8.7 Hybrid Systems and Control

In this section we present an overview for the development of complex discrete event and hybrid systems within the robotics, automation, and intelligent system domain. We start by presenting an overview of discrete event and hybrid systems, and then illustrate the concept by an example from the robotics and automation domain. The application discussed is for formulating an observer for manipulating agents. Hybrid systems, in which digital and analogue devices and sensors interact over time, is attracting the attention of researchers. Representation of states and the physical system condition includes continuous and discrete numerics, in addition to symbols and logical parameters. Most of the current robotics, automation, and intelligent systems problems, as well as problems in other domains, fall within the description of hybrid systems. There are many issues that need to be resolved, among them, deenitions for observability, stability and stabilizability, controllability in general, uncertainty of state transitions and identiication of the system. The underlying mathematical representation of complex computer-controlled systems is still insuucient to create a set of models which accurately captures the dynamics of the systems over the entire range of system operation. We remain in a situation where we must tradeoo the accuracy of our models with the manageability of the models. Closed-form solutions of mathematical models are almost exclusively limited to linear system models. Computer simulation of nonlinear and discrete-event models provide a means for oo-line design of control systems. Guarantees of system performance are limited to those regions where the robustness conditions apply. These conditions may not apply during startup and shutdown or during periods of anomalous operation. Recently, attempts have been made to model low and high-level system changes in automated and semi-automatic systems as discrete event dynamic systems (DEDS). Several attempts to improve the modeling capabilities are focused on mapping the continuous world into a discrete one. However, repeated results are available which indicate that large interactive systems evolve into states where minor events can lead to a catastrophe. Discrete event and hybrid system formulations have been used in many domains to model and control system state changes within a process. A number of tools and modeling techniques are being used to model and control discrete event systems in the above domains. Some of the modeling strategies include: Timed,