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Quantified Mu-Calculus for Control Synthesis [chapter]

Stéphane Riedweg, Sophie Pinchinat
2003 Lecture Notes in Computer Science  
This extension is obtained by quantifying atomic propositions, we call the resulting logic quanti ed mu-calculus.  ...  We consider an extension of the mu-calculus as a general framework to describe and synthesize controllers.  ...  As in 57 , we extend a temporal logic the mu-calculus by quantifying atomic propositions. We call the resulting logic quanti ed mu-calculus.  ... 
doi:10.1007/978-3-540-45138-9_58 fatcat:4qnswquuxzhh3kl74iqihre554

A decidable class of problems for control under partial observation

Sophie Pinchinat, Stéphane Riedweg
2005 Information Processing Letters  
The paper is organized as follows: Sec.1 introduces the quantified mu-calculus and show its adequacy to control specification ; Sec.2 is dedicated to the control synthesis for the decidable fragment of  ...  An immediate important corollary is the synthesis of maximally permissive controllers under partial observation for mu-calculus definable control objectives.  ...  Quantified Mu-Calculus for Control Specifications We assume given a finite set of events Ev = {α, σ, σ , . . . } and a finite set of atomic propositions AP = {c, p, . . . }.  ... 
doi:10.1016/j.ipl.2005.04.011 fatcat:vhkzloxgdbeilm73mgb7nx7adm


Sophie Pinchinat, Jean-Baptiste Raclet
2005 IFAC Proceedings Volumes  
In particular, these transformations are used to reduce control problems for nondeterministic systems to control problems under partial observation for deterministic systems.  ...  We answer a wide range of control problems for nondeterministic discrete-event systems, relying on recent works based on a second order logic approach for deterministic systems.  ...  As first proposed by (Riedweg and Pinchinat, 2003) , the Mu-calculus extends to the Quantified Mu-calculus by allowing quantifications of the form ∃Λ for a set of atomic propositions Λ.  ... 
doi:10.3182/20050703-6-cz-1902.00296 fatcat:7dsq3giud5hmfe2dlh7wc7jn4a

The mu-calculus and Model Checking [chapter]

Julian Bradfield, Igor Walukiewicz
2018 Handbook of Model Checking  
The chapter describes in length the game characterization of the semantics of the mu-calculus.  ...  Then it develops the notion of modal automaton: an automaton-based model behind the mu-calculus.  ...  Let us remark that the Church synthesis problem [33, 117] for the mu-calculus formulas is an instance of the above for a particular choice of M.  ... 
doi:10.1007/978-3-319-10575-8_26 fatcat:7adhegoggvcjthaa5x5uhfpt24

Quotient-based Control Synthesis for Non-Deterministic Plants with Mu-Calculus Specifications

Samik Basu, Ratnesh Kumar
2006 Proceedings of the 45th IEEE Conference on Decision and Control  
Thus the control problem is reduced to one of mu-calculus satisfiability. We also present a tableau-based satisfiability solving algorithm that identifies a model for the quotiented formula.  ...  We study the control of a nondeterministic discrete event system (DES) subject to a control specification expressed in the propositional mu-calculus, under complete observation of events.  ...  An extension of mu-calculus, called quantified mu-calculus, to express the existence of a supervisor as part of the specification logic was introduced.  ... 
doi:10.1109/cdc.2006.376737 dblp:conf/cdc/0001006a fatcat:q3b6r65kmfewtelbyjcmhkzp2y

PhD Abstracts

2015 Journal of functional programming  
If a student or advisor would like to submit a dissertation abstract for publication in this series, please contact the editor for further details.  ...  The abstracts are made freely available on the JFP website, i.e. not behind any paywall, and do not require any transfer for copyright, merely a license from the author.  ...  Outline: In Part I, we analyze some variants of lambda mu-calculus (an extension of lambda calculus with two control operators for manipulating continuations), with special attention to the calculus of  ... 
doi:10.1017/s0956796815000040 fatcat:g7yt23qxivevte45fkiqv6xwna

Quotient-based control synthesis for partially observed non-deterministic plants with mu-calculus specifications

Samik Basu, Ratnesh Kumar
2007 2007 46th IEEE Conference on Decision and Control  
We study the control of a nondeterministic plant subject to a specification expressed in the propositional µcalculus under a partial observability of events.  ...  We present the syntax and semantics of O−µ-calculus and present a tableau-based satisfiability solving algorithm that also discovers a model for the quotiented formula when one exists. 1.  ...  [12] , [11] also presented an automata-theoretic quotienting approach for supervisor synthesis for enforcing µcalculus specifications.  ... 
doi:10.1109/cdc.2007.4434955 dblp:conf/cdc/BasuK07 fatcat:igfeachhtfc3xeu4dqg4b3ue6m

Automating Quantified Multimodal Logics in Simple Type Theory -- A Case Study [article]

Christoph Benzmueller
2009 arXiv   pre-print
In our experiments we exploit the new TPTP infrastructure for classical higher-order logic.  ...  In a case study we investigate whether off the shelf higher-order theorem provers and model generators can be employed to automate reasoning in and about quantified multimodal logics.  ...  %---thf(peter,type,( peter: mu > mu > $o )). thf(john,type,( john: mu > mu > $o )). thf(wife,type,(wife: ( mu > mu > $o ) > mu > mu > $o )).  ... 
arXiv:0905.4369v1 fatcat:bcudk2sfdbfq3buikviucbzedu

GOLOG: A logic programming language for dynamic domains

Hector J. Levesque, Raymond Reiter, Yves Lespérance, Fangzhen Lin, Richard B. Scherl
1997 The Journal of Logic Programming  
The language appears well suited for applications in high level control of robots and industrial processes, intelligent software agents, discrete event simulation, etc.  ...  It is based on a formal theory of action specified in an extended version of the situation calculus. A prototype implementation in Prolog has been developed. 0 Elsevier Science Inc., 1997 a  ...  The price we pay for this is a less expressive formalism. For example, we cannot quantify over complex actions, since these are not objects in the language of the situation calculus.  ... 
doi:10.1016/s0743-1066(96)00121-5 fatcat:4fn7qhkw7veuvlewbnexmutizq

The Complexity of Tree Automata and Logics of Programs

E. Allen Emerson, Charanjit S. Jutla
1999 SIAM journal on computing (Print)  
Another consequence is that satisfiability for propositional dynamic logic (PDL) with a repetition construct (PDL-delta) and for the propositional Mu-calculus (Lµ) can be tested in deterministic single  ...  For example, it follows that satisfiability for the full branching time logic CTL * can be tested in deterministic double exponential time.  ...  The algorithm is based on a type of "pseudomodel checking" for certain restricted Mu-calculus formulae.  ... 
doi:10.1137/s0097539793304741 fatcat:xtzi4v7rjnfj7hsmkuglf5kwne

A verified model checker for the modal Μ-calculus in Coq [chapter]

Christoph Sprenger
1998 Lecture Notes in Computer Science  
We report on the formalisation and correctness proof of a model checker for the modal #-calculus in Coq's constructive type theory.  ...  I would like to thank the Coq development team at INRIA Rocquencourt for helpful discussions and in particular Hugo Herbelin for inviting me there.  ...  A realizer for the control structure.  ... 
doi:10.1007/bfb0054171 fatcat:vf6c3n74lffhxjbsi2g64wbxe4

Verification of Infinite State Systems [chapter]

Ahmed Bouajjani
2003 Lecture Notes in Computer Science  
., in telecommunication, chemical and physical process control, transportation systems, etc.  ...  Both process algebras (or term rewriting systems) and automata (or finite control machines) are being used as specification formalisms.  ...  18 [2] in a model checking procedure for modal mu-calculus formulae and context-free processes.  ... 
doi:10.1007/978-3-540-45220-1_7 fatcat:4j5lzdbfc5hd7ptdo4tpwvmd2m

Optimal design of fractional order linear system with stochastic inputs/parametric uncertainties by hybrid spectral method

Pham Luu Trung Duong, Moonyong Lee
2014 Journal of Process Control  
The design methods were based on the hybrid spectral method for expanding the system signals over orthogonal functions.  ...  Hence, it is more suitable for the optimal design. The proposed method can be used for the synthesis colored noise from the arbitrary given noise.  ...  Generalized polynomial chaos (gPC) [11] [12] [13] is a more recent approach for quantifying the uncertainty within system models.  ... 
doi:10.1016/j.jprocont.2014.08.009 fatcat:e4pkb7527febvfje2n53kipbtu

Infinite States Verification in Game-Theoretic Logics: Case Studies and Implementation [chapter]

Slawomir Kmiec, Yves Lespérance
2014 Lecture Notes in Computer Science  
De Giacomo, Lespérance, and Pearce have proposed a situation calculus-based logical framework for representing such infinite state game-type problems together with a verification method based on fixpoint  ...  Many practical problems where the environment is not in the system's control can be modelled in game-theoretic logics (e.g., ATL).  ...  They also define a logic that combines the µ-calculus, game-theoretic path quantifiers (as in ATL), and first-order quantification, for specifying properties about such game settings.  ... 
doi:10.1007/978-3-319-14484-9_14 fatcat:h4jrjdtmujeirigjky4qxuzyw4

Fractional-Order Approximation and Synthesis of a PID Controller for a Buck Converter

Allan G. Soriano-Sánchez, Martín A. Rodríguez-Licea, Francisco J. Pérez-Pinal, José A. Vázquez-López
2020 Energies  
The synthesis and tuning process of the non-integer PID controller is described step by step.  ...  The comparison between typical PID controllers and the non-integer PID controller is provided to quantify the regulation speed introduced by the fractional-order PID approximation.  ...  Acknowledgments: Authors would like to thank to CONACYT México for cátedra ID 6782 and 4155. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/en13030629 fatcat:vnetn4pvmvbz7l7qsmuz6ini4u
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