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Hierarchical, Decentralized and/or Modular Control Architectures

[see also: hybrid control system design]

Input/Output-Based Design of Hierarchical Control Systems

Supervisory Control Theory, as originally proposed by P.J. Ramadge and W.M. Wonham, in the late 1980's, provides a sound control theoretic methodology for discrete event systems (DES). In particular, the systematic design of supervisory controllers is addressed within that framework and the resulting controllers can be used to generate provably correct code for programmable logic controllers. However, the overall algorithmic complexity is exponential in the number of plant components. For this reason, hierarchical and/or modular approaches have been discussed in the recent literature. In this research project, we propose to use a variation of J.C. Willems notion of inputs and outputs as a technical basis for a hierarchcal control architecture.

Starting at the plant-layer, each individual plant component is modelled by a formal language that satisfies certain conditions that express two pairs inputs and outputs, one to interact with the plant environment and to interact with a controller. On a per component basis, we design low-level controllers to implement high-level commands and the effect that they are expected to take on the environment. The formal specification at this stage is a superset language of the low-level closed-loop behaviour.

When proceeding to the next layer of the hierarchy, groups of several plant components and their respective low-level controllers are composed. In this step, the interaction among components in each group is described by a dynamic environment model. The composition, however is not based on the actual low-level closed-loop, but by the respective specification. The latter is, by design, a superset of the actual behaviour and can, thus, serve as an abstraction.

Since component composition, controller synthesis and abstraction alternate, we expect for relevant applications a drastic reduction of the computetional complexity. This hypothesis has been validated by an idealized transport system, where the overall complexity turned out almost linear in the number of components; see also libFAUDES HioSys plug-in.

This project has been supported by the German National Research Foundation (Deutsche Forschungsgemeinschaft, DFG). Results for star-languages have been presented at WODES and form the basis of Sebastian Perk's PhD thesis. In our current work, we investigate the situation for omega-languages in order to address more general liveness properties. For more information on this project, please contact Christine Baier.

Hierarchical Control of Structural Decentralized Discrete Event Systems

This work deals with a special class of discrete event systems which are naturally decomposed into subsystems which mainly evolve independent from each other but which perform cooperation actions represented by shared events in the DES framework. Thus there are two main features of these so-called structural decentralized DES:

• On a local level (i.e. each subsystem is considered seperately) the dynamical behavior of each of the subsystems is independent of the dynamical behavior of the other subsystems. This independence is captured in two properties called the mutual controllability and shared event marking condition [Lee and Wong]. These properties allow for DES - controllers which only control the local behavior of one particular subsystem.

• The execution of cooperation actions of two or more subsystems is associated with the occurence of shared events, i.e. for coordination of these actions a controller which only considers the shared behavior of the subsystems can be implemented. The shared behavior can be regarded as a high-level abstracted behavior of the interacting subsystems. Here, we impose variations of so called natural observers [Wang and Wonham] to ensure a non-blocking closed-loop behaviour under high-level supervision.

For the structural decentralized DES described above we are investigating a two level hierarchical control architecture in which the high-level events are identified with the shared events of the subsystems and thus the high-level system captures the concurrent behavior of the subsystems. Each subsystem is equiped with a local controller which controls the local dynamical evolution. In addition to this there is a high-level controller which coordinates the shared behavior (represented by the shared event sequences) of the subsystems. We are investigating the properties of hierarchical consistency for the proposed architecture. Extensions to multi-level hierarchy conclude our work.

This research was initiated by Klaus Schmidt as his PhD project.