A behavioral framework for compositionality: linear systems, discrete event systems and hybrid systems

In this paper we formulate a general framework based on the behavioral approach to dynamical systems, in which various issues regarding interconnection of systems can be addressed. The main part of the framework is that interconnections or compositions of systems can be modelled with interconnection of behaviors and generalized projection operations. Control problems such as supervisory control problem or feedback control problem can be expressed in terms of behavioral interconnection, and therefore can be put into this framework. In the paper we discuss some variants of control problems and provide solutions to them

Behavioural hybrid process calculus

Process algebra is a theoretical framework for the modelling and analysis of the behaviour of concurrent discrete event systems that has been developed within computer science in past quarter century. It has generated a deeper nderstanding of the nature of concepts such as observable behaviour in the presence of nondeterminism, system composition by interconnection of concurrent component systems, and notions of behavioural equivalence of such systems. It has contributed fundamental concepts such as bisimulation, and has been successfully used in a wide range of problems and practical applications in concurrent systems. We believe that the basic tenets of process algebra are highly compatible with the behavioural approach to dynamical systems. In our contribution we present an extension of classical process algebra that is suitable for the modelling and analysis of continuous and hybrid dynamical systems. It provides a natural framework for the concurrent composition of such systems, and can deal with nondeterministic behaviour that may arise from the occurrence of internal switching events. Standard process algebraic techniques lead to the characterisation of the observable behaviour of such systems as equivalence classes under some suitably adapted notion of bisimulation

A Control-Oriented Notion of Finite State Approximation

We consider the problem of approximating discrete-time plants with finite-valued sensors and actu- ators by deterministic finite memory systems for the purpose of certified-by-design controller synthesis. Building on ideas from robust control, we propose a control-oriented notion of finite state approximation for these systems, demonstrate its relevance to the control synthesis problem, and discuss its key features.Comment: IEEE Transactions on Automatic Control, to appea

Discrete Simulation of Behavioural Hybrid Process Calculus

Hybrid systems combine continuous-time and discrete behaviours. Simulation is one of the tools to obtain insight in dynamical systems behaviour. Simulation results provide information on performance of system and are helpful in detecting potential weaknesses and errors. Moreover, the results are handy in choosing adequate control strategies and parameters. In our contribution we report a work in progress, a technique for simulation of Behavioural Hybrid Process Calculus, an extension of process algebra that is suitable for the modelling and analysis of hybrid systems

Bisimulation as congruence in the behavioral setting

We cast the notion of bisimulation in the Willems' behavioral setting. We show that in this setting, bisimulation is also a congruence, as it is known in the field of concurrent processes. Bisimulation is a congruence means if A and A' are bisimilar systems, then A || B and A' || B are also bisimilar. Here, the operator || denotes systems composition, and B is any other system that is composed with A or A'