller is provided by an interface which can convert signals from the continuous domain of the plant to the discrete, symbolic domain of the controller, and vise-versa. When designing a controller for a hybrid system, the designer may or may not be free to design the interface as well. This paper examines these two cases. First, a methodology is presented for designing a controller when the interface and plant are given. This approach is based on the methodology for controller design in logical discrete event systems. Second, a method is presented to design both the interface and controller. This approach is based on the natural invariants of the system.

Event Identification and Intelligent Hybrid Control

Hybrid dynamical systems consist of two types of systems, a continuous state system called the plant and a discrete event system called the supervisor. Since the plant and supervisor are different types of systems, an interface is required to facilitate communication. An important issue in the design of hybrid control systems is the determination of this interface. Essentially, the interface associates logical symbols used by the supervisor with nonsymbolic events representative of the plants behaviour. This chapter discusses a method for learning a hybrid system interface where symbols and events are bound in a way which is compatible with the goal of plant stabilization. The method is called event identification and provides an on-line method for adapting hybrid dynamical systems in the face of unforseen plant variations.

On the controllability of hybrid control systems

It is shown how existing discrete event system (DES) methods can be used to design controllers for hybrid control systems. Specifically, the authors concentrate on the notions of controllability and of the supremal controllable sublanguage, developed by Ramadge and Wonham (1989), and extend those notions to analyze hybrid control control systems using models developed by the authors. Using this notion of controllability, the authors are able to extend DES controller design methods and to design controllers for hybrid control systems.<<ETX>>

Digital control from a hybrid perspective

The framework of hybrid control systems can be used to examine digital control systems. This paper shows how digital control systems can be modeled as hybrid control systems. A technique for designing interfaces for hybrid control systems is presented. An example is employed to demonstrate how this technique, as well as a DES controller design methodology developed earlier, can be applied to improve a digital control system.<<ETX>>

An Invariant based Approach to the Design of Hybrid Control Systems

In this paper, a methodology for hybrid control design is presented. The hybrid systems of interest are characterized by a feedback architecture of a continuous nonlinear plant with a discrete-event controller. The natural invariants of the continuous dynamics are used to partition the state space into regions and to synthesize simple and eAEcient control laws. The paper contains a complete description of the approach including a description of the hybrid control system modeling, of the invariant based approach for the design of the partition, and of the controller synthesis methodology illustrated by examples. The implementation and optimization of the approach are also discussed. The approach presented in this paper not only describes a viable methodology to hybrid design, but also addresses fundamental issues in hybrid system theory that arise in reachability analysis and veri cation approaches that are based on partitions of the continuous state space.

Hybrid control system design based on natural invariants

The hybrid control systems considered here consist of a continuous plant under the control of a discrete event system. Communication between the plant and controller is provided by an interface that can convert signal from the continuous domain to the symbolic domain, and vise-versa. Hybrid control system design generally involves designing a controller, possibly designing some or all of the interface, and in some cases, designing a continuous controller that will become part of the continuous-time plant. This paper examines the case where the interface is partially given, along with the plant and a set of control goals. A method is presented which designs the symbol generating portion of the interface and also yields a controller for the system. The method is based on the natural invariants of the plant. This technique is illustrated by an example in which the design process is simulated via a computer program for an unmanned underwater vehicle.