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

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

Towards Physical Hybrid Systems

Some hybrid systems models are unsafe for mathematically correct but physically unrealistic reasons. For example, mathematical models can classify a system as being unsafe on a set that is too small to have physical importance. In particular, differences in measure zero sets in models of cyber-physical systems (CPS) have significant mathematical impact on the mathematical safety of these models even though differences on measure zero sets have no tangible physical effect in a real system. We develop the concept of "physical hybrid systems" (PHS) to help reunite mathematical models with physical reality. We modify a hybrid systems logic (differential temporal dynamic logic) by adding a first-class operator to elide distinctions on measure zero sets of time within CPS models. This approach facilitates modeling since it admits the verification of a wider class of models, including some physically realistic models that would otherwise be classified as mathematically unsafe. We also develop a proof calculus to help with the verification of PHS.Comment: CADE 201

Progress in AI Planning Research and Applications

Planning has made significant progress since its inception in the 1970s, in terms both of the efficiency and sophistication of its algorithms and representations and its potential for application to real problems. In this paper we sketch the foundations of planning as a sub-field of Artificial Intelligence and the history of its development over the past three decades. Then some of the recent achievements within the field are discussed and provided some experimental data demonstrating the progress that has been made in the application of general planners to realistic and complex problems. The paper concludes by identifying some of the open issues that remain as important challenges for future research in planning

CASP Solutions for Planning in Hybrid Domains

CASP is an extension of ASP that allows for numerical constraints to be added in the rules. PDDL+ is an extension of the PDDL standard language of automated planning for modeling mixed discrete-continuous dynamics. In this paper, we present CASP solutions for dealing with PDDL+ problems, i.e., encoding from PDDL+ to CASP, and extensions to the algorithm of the EZCSP CASP solver in order to solve CASP programs arising from PDDL+ domains. An experimental analysis, performed on well-known linear and non-linear variants of PDDL+ domains, involving various configurations of the EZCSP solver, other CASP solvers, and PDDL+ planners, shows the viability of our solution.Comment: Under consideration in Theory and Practice of Logic Programming (TPLP

The Structure of Differential Invariants and Differential Cut Elimination

The biggest challenge in hybrid systems verification is the handling of differential equations. Because computable closed-form solutions only exist for very simple differential equations, proof certificates have been proposed for more scalable verification. Search procedures for these proof certificates are still rather ad-hoc, though, because the problem structure is only understood poorly. We investigate differential invariants, which define an induction principle for differential equations and which can be checked for invariance along a differential equation just by using their differential structure, without having to solve them. We study the structural properties of differential invariants. To analyze trade-offs for proof search complexity, we identify more than a dozen relations between several classes of differential invariants and compare their deductive power. As our main results, we analyze the deductive power of differential cuts and the deductive power of differential invariants with auxiliary differential variables. We refute the differential cut elimination hypothesis and show that, unlike standard cuts, differential cuts are fundamental proof principles that strictly increase the deductive power. We also prove that the deductive power increases further when adding auxiliary differential variables to the dynamics