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Control and system theory of discrete-time stochastic systems / / Jan H. van Schuppen
| Control and system theory of discrete-time stochastic systems / / Jan H. van Schuppen |
| Autore | Schuppen J. H. van |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (940 pages) |
| Disciplina | 629.8312 |
| Collana | Communications and Control Engineering |
| Soggetto topico |
Stochastic control theory
Stochastic systems Discrete-time systems Teoria de control Processos estocàstics Sistemes estocàstics Sistemes de temps discret |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-66952-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910495184703321 |
Schuppen J. H. van
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| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Stochastic systems with time delay : probabilistic and thermodynamic descriptions of non-Markovian processes far from equilibrium / / Sarah A.M. Loos
| Stochastic systems with time delay : probabilistic and thermodynamic descriptions of non-Markovian processes far from equilibrium / / Sarah A.M. Loos |
| Autore | Loos Sarah A. M. |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (296 pages) |
| Disciplina | 003.76 |
| Collana | Springer Theses |
| Soggetto topico |
Stochastic systems
Time delay systems Thermodynamics - Mathematics Sistemes estocàstics Termodinàmica |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-80771-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Supervisor's Foreword -- Abstract -- Acknowledgements -- Publications by Sarah A. M. Loos -- Contents -- Abbreviations and Symbols -- Abbreviations -- Symbols -- 1 Introduction -- 1.1 Outline of the Thesis -- References -- Part I Theoretical Background and State of the Art -- 2 The Langevin Equation -- 2.1 The Stochastic Way of Describing Things -- 2.1.1 Brownian Motion -- 2.1.2 Colloidal Suspensions -- 2.1.3 Side Note: A More General View -- 2.2 The Markovian Langevin Equation -- 2.2.1 Gaussian White Noise -- 2.2.2 Ensemble Averages and Probability Density -- 2.2.3 Solutions of the Langevin Equation and the Overdamped Limit -- 2.2.4 Ornstein-Uhlenbeck Process -- 2.2.5 White Noise-Wiener Process-Stochastic Calculus -- 2.2.6 Path Integral Representation -- 2.3 Generalised Langevin Equations-How Stochastic Motion … -- 2.3.1 Infinite Harmonic Oscillators Bath-An Example of a Mori-Zwanzig Projection -- 2.3.2 Coarse-Graining-Forgetting Some Details -- 2.3.3 Side Node: Taking this Simplified Model Serious -- 2.3.4 The Markov Assumption -- 2.3.5 Real-World Complications -- 2.3.6 Time-Reversal Symmetry and Causality -- 2.4 Introduction to the Langevin Equation with Time Delay -- 2.4.1 Optical Traps-An Experimental Tool to Control -- 2.4.2 Time-Delayed Feedback -- 2.4.3 The Langevin Equation with Time Delay -- 2.4.4 Side Note: Delay Differential Equations -- 2.4.5 Linear Systems with Time Delay -- 2.5 Nonlinear Example Systems with Time Delay -- 2.5.1 Bistable System: The Doublewell Potential -- 2.5.2 Periodic System: The Washboard Potential -- 2.5.3 Scaling -- 2.6 Timescales -- 2.6.1 Kramers Escape Times -- 2.7 Delay-Induced Oscillations and Coherence Resonance -- 2.7.1 Delay-Induced Oscillations -- 2.7.2 Coherence Resonance -- 2.7.3 Bifurcation Theoretical Perspective on Delay-Induced Oscillations -- References -- 3 Fokker-Planck Equations.
3.1 Markovian Case -- 3.1.1 Natural Boundary Conditions -- 3.1.2 Joint Probability Densities -- 3.1.3 The Probability Current and Steady States -- 3.2 Introduction to Fokker-Planck Descriptions of Systems with Time Delay -- 3.2.1 Earlier Approximation Schemes -- 3.2.2 Probability Current and Apparent Equilibrium of Time-Delayed Systems -- 3.2.3 Side Note: Delay in Ensemble-Averaged Quantities -- References -- 4 Stochastic Thermodynamics -- 4.1 Side Note: Some Historical Notes and Where Is Stochastic … -- 4.2 Stochastic Energetics -- 4.2.1 Steady States -- 4.3 Fluctuating Entropy -- 4.3.1 Thermal Equilibrium & -- Nonequilibrium Steady States -- 4.4 Fluctuation Theorems -- 4.4.1 Route to First Principles-Axiom of Causality -- 4.5 Information -- 4.5.1 Mutual Information and Its Generalization -- 4.5.2 Information Flow -- 4.6 Previous Results, Expectations and Apparent Problems for Systems with Time Delay -- 4.6.1 Energetics in the Presence of Delay -- 4.6.2 Entropic Description -- 4.6.3 The Acausality Issue -- 4.6.4 Short Comment on Effective Thermodynamics -- 4.7 Side Note: Active Particles & -- Non-reciprocal Interactions -- 4.7.1 Active Ornstein-Uhlenbeck Particles -- 4.7.2 Connection Between Active Matter and Time-Delayed Systems -- 4.7.3 Non-reciprocal Interactions -- References -- Part II Probabilistic Descriptions for Systems with Time Delay -- 5 Infinite Fokker-Planck Hierarchy -- 5.1 Derivation of Fokker-Planck Hierarchy from Novikov's Theorem -- 5.1.1 Alternative Approach with Two Time Arguments -- 5.2 Exact Probabilistic Solutions for Linear Systems with Time Delay -- 5.2.1 Derivation of the Second Member of the Fokker-Planck Hierarchy -- 5.2.2 Steady-State Solutions -- 5.2.3 The Notion of Effective Temperature -- 5.2.4 Markovian Versus Non-Markovian Two-Time Probability Density -- References. 6 Markovian Embedding-A New Derivation of the Fokker-Planck Hierarchy -- 6.1 Markovian Embedding-A Different View on Memory -- 6.1.1 Projection, Memory Kernel & -- Colored Noise -- 6.1.2 Limit ntoinfty -- 6.1.3 Interpretation of the Xj Variables -- 6.1.4 Initial Condition -- 6.1.5 (n+1)-dimensional Markovian Fokker-Planck Equation -- 6.2 Derivation of First Member of Fokker-Planck Hierarchy -- 6.3 Derivation of Higher Members via Markovian Embedding -- 6.3.1 Comparison to Equation from Novikov's Theorem -- 6.4 Side Note: Discrete Versus Distributed Delay -- 6.4.1 Distributed Delay -- 6.4.2 Probability Densities in the Presence of Discrete and Distributed Delay -- References -- 7 Force-Linearization Closure -- 7.1 Details of the Approximation -- 7.1.1 Linearization of the Deterministic Forces -- 7.1.2 Analytical Probabilistic Solution for Linearized Forces -- 7.1.3 Vanishing Steady-State Probability Current -- 7.1.4 Specification to Linear Delay Force -- 7.2 Comparison to Earlier Approaches -- 7.2.1 Small Delay Expansion -- 7.2.2 Perturbation Theory -- 7.2.3 Effective Temperatures -- 7.3 Application to the Periodic Potential -- 7.3.1 Discussion of Results -- 7.4 Application to the Bistable Potential -- 7.4.1 Discussion of Results -- 7.5 Estimation of Escape Times -- 7.5.1 Interwell Dynamics -- 7.5.2 The Kramers-FLC Estimate -- 7.5.3 Comparison with Numerical Results -- 7.5.4 Delay-Induced Oscillations -- 7.5.5 Side Note: Normal Diffusion Despite Non-Markovianity -- References -- 8 Approximation for the Two-time Probability density -- 8.1 Application to the Bistable Delayed System -- 8.1.1 Comparison with Approaches for One-time Probability Density -- 8.2 Concluding Remarks -- References -- Part III Thermodynamic Notions for Systems with Time Delay -- 9 The Heat Flow Induced by a Discrete Delay -- 9.1 Main Idea -- 9.1.1 Polynomial Energy Landscapes. 9.2 Mean Heat Rate & -- Medium Entropy Production -- 9.2.1 Linear Systems -- 9.2.2 Markovian Limits in Nonlinear Systems -- 9.2.3 Limit of Vanishing Delay Time -- 9.2.4 Influence of Inertia Term -- 9.2.5 Discussion of the Behavior for Small Delay Times -- 9.3 Application to the Bistable Potential -- 9.3.1 Low Thermal Energy-Intrawell Dynamics -- 9.3.2 High Thermal Energy-Interwell Dynamics -- 9.4 Preliminary Numerical Results for Fluctuation of Heat, Work and Internal Energy -- 9.5 Concluding Remarks -- References -- 10 Entropy, Information and Energy Flows -- 10.1 Emergence of Non-monotonic Memory -- 10.1.1 Interpretation of Xj> -- 0 in the Case of a Feedback Controller -- 10.2 The Role of Non-reciprocal Coupling-Connection to Active Matter -- 10.2.1 A Generic Model with Non-reciprocal Coupling -- 10.3 Non-reciprocal Coupling and Non-equilibrium -- 10.3.1 Fluctuation-Dissipation Relation -- 10.3.2 Total Entropy Production -- 10.3.3 Analytical Solutions -- 10.4 Non-reciprocal Coupling and Activity -- 10.4.1 Mapping Non-reciprocity of the Coupling to a Temperature Gradient Between the Coupled Entities -- 10.4.2 Reversed Heat Flow -- 10.5 Non-reciprocal Coupling and Information -- 10.5.1 Information Flow and Generalized Second Law -- 10.5.2 Information-Theoretic Perspective on Feedback Control -- 10.6 Total Entropy Production and Heat Flow in the Presence of Non-monotonic Memory -- 10.6.1 Limit of Discrete Delay -- 10.6.2 Impact of Measurement Errors -- 10.7 Irreversibility and Coarse-Graining -- References -- Part IV Concluding Remarks -- 11 Summary -- References -- 12 Outlook-Open Questions and Further Perspectives -- References -- Appendix Appendix -- A.1 Numerical Methods -- A.2 Derivation of Novikov's Theorem -- A.3 Green's Function Method -- A.4 Connection to Fokker-Planck Hierarchy from Novikov's Theorem. A.5 Fluctuation-Dissipation Relation for Unidirectional Ring of Arbitrary Length n -- Appendix About the Author. |
| Record Nr. | UNINA-9910502633203321 |
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Loos Sarah A. M.
|
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| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Stochastic systems with time delay : probabilistic and thermodynamic descriptions of non-Markovian processes far from equilibrium / / Sarah A.M. Loos
| Stochastic systems with time delay : probabilistic and thermodynamic descriptions of non-Markovian processes far from equilibrium / / Sarah A.M. Loos |
| Autore | Loos Sarah A. M. |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (296 pages) |
| Disciplina | 003.76 |
| Collana | Springer Theses |
| Soggetto topico |
Stochastic systems
Time delay systems Thermodynamics - Mathematics Sistemes estocàstics Termodinàmica |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-80771-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Supervisor's Foreword -- Abstract -- Acknowledgements -- Publications by Sarah A. M. Loos -- Contents -- Abbreviations and Symbols -- Abbreviations -- Symbols -- 1 Introduction -- 1.1 Outline of the Thesis -- References -- Part I Theoretical Background and State of the Art -- 2 The Langevin Equation -- 2.1 The Stochastic Way of Describing Things -- 2.1.1 Brownian Motion -- 2.1.2 Colloidal Suspensions -- 2.1.3 Side Note: A More General View -- 2.2 The Markovian Langevin Equation -- 2.2.1 Gaussian White Noise -- 2.2.2 Ensemble Averages and Probability Density -- 2.2.3 Solutions of the Langevin Equation and the Overdamped Limit -- 2.2.4 Ornstein-Uhlenbeck Process -- 2.2.5 White Noise-Wiener Process-Stochastic Calculus -- 2.2.6 Path Integral Representation -- 2.3 Generalised Langevin Equations-How Stochastic Motion … -- 2.3.1 Infinite Harmonic Oscillators Bath-An Example of a Mori-Zwanzig Projection -- 2.3.2 Coarse-Graining-Forgetting Some Details -- 2.3.3 Side Node: Taking this Simplified Model Serious -- 2.3.4 The Markov Assumption -- 2.3.5 Real-World Complications -- 2.3.6 Time-Reversal Symmetry and Causality -- 2.4 Introduction to the Langevin Equation with Time Delay -- 2.4.1 Optical Traps-An Experimental Tool to Control -- 2.4.2 Time-Delayed Feedback -- 2.4.3 The Langevin Equation with Time Delay -- 2.4.4 Side Note: Delay Differential Equations -- 2.4.5 Linear Systems with Time Delay -- 2.5 Nonlinear Example Systems with Time Delay -- 2.5.1 Bistable System: The Doublewell Potential -- 2.5.2 Periodic System: The Washboard Potential -- 2.5.3 Scaling -- 2.6 Timescales -- 2.6.1 Kramers Escape Times -- 2.7 Delay-Induced Oscillations and Coherence Resonance -- 2.7.1 Delay-Induced Oscillations -- 2.7.2 Coherence Resonance -- 2.7.3 Bifurcation Theoretical Perspective on Delay-Induced Oscillations -- References -- 3 Fokker-Planck Equations.
3.1 Markovian Case -- 3.1.1 Natural Boundary Conditions -- 3.1.2 Joint Probability Densities -- 3.1.3 The Probability Current and Steady States -- 3.2 Introduction to Fokker-Planck Descriptions of Systems with Time Delay -- 3.2.1 Earlier Approximation Schemes -- 3.2.2 Probability Current and Apparent Equilibrium of Time-Delayed Systems -- 3.2.3 Side Note: Delay in Ensemble-Averaged Quantities -- References -- 4 Stochastic Thermodynamics -- 4.1 Side Note: Some Historical Notes and Where Is Stochastic … -- 4.2 Stochastic Energetics -- 4.2.1 Steady States -- 4.3 Fluctuating Entropy -- 4.3.1 Thermal Equilibrium & -- Nonequilibrium Steady States -- 4.4 Fluctuation Theorems -- 4.4.1 Route to First Principles-Axiom of Causality -- 4.5 Information -- 4.5.1 Mutual Information and Its Generalization -- 4.5.2 Information Flow -- 4.6 Previous Results, Expectations and Apparent Problems for Systems with Time Delay -- 4.6.1 Energetics in the Presence of Delay -- 4.6.2 Entropic Description -- 4.6.3 The Acausality Issue -- 4.6.4 Short Comment on Effective Thermodynamics -- 4.7 Side Note: Active Particles & -- Non-reciprocal Interactions -- 4.7.1 Active Ornstein-Uhlenbeck Particles -- 4.7.2 Connection Between Active Matter and Time-Delayed Systems -- 4.7.3 Non-reciprocal Interactions -- References -- Part II Probabilistic Descriptions for Systems with Time Delay -- 5 Infinite Fokker-Planck Hierarchy -- 5.1 Derivation of Fokker-Planck Hierarchy from Novikov's Theorem -- 5.1.1 Alternative Approach with Two Time Arguments -- 5.2 Exact Probabilistic Solutions for Linear Systems with Time Delay -- 5.2.1 Derivation of the Second Member of the Fokker-Planck Hierarchy -- 5.2.2 Steady-State Solutions -- 5.2.3 The Notion of Effective Temperature -- 5.2.4 Markovian Versus Non-Markovian Two-Time Probability Density -- References. 6 Markovian Embedding-A New Derivation of the Fokker-Planck Hierarchy -- 6.1 Markovian Embedding-A Different View on Memory -- 6.1.1 Projection, Memory Kernel & -- Colored Noise -- 6.1.2 Limit ntoinfty -- 6.1.3 Interpretation of the Xj Variables -- 6.1.4 Initial Condition -- 6.1.5 (n+1)-dimensional Markovian Fokker-Planck Equation -- 6.2 Derivation of First Member of Fokker-Planck Hierarchy -- 6.3 Derivation of Higher Members via Markovian Embedding -- 6.3.1 Comparison to Equation from Novikov's Theorem -- 6.4 Side Note: Discrete Versus Distributed Delay -- 6.4.1 Distributed Delay -- 6.4.2 Probability Densities in the Presence of Discrete and Distributed Delay -- References -- 7 Force-Linearization Closure -- 7.1 Details of the Approximation -- 7.1.1 Linearization of the Deterministic Forces -- 7.1.2 Analytical Probabilistic Solution for Linearized Forces -- 7.1.3 Vanishing Steady-State Probability Current -- 7.1.4 Specification to Linear Delay Force -- 7.2 Comparison to Earlier Approaches -- 7.2.1 Small Delay Expansion -- 7.2.2 Perturbation Theory -- 7.2.3 Effective Temperatures -- 7.3 Application to the Periodic Potential -- 7.3.1 Discussion of Results -- 7.4 Application to the Bistable Potential -- 7.4.1 Discussion of Results -- 7.5 Estimation of Escape Times -- 7.5.1 Interwell Dynamics -- 7.5.2 The Kramers-FLC Estimate -- 7.5.3 Comparison with Numerical Results -- 7.5.4 Delay-Induced Oscillations -- 7.5.5 Side Note: Normal Diffusion Despite Non-Markovianity -- References -- 8 Approximation for the Two-time Probability density -- 8.1 Application to the Bistable Delayed System -- 8.1.1 Comparison with Approaches for One-time Probability Density -- 8.2 Concluding Remarks -- References -- Part III Thermodynamic Notions for Systems with Time Delay -- 9 The Heat Flow Induced by a Discrete Delay -- 9.1 Main Idea -- 9.1.1 Polynomial Energy Landscapes. 9.2 Mean Heat Rate & -- Medium Entropy Production -- 9.2.1 Linear Systems -- 9.2.2 Markovian Limits in Nonlinear Systems -- 9.2.3 Limit of Vanishing Delay Time -- 9.2.4 Influence of Inertia Term -- 9.2.5 Discussion of the Behavior for Small Delay Times -- 9.3 Application to the Bistable Potential -- 9.3.1 Low Thermal Energy-Intrawell Dynamics -- 9.3.2 High Thermal Energy-Interwell Dynamics -- 9.4 Preliminary Numerical Results for Fluctuation of Heat, Work and Internal Energy -- 9.5 Concluding Remarks -- References -- 10 Entropy, Information and Energy Flows -- 10.1 Emergence of Non-monotonic Memory -- 10.1.1 Interpretation of Xj> -- 0 in the Case of a Feedback Controller -- 10.2 The Role of Non-reciprocal Coupling-Connection to Active Matter -- 10.2.1 A Generic Model with Non-reciprocal Coupling -- 10.3 Non-reciprocal Coupling and Non-equilibrium -- 10.3.1 Fluctuation-Dissipation Relation -- 10.3.2 Total Entropy Production -- 10.3.3 Analytical Solutions -- 10.4 Non-reciprocal Coupling and Activity -- 10.4.1 Mapping Non-reciprocity of the Coupling to a Temperature Gradient Between the Coupled Entities -- 10.4.2 Reversed Heat Flow -- 10.5 Non-reciprocal Coupling and Information -- 10.5.1 Information Flow and Generalized Second Law -- 10.5.2 Information-Theoretic Perspective on Feedback Control -- 10.6 Total Entropy Production and Heat Flow in the Presence of Non-monotonic Memory -- 10.6.1 Limit of Discrete Delay -- 10.6.2 Impact of Measurement Errors -- 10.7 Irreversibility and Coarse-Graining -- References -- Part IV Concluding Remarks -- 11 Summary -- References -- 12 Outlook-Open Questions and Further Perspectives -- References -- Appendix Appendix -- A.1 Numerical Methods -- A.2 Derivation of Novikov's Theorem -- A.3 Green's Function Method -- A.4 Connection to Fokker-Planck Hierarchy from Novikov's Theorem. A.5 Fluctuation-Dissipation Relation for Unidirectional Ring of Arbitrary Length n -- Appendix About the Author. |
| Record Nr. | UNISA-996466397303316 |
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Loos Sarah A. M.
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| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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