Data-driven and model-based methods for verification and control of physical systems

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[1]  Richard M. Murray,et al.  Synthesis of correct-by-construction control protocols for hybrid systems using partial state information , 2014, 2014 American Control Conference.

[2]  George J. Pappas,et al.  Approximations of Stochastic Hybrid Systems , 2009, IEEE Transactions on Automatic Control.

[3]  M. Zarrop A Chebyshev system approach to optimal input design , 1979 .

[4]  Reinhard Wilhelm,et al.  Modeling, Analysis, and Verification - The Formal Methods Manifesto 2010 (Dagstuhl Perspectives Workshop 10482) , 2011, Dagstuhl Manifestos.

[5]  Yingke Chen,et al.  Active Learning of Markov Decision Processes for System Verification , 2012, 2012 11th International Conference on Machine Learning and Applications.

[6]  R. Khan,et al.  Sequential Tests of Statistical Hypotheses. , 1972 .

[7]  Gregor Gößler,et al.  Component-Based Modeling and Reachability Analysis of Genetic Networks , 2011, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[8]  Kim Guldstrand Larsen,et al.  Specification and refinement of probabilistic processes , 1991, [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science.

[9]  Kim G. Larsen,et al.  Reduction and Refinement Strategies for Probabilistic Analysis , 2002, PAPM-PROBMIV.

[10]  Radha Jagadeesan,et al.  Metrics for labelled Markov processes , 2004, Theor. Comput. Sci..

[11]  Alessandro Abate,et al.  On the effect of perturbation of conditional probabilities in total variation , 2014 .

[12]  Meeko M. K. Oishi,et al.  Reachability for partially observable discrete time stochastic hybrid systems , 2014, Autom..

[13]  K. Chaloner,et al.  Bayesian Experimental Design: A Review , 1995 .

[14]  Thomas A. Henzinger,et al.  Alternating Refinement Relations , 1998, CONCUR.

[15]  Ezio Bartocci,et al.  Learning Temporal Logical Properties Discriminating ECG models of Cardiac Arrhytmias , 2013, ArXiv.

[16]  V. Borkar Probability Theory: An Advanced Course , 1995 .

[17]  Fred Kröger,et al.  Temporal Logic of Programs , 1987, EATCS Monographs on Theoretical Computer Science.

[18]  Paul M. J. Van den Hof,et al.  Identification and control - Closed-loop issues , 1995, Autom..

[19]  Ian R. Petersen,et al.  Monotonicity and stabilizability- properties of solutions of the Riccati difference equation: Propositions, lemmas, theorems, fallacious conjectures and counterexamples☆ , 1985 .

[20]  B. Wahlberg,et al.  Modelling and Identification with Rational Orthogonal Basis Functions , 2000 .

[21]  Marco Forgione,et al.  Least costly closed-loop performance diagnosis and plant re-identification , 2015, Int. J. Control.

[22]  Luca Bortolussi,et al.  Smoothed model checking for uncertain Continuous-Time Markov Chains , 2014, Inf. Comput..

[23]  Paulo Tabuada,et al.  Model Checking LTL over Controllable Linear Systems Is Decidable , 2003, HSCC.

[24]  Lubos Brim,et al.  Exploring Parameter Space of Stochastic Biochemical Systems Using Quantitative Model Checking , 2013, CAV.

[25]  Henrik Madsen,et al.  Identifying suitable models for the heat dynamics of buildings , 2011 .

[26]  L.C.G.J.M. Habets,et al.  Control of multi-affine systems on rectangles with applications to hybrid biomolecular networks , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[27]  Pravin Varaiya,et al.  Decidability of Hybrid Systems with Rectangular Differential Inclusion , 1994, CAV.

[28]  Håkan Hjalmarsson,et al.  Identification for control of multivariable systems: Controller validation and experiment design via LMIs , 2008, Autom..

[29]  Abbas Edalat,et al.  Semi-pullbacks and bisimulation in categories of Markov processes , 1999, Mathematical Structures in Computer Science.

[30]  Guido Sanguinetti,et al.  Learning and Designing Stochastic Processes from Logical Constraints , 2015, Log. Methods Comput. Sci..

[31]  Xavier Bombois,et al.  Optimal experiment design for open and closed-loop system identification , 2011, Commun. Inf. Syst..

[32]  Franco Blanchini,et al.  Set-theoretic methods in control , 2007 .

[33]  Abbas Edalat,et al.  Bisimulation for labelled Markov processes , 1997, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science.

[34]  E. Walter,et al.  Robust experiment design via maximin optimization , 1988 .

[35]  Håkan Hjalmarsson,et al.  Identification of ARX systems with non-stationary inputs - asymptotic analysis with application to adaptive input design , 2009, Autom..

[36]  Jay H. Lee,et al.  Control-relevant experiment design for multivariable systems described by expansions in orthonormal bases , 2001, Autom..

[37]  Nathan Mendes,et al.  Predicting the Temperature Profile of Indoor Buildings by using Orthonormal Basis Functions , 2009 .

[38]  D. L. Loveday,et al.  Model-based control for HVAC applications , 1994, 1994 Proceedings of IEEE International Conference on Control and Applications.

[39]  Edmund M. Clarke,et al.  Statistical Model Checking for Markov Decision Processes , 2012, 2012 Ninth International Conference on Quantitative Evaluation of Systems.

[40]  Jonathan P. Bowen,et al.  Formal Methods , 2010, Computing Handbook, 3rd ed..

[41]  Xavier Bombois,et al.  Experiment Design for Closed-loop Performance Diagnosis , 2012 .

[42]  A. Abate,et al.  Piecewise affine approximations of fluxes and enzyme kinetics from in vivo 13C labeling experiments , 2012 .

[43]  Gopal Gupta,et al.  A logic-based modeling and verification of CPS , 2011, SIGBED.

[44]  D. Mayne,et al.  On the discrete time matrix Riccati equation of optimal control , 1970 .

[45]  Alessandro Abate,et al.  Adaptive and Sequential Gridding Procedures for the Abstraction and Verification of Stochastic Processes , 2013, SIAM J. Appl. Dyn. Syst..

[46]  Moshe Y. Vardi From Philosophical to Industrial Logics , 2009, ICLA.

[47]  Peter Kazanzides,et al.  Certifying the safe design of a virtual fixture control algorithm for a surgical robot , 2013, HSCC '13.

[48]  Håkan Hjalmarsson,et al.  System identification of complex and structured systems , 2009, 2009 European Control Conference (ECC).

[49]  L. Pronzato Adaptive optimization and $D$-optimum experimental design , 2000 .

[50]  Abbas Edalat,et al.  A logical characterization of bisimulation for labeled Markov processes , 1998, Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226).

[51]  Daniel Kroening,et al.  Unbounded-Time Analysis of Guarded LTI Systems with Inputs by Abstract Acceleration , 2015, SAS.

[52]  Edmund M. Clarke,et al.  Bayesian statistical model checking with application to Stateflow/Simulink verification , 2013, Formal Methods Syst. Des..

[53]  Paulo Tabuada,et al.  Verification and Control of Hybrid Systems , 2009 .

[54]  Carsten W. Scherer,et al.  Multi-Objective Output-Feedback Control via LMI Optimization , 1996 .

[55]  H. D. De Kanter [The philosophy of statistics]. , 1972, Ginecología y Obstetricia de México.

[56]  Ufuk Topcu,et al.  Probably Approximately Correct MDP Learning and Control With Temporal Logic Constraints , 2014, Robotics: Science and Systems.

[57]  P. V. D. Hof,et al.  A generalized orthonormal basis for linear dynamical systems , 1995, IEEE Trans. Autom. Control..

[58]  Paulo Tabuada,et al.  Linear Time Logic Control of Discrete-Time Linear Systems , 2006, IEEE Transactions on Automatic Control.

[59]  Axel Legay,et al.  Lightweight Monte Carlo Algorithm for Markov Decision Processes , 2013, ArXiv.

[60]  Calin Belta,et al.  A probabilistic approach for control of a stochastic system from LTL specifications , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[61]  X. Huan,et al.  Sequential Bayesian optimal experimental design via approximate dynamic programming , 2016, 1604.08320.

[62]  K. Shanmugan,et al.  Random Signals: Detection, Estimation and Data Analysis , 1988 .

[63]  John Lygeros,et al.  Probabilistic reachability and safety for controlled discrete time stochastic hybrid systems , 2008, Autom..

[64]  Gene F. Franklin,et al.  Feedback Control of Dynamic Systems , 1986 .

[65]  Michel Gevers,et al.  Minimizing the worst-case ν-gap by optimal input design , 2003 .

[66]  Antonio Bicchi,et al.  Symbolic planning and control of robot motion [Grand Challenges of Robotics] , 2007, IEEE Robotics & Automation Magazine.

[67]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[68]  Calin Belta,et al.  Model Checking Genetic Regulatory Networks with Parameter Uncertainty , 2007, HSCC.

[69]  O. Hernández-Lerma,et al.  Discrete-time Markov control processes , 1999 .

[70]  Håkan Hjalmarsson,et al.  For model-based control design, closed-loop identification gives better performance , 1996, Autom..

[71]  W. Wonham On the Separation Theorem of Stochastic Control , 1968 .

[72]  Domitilla Del Vecchio,et al.  Partial order techniques for vehicle collision avoidance: Application to an autonomous roundabout test-bed , 2009, 2009 IEEE International Conference on Robotics and Automation.

[73]  Christian A. Larsson Application-oriented experiment design for industrial model predictive control , 2014 .

[74]  Nancy A. Lynch,et al.  Probabilistic Simulations for Probabilistic Processes , 1994, Nord. J. Comput..

[75]  John Lygeros,et al.  Symbolic Control of Stochastic Systems via Approximately Bisimilar Finite Abstractions , 2013, IEEE Transactions on Automatic Control.

[76]  Alessandro Abate,et al.  Approximation Metrics Based on Probabilistic Bisimulations for General State-Space Markov Processes: A Survey , 2013, Hybrid Autonomous Systems@ETAPS.

[77]  Xavier Bombois,et al.  Least costly identification experiment for control , 2006, Autom..

[78]  Sumit Kumar Jha,et al.  A Counterexample-Guided Approach to Parameter Synthesis for Linear Hybrid Automata , 2008, HSCC.

[79]  François Laviolette,et al.  Approximate Analysis of Probabilistic Processes: Logic, Simulation and Games , 2008, 2008 Fifth International Conference on Quantitative Evaluation of Systems.

[80]  H. Jansson Experiment design with applications in identification for control , 2004 .

[81]  Csaba Szepesvári,et al.  Finite-Time Bounds for Fitted Value Iteration , 2008, J. Mach. Learn. Res..

[82]  T. Lindvall Lectures on the Coupling Method , 1992 .

[83]  Benjamin M. Gyori,et al.  Probabilistic verification of partially observable dynamical systems , 2014, ArXiv.

[84]  Calin Belta,et al.  LTL receding horizon control for finite deterministic systems , 2014, Autom..

[85]  D. A. Edwards On the existence of probability measures with given marginals , 1978 .

[86]  Sofie Haesaert,et al.  Data-driven and model-based verification: A Bayesian identification approach , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[87]  E. Walter,et al.  Robust experiment design via stochastic approximation , 1985 .

[88]  Alessandro Abate,et al.  FAUST 2 : Formal Abstractions of Uncountable-STate STochastic Processes , 2014, TACAS.

[89]  Abhijit Gosavi,et al.  Reinforcement Learning: A Tutorial Survey and Recent Advances , 2009, INFORMS J. Comput..

[90]  Xin Chen,et al.  Current Challenges in the Verification of Hybrid Systems , 2015, CyPhy.

[91]  Robert M. Keller,et al.  Formal verification of parallel programs , 1976, CACM.

[92]  Sofie Haesaert,et al.  Experiment design for formal verification via stochastic optimal control , 2016, 2016 European Control Conference (ECC).

[93]  Graham C. Goodwin,et al.  Robust optimal experiment design for system identification , 2007, Autom..

[94]  Edmund M. Clarke,et al.  Formal Methods: State of the Art and Future Directions Working Group Members , 1996 .

[95]  H. Witsenhausen Separation of estimation and control for discrete time systems , 1971 .

[96]  C. Striebel Sufficient statistics in the optimum control of stochastic systems , 1965 .

[97]  Marco Forgione,et al.  A unified experiment design framework for detection and identification in closed-loop performance diagnosis , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[98]  Edsger W. Dijkstra,et al.  Notes on structured programming , 1970 .

[99]  B. Chatterjee,et al.  Linear Control Theory , 1980, IEEE Transactions on Systems, Man, and Cybernetics.

[100]  Michel Gevers,et al.  Identification for Control: From the Early Achievements to the Revival of Experiment Design , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[101]  Jun Pang,et al.  On Probabilistic Alternating Simulations , 2010, IFIP TCS.

[102]  Alessandro Abate,et al.  Controller Synthesis for Probabilistic Safety Specifications using Observers , 2015, ADHS.

[103]  Kim G. Larsen,et al.  Bisimulation through probabilistic testing (preliminary report) , 1989, POPL '89.

[104]  Antoine Girard,et al.  Approximate bisimulation relations for constrained linear systems , 2007, Autom..

[105]  E. Yaz Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[106]  Roberto Segala,et al.  Modeling and verification of randomized distributed real-time systems , 1996 .

[107]  Manfred Jaeger,et al.  Learning and Model-Checking Networks of I/O Automata , 2012, ACML.

[108]  Alessandro Abate,et al.  Probabilistic Model Checking of Labelled Markov Processes via Finite Approximate Bisimulations , 2014, Horizons of the Mind.

[109]  Håkan Hjalmarsson,et al.  Iterative feedback tuning—an overview , 2002 .

[110]  G. Goodwin,et al.  Optimal test signal design for linear S.I.S.O. system identification , 1973 .

[111]  Markus N. Rabe,et al.  Verification of Partial-Information Probabilistic Systems Using Counterexample-Guided Refinements , 2012, ATVA.

[112]  Charles W. Therrien,et al.  Discrete Random Signals and Statistical Signal Processing , 1992 .

[113]  Alessandro Abate,et al.  On infinite-horizon probabilistic properties and stochastic bisimulation functions , 2011, IEEE Conference on Decision and Control and European Control Conference.

[114]  Sofie Haesaert,et al.  Correct-by-design output feedback of LTI systems , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[115]  Manuel Mazo PESSOA : towards the automatic synthesis of correct-bydesign control software ∗ , 2010 .

[116]  B. Anderson,et al.  Digital control of dynamic systems , 1981, IEEE Transactions on Acoustics, Speech, and Signal Processing.

[117]  Domitilla Del Vecchio,et al.  Control for Safety Specifications of Systems With Imperfect Information on a Partial Order , 2014, IEEE Transactions on Automatic Control.

[118]  David Q. Mayne,et al.  “On the discrete time matrix Riccati equation of optimal control-a correction” , 1971 .

[119]  Antoine Girard,et al.  SpaceEx: Scalable Verification of Hybrid Systems , 2011, CAV.

[120]  Dimitri P. Bertsekas,et al.  Stochastic optimal control : the discrete time case , 2007 .

[121]  Mahesh Viswanathan,et al.  Statistical Model Checking of Black-Box Probabilistic Systems , 2004, CAV.

[122]  George J. Pappas,et al.  Hierarchical control system design using approximate simulation , 2001 .

[123]  Håkan Hjalmarsson,et al.  Optimal experiment design for hypothesis testing applied to functional magnetic resonance imaging , 2011 .

[124]  John Lygeros,et al.  Verification of discrete time stochastic hybrid systems: A stochastic reach-avoid decision problem , 2010, Autom..

[125]  H. Hjalmarsson,et al.  Adaptive input design in system identification , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[126]  Krishnendu Chatterjee,et al.  Qualitative analysis of POMDPs with temporal logic specifications for robotics applications , 2014, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[127]  J. K. Hunter,et al.  Measure Theory , 2007 .

[128]  Håkan Hjalmarsson,et al.  From experiment design to closed-loop control , 2005, Autom..

[129]  J. D. Stigter,et al.  On adaptive optimal input design: A bioreactor case study , 2006 .

[130]  Luc Pronzato,et al.  Optimal experimental design and some related control problems , 2008, Autom..

[131]  Mahesh Viswanathan,et al.  Learning continuous time Markov chains from sample executions , 2004, First International Conference on the Quantitative Evaluation of Systems, 2004. QEST 2004. Proceedings..

[132]  Christel Baier,et al.  Principles of model checking , 2008 .

[133]  Chun. Loo,et al.  BAYESIAN APPROACH TO SYSTEM IDENTIFICATION , 1981 .

[134]  Mihail Zervos,et al.  A new proof of the discrete-time LQG optimal control theorems , 1995, IEEE Trans. Autom. Control..

[135]  Ondrej Holub,et al.  HVAC simulation model for advanced diagnostics , 2013, 2013 IEEE 8th International Symposium on Intelligent Signal Processing.

[136]  Radha Jagadeesan,et al.  Approximating labelled Markov processes , 2003, Inf. Comput..

[137]  Joost-Pieter Katoen,et al.  Robust PCTL model checking , 2012, HSCC '12.

[138]  Lijun Zhang,et al.  Logic and Model Checking for Hidden Markov Models , 2005, FORTE.

[139]  C. Belta,et al.  Model checking discrete-time Piecewise Affine systems: Application to gene networks , 2007, 2007 European Control Conference (ECC).

[140]  Sofie Haesaert,et al.  Data-Efficient Bayesian Verification of Parametric Markov Chains , 2016, QEST.

[141]  Alessandro Abate,et al.  Adaptive Gridding for Abstraction and Verification of Stochastic Hybrid Systems , 2011, 2011 Eighth International Conference on Quantitative Evaluation of SysTems.

[142]  Axel Legay,et al.  Statistical Model Checking: An Overview , 2010, RV.

[143]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[144]  Thomas A. Henzinger,et al.  Using HyTech to Synthesize Control Parameters for a Steam Boiler , 1995, Formal Methods for Industrial Applications.

[145]  Calin Belta,et al.  Motion planning and control from temporal logic specifications with probabilistic satisfaction guarantees , 2010, 2010 IEEE International Conference on Robotics and Automation.

[146]  A. Antoulas,et al.  A Survey of Model Reduction by Balanced Truncation and Some New Results , 2004 .

[147]  Robert K. Cunningham,et al.  The Real Cost of Software Errors , 2009, IEEE Security & Privacy.

[148]  Sofie Haesaert,et al.  Data-driven property verification of grey-box systems by bayesian experiment design , 2015, 2015 American Control Conference (ACC).

[149]  Sofie Haesaert,et al.  Sampling-based Approximations with Quantitative Performance for the Probabilistic Reach-Avoid Problem over General Markov Processes , 2014, ArXiv.

[150]  Jozsef Bokor,et al.  System identification with generalized orthonormal basis functions , 1995, Autom..

[151]  A. Saberi,et al.  The discrete algebraic Riccati equation and linear matrix inequality , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[152]  Edmund M. Clarke,et al.  The Birth of Model Checking , 2008, 25 Years of Model Checking.