Jasen Markovski

Coordination of Resources using Generalized State-Based Requirements

Abstract Control and coordination is an important aspect of the development of complex machines due to an ever increasing demand for better functionality, quality, and performance. We develop a coordinator for maintenance procedures for a high-tech Oce printer that eliminates undesired behavior which stems from unrestricted interaction of its distributed components. To this end, we extend and employ a model-based engineering framework for supervisory controller synthesis. We generalize standard state-based control requirements to increase modeling convenience. We model the use case with 23 generalized state-based requirements, which translate to 500+ requirements in the original form.

A state-based framework for supervisory control synthesis and verification

We extend an existing model-based framework for supervisory control synthesis with generalized control and verification state-based requirements. The former stem from the need for intuitive specification of the control requirements, whereas the latter are employed for liveness verification in order to ensure that the supervisor does not disable desired functionalities of the plant. First, we introduce generalized control requirements and show them provably equivalent to the standard state-based control requirements. In the process, we identify a class of state-based liveness requirements, which can be efficiently verified and employed in the supervisor synthesis framework to provide early feedback to the modeler.

CIF 3 : model-based engineering of supervisory controllers

The engineering of supervisory controllers for large and complex cyber-physical systems requires dedicated engineering support. The Compositional Interchange Format language and toolset have been developed for this purpose. We highlight a model-based engineering framework for the engineering of supervisory controllers and explain how the CIF language and accompanying tools can be used for typical activities in that framework such as modeling, supervisory control synthesis, simulation-based validation, verification, and visualization, real-time testing, and code generation. We mention a number of case studies for which this approach was used in the recent past. We discuss future developments on the level of language and tools as well as research results that may be integrated in the longer term.

A process algebra for supervisory coordination

A supervisory controller controls and coordinates the behavior of different components of a complex machine by observing their discrete behaviour. Supervisory control theory studies automated synthesis of controller models, known as supervisors, based on formal models of the machine components and a formalization of the requirements. Subsequently, code generation can be used to implement this supervisor in software, on a PLC, or embedded microprocessor. In this article, we take a closer look at the control loop that couples the supervisory controller and the machine. We model both event-based and state-based observations using process algebra and bisimulation-based semantics. The main application area of supervisory control that we consider is coordination, referred to as supervisory coordination, and we give an academic and an industrial example, discussing the process-theoretic concepts employed.

Verifying Performance of Supervised Plants

Supervisory control theory deals with synthesis of models of supervisory controllers that ensure safe and nonblocking behavior, based on discrete-event models of the uncontrolled system and the control requirements. Extensions, like optimal supervision, additionally ascertain that given performance requirements are met by the controller as well. Unfortunately, ensuring optimality during supervisor synthesis proved to be computationally challenging. Therefore, we propose to separate supervisor synthesis and ensuring performance. To handle the stochastic behavior efficiently, we treat the Markovian delays syntactically and we employ existing synthesis tools for non-stochastic plants. To this end, we develop a process theory that can specify control loops of nondeterministic stochastic systems with state-based observations. After obtaining the model of the supervised system, we verify that the supervised system adheres to the given performance requirements by deriving the underlying Markov process and feeding it to a stochastic model checker. We illustrate the approach by estimating performance and reliability measures for the printing process of a high-tech Océ printer.

Towards Supervisory Control of Interactive Markov Chains: Controllability

We propose a model-based systems engineering framework for supervisory control of stochastic discrete-event systems with unrestricted nondeterminism. We intend to develop the proposed framework in four phases outlined in this paper. Here, we study in detail the first step which comprises investigation of the underlying model and development of a corresponding notion of controllability. The model of choice is termed Interactive Markov Chains, which is a natural semantic model for stochastic variants of process calculi and Petri nets, and it requires a process-theoretic treatment of supervisory control theory. To this end, we define a new behavioral preorder, termed Markovian partial bisimulation, that captures the notion of controllability while preserving correct stochastic behavior. We provide a sound and ground-complete axiomatic characterization of the preorder and, based on it, we define two notions of controllability. The first notion conforms to the traditional way of reasoning about supervision and control requirements, whereas in the second proposal we abstract from the stochastic behavior of the system. For the latter, we intend to separate the concerns regarding synthesis of an optimal supervisor. The control requirements cater only for controllability, whereas we ensure that the stochastic behavior of the supervised plant meets the performance specification by extracting directive optimal supervisors.

Lumping Markov Chains with Silent Steps

A silent step in a dynamic system is a step that is considered unobservable and that can be eliminated. We define a Markov chain with silent steps as a class of Markov chains parameterized with a special real number tau. When tau goes to infinity silent steps become immediate, i.e. timeless, and therefore unobservable. To facilitate the elimination of these steps while preserving performance measures, we introduce a notion of lumping for the new setting. To justify the lumping we first extend the standard notion of ordinary lumping to the setting of discontinuous Markov chains, processes that can do infinitely many transitions in finite time. Then, we give a direct connection between the two lumpings for the case when tau is infinite. The results of this paper can serve as a correctness criterion and a method for the elimination of silent (tau) steps in Markovian process algebras

Reconciling urgency and variable abstraction in a hybrid compositional setting

The extension of timed formalisms to a hybrid setting with urgency, has been carried out in a rather straightforward manner, seemingly without difficulty. However, in this paper, we show that the combination of urgency with abstraction from continuous variables leads to undesired behavior. Abstraction from continuous variables ultimately leads to a timed system again, but with a much richer set of possible branching behaviors than a timed system that comprises only clocks. As it turns out, the formal definition of urgency, as defined for timed systems with clocks, does not fit our intuition of urgency anymore when applied to a timed system that is an abstraction of a hybrid system. Therefore, we propose to extend the formal semantics of timed and hybrid systems with guard trajectories. In this way, the continuous branching behavior introduced by hybrid systems remains visible even after abstraction from continuous variables. The practical applicability of the introduction of guard trajectories is illustrated by our revision of the structured operational semantics of the CIF language. The interplay between urgency and abstraction now adheres to our intuition, while compositionality with respect to urgency, variable abstraction, and parallel composition, is retained. In the future, symbolic elimination of urgency can be used to ensure that guard trajectories do not need to be actually calculated.

Communicating Processes with Data for Supervisory Coordination

We employ supervisory controllers to safely coordinate high-level discrete(-event) behavior of distributed components of complex systems. Supervisory controllers observe discrete-event system behavior, make a decision on allowed activities, and communicate the control signals to the involved parties. Models of the supervisory controllers can be automatically synthesized based on formal models of the system components and a formalization of the safe coordination (control) requirements. Based on the obtained models, code generation can be used to implement the supervisory controllers in software, on a PLC, or an embedded (micro)processor. In this article, we develop a process theory with data that supports a model-based systems engineering framework for supervisory coordination. We employ communication to distinguish between the different flows of information, i.e., observation and supervision, whereas we employ data to specify the coordination requirements more compactly, and to increase the expressivity of the framework. To illustrate the framework, we remodel an industrial case study involving coordination of maintenance procedures of a printing process of a high-tech Oc´e printer.

Saving Time in a Space-Efficient Simulation Algorithm

We present an efficient algorithm for computing the simulation preorder and equivalence for labeled transition systems. The algorithm improves an existing space-efficient algorithm and improves its time complexity by employing a variant of the stability condition and exploiting properties of the underlying relations and partitions. It has comparable space and time complexity with the most efficient counterpart algorithms for Kripke structures.