Thomas Moor

Nonblocking Hierarchical Control of Decentralized Discrete Event Systems

This contribution investigates the hierarchical control of decentralized discrete event systems (DES) that are synchronized by shared events. A hierarchical control architecture providing hierarchical consistency is introduced. Moreover, it allows for composition of decentralized subsystems on the high-level of the hierarchy and hence reduces the computational complexity of supervisory control synthesis for language inclusion specifications. In this context, a crucial issue is the nonblocking operation of the overall system. Our main theorem identifies sufficient conditions for this desirable property.

Supervisory control of hybrid systems within a behavioural framework

Abstract This contribution addresses the synthesis of supervisory control for hybrid systems Σ with discrete external signals. Such systems are in general neither l -complete nor can they be represented by finite state machines. We find an l -complete approximation (abstraction) Σ l for Σ , represent it by a finite state machine, and investigate the control problem for the approximation. If a solution exists, we synthesize the maximally permissive supervisor for Σ l . We show that it also solves the control problem for the hybrid system Σ . If no solution exists, approximation accuracy can be increased by computing a k -complete abstraction Σ k , k>l . This paper is entirely set within the framework on Willems’ behavioural systems theory.

Non-deterministic temporal logics for general flow systems

In this paper, we use the constructs of branching temporal logic to formalize reasoning about a class of general flow systems, including discrete-time transition systems, continuous-time differential inclusions, and hybrid-time systems such as hybrid automata. We introduce Full General Flow Logic, GFL ⋆ , which has essentially the same syntax as the well-known Full Computation Tree Logic, CTL ⋆ , but generalizes the semantics to general flow systems over arbitrary time-lines. We propose an axiomatic proof system for GFL ⋆ and establish its soundness w.r.t. the general flow semantics.

Robust Controller Synthesis for Hybrid Systems Using Modal Logic

In this paper, we formulate and robustly solve a quite general class of hybrid controller synthesis problems. The type of controller we investigate is the switching control mechanism of a hybrid automaton (via guard and mode invariant sets), and the robustness result is with respect to variations in the right hand sides of the differential equations that depend continuously on a parameter. We present a novel methodology for controller design and synthesis which uses modal logic as a formalism for reasoning about sets of plant states, and various operators on sets arising from the differential equations and from metric tolerance relations on the state space.

Abstraction based supervisory controller synthesis for high order monotone continuous systems

Abstraction based approaches to hybrid control systems synthesis have so far been mostly limited to problems with low-order linear continuous dynamics. In this paper, results from the theory of monotone dynamical systems are used to efficiently compute discrete abstractions for a class of nonlinear models. Furthermore, a situation is investigated where the high-dimensional plant state converges to a low-dimensional manifold; in the proposed approach the computational effort is governed by the dimension of the low-order manifold without neglecting the high-order dynamics. Results are applied to synthesize a discrete event controller for the automatic start-up of a nonlinear distillation column model of order 42.

Fault-Tolerant Control of Discrete Event Systems based on Fault-Accommodating Models

Abstract Fault-tolerant control systems with discrete-event dynamics allow for differing sets of design requirements, that specify the systems behaviour during nominal operation and in the case of component degradation or component malfunction. This paper is concerned with the design of fault-tolerant control algorithms for discrete event systems in the framework of supervisory control theory. Its main contribution is a modelling framework that describes the evolution of systems which are potentially subject to faults. These models are called fault-accommodating models. Within this context, the occurrence of faults is modelled by means of unobservable and uncontrollable events. Hence, the design problem of fault-tolerant controllers is transformed to a supervisory control problem under partial observation. Consequently, there is no need for explicitly diagnosing the occurrence of faults and relaxed diagnosability conditions are applied. Finally, the paper provides extensive examples in order to illustrate the application of all derived methodological results. All computations needed for controller design and system analysis were implemented using a freely available software toolbox.

Controller synthesis for an I/O-Based hierarchical system architecture

In our previous work, a framework for the hierarchical design of discrete event systems has been introduced that is based on a notion of inputs and outputs. I/O-plant models describe the interaction of each subsystem with the operator (or controller) and the environment. By alternation of subsystem composition and controller synthesis, a hierarchy of controllers is obtained that complements a hierarchy of environment models. An admissibility condition was presented that implies liveness while allowing for abstraction-based control. In this paper, we address the according controller synthesis problem and present an algorithmic synthesis procedure that respects admissibility and yields a solution to this problem. We illustrate our statements by the conceptional application example of a transport unit.

Admissibility criteria for a hierarchical design of hybrid control systems

Abstract Many hybrid control problems of practical interest can be decomposed in a hierarchy of control objectives, where each objective refers to a particular time scale and to a particular level of measurement aggregation. It is Common engineering practice to exploit this hierarchical structure in the developnlent of ad hoc solutions to hybrid control problems that are far beyond the computational limitations of known methods for systematic hybrid system design. This paper extends a known design method to (i) benefit from hierarchical decompositions provided by engineering intuition, and to (ii) allow for a formal proof that the composition of the individual layers forms an overall solution

Hierarchical Hybrid Control Synthesis and its Application to a Multiproduct Batch Plant

This paper presents a hierarchical approach to hybrid control systems synthesis. It is set in a general behavioural framework and therefore allows a combination of continuous and discrete layers in the resulting overall controller. Compared to unstructured approaches, it drastically reduces computational complexity and hence enlarges the class of continuous-discrete control problems that can be addressed using methods from hybrid systems theory. The potential of our approach is demonstrated by applying it to a multiproduct batch control problem.

On the Computation of Supremal Sublanguages Relevant to Supervisory Control

Abstract Given a specification language, this paper discusses an iterative procedure for the computation of the supremal sublanguage, that possesses a conjunction of certain closed-loop properties, including controllability, normality and completeness. The iteration is stated in terms of (i) supremal sublanguage operators for each individual property, (ii) prefix-closures, and, (iii) language intersections. Within the iteration, the individual supremal sublanguage operators are only applied on prefix-closed languages, while the overall specification is not required to be prefix-closed. Our main result establishes finite convergence, provided that all parameters are regular.