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Record Nr. |
UNISA996503550703316 |
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Autore |
You Huan |
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Titolo |
Traffic congestion control by PDE backstepping / / Huan Yu and Miroslav Krstic |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2022] |
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©2022 |
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ISBN |
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Descrizione fisica |
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1 online resource (363 pages) |
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Collana |
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Systems and Control: Foundations and Applications |
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Disciplina |
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Soggetti |
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Automatic control |
Traffic congestion |
Congestió del trànsit |
Models matemàtics |
Control automàtic |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Intro -- Preface -- What Does the Book Cover? -- Who Is the Book For? -- Acknowledgments -- Contents -- Acronyms -- 1 Introduction -- 1.1 Before Control-Models -- 1.2 The Basics of Traffic Flow Modeling -- Macroscopic and Microscopic Models -- LWR and ARZ Macroscopic Models -- 1.3 Macroscopic Traffic PDE Models -- Lighthill-Whitham-Richards Model -- Aw-Rascle-Zhang Model -- 1.4 Linearized Models and Free/Congested Regimes -- Linearized LWR Model -- Linearized ARZ Model -- 1.5 Traffic Actuation -- Control Measures: Ramp Metering (RM) and Variable Speed Limits (VSL) -- Distributed and In-Domain Actuation: CAVs -- 1.6 A Brief Review of Literature on Traffic Control -- Control Employing PI and Backstepping Feedback -- Optimal Control -- Model Predictive Control -- Other Control Problems and Strategies -- 1.7 Boundary Control by RM or VSL -- Traffic Flow Boundary Control by Ramp Metering -- Traffic Velocity Boundary Control by Varying Speed Limits -- 1.8 Open-Loop Stability -- Linear Stability of LWR Model -- Linear Stability of ARZ Model -- 1.9 Numerical Simulation -- Numerical Simulation of the LWR PDE Model -- |
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Numerical Simulation of the ARZ PDE Model -- 1.10 Notes and References -- 2 Backstepping for Coupled Hyperbolic PDEs -- 2.1 A Brief History of PDE Backstepping -- 2.2 Coupled Hyperbolic PDEs -- 2.3 Backstepping Control for Coupled Hyperbolic PDEs -- Target System -- Backstepping Transformation -- Full-State Feedback Design -- 2.4 Observer and Output-Feedback Design for General Hyperbolic PDEs -- Boundary Sensing for State Estimation -- Output Feedback Design -- 2.5 Backstepping Control for Second-Order Hyperbolic PDEs -- Target System -- Lyapunov Stability Analysis -- Full-State Feedback Design -- 2.6 Observer and Collocated Output-Feedback Design for Second-Order Hyperbolic PDEs -- Boundary Sensing for State Estimation. |
Output Feedback Design -- 2.7 Notes and References -- Part I Basic Backstepping Control of Freeway Traffic -- 3 Stabilization of ARZ Model -- 3.1 What Can Be Controlled and Is It Worth Controlling with Ramp Metering? -- 3.2 Stop-and-Go Instabilities -- 3.3 Boundary Control Model -- DORM Control -- UORM Control -- Spectrum Analysis of Control Models with Zero Input -- 3.4 DORM Control Design -- 3.5 UORM Control Designs -- UORM Full-State Feedback Control Design -- UORM Anti-Collocated Boundary Observer Design -- UORM Collocated Boundary Observer Design -- UORM Output-Feedback Control Design -- 3.6 Numerical Simulation -- 3.7 Notes and References -- 4 Observer Validation on Freeway Data -- 4.1 Testing PDE Backstepping Observers on Real Freeway Data -- 4.2 Introduction to Traffic State Estimation -- 4.3 Boundary Observer Design -- Output Injection for the Linearized ARZ Model -- 4.4 Nonlinear Observer -- 4.5 Numerical Simulation -- 4.6 Model Calibration with NGSIM Data -- Data Reconstruction -- Calibration of Model Parameters -- 4.7 Data Validation of Observer with Calibrated Parameters -- 4.8 Notes and References -- 5 Adaptive Control of ARZ Traffic Model -- 5.1 Parametric Uncertainties in the ARZ Model -- 5.2 Adaptive Control for PDEs Enabled by Backstepping -- 5.3 Adaptive Output Feedback: Simultaneous Identification, Observer, and Control Design -- 5.4 Validation of Adaptive Design: Stability Proof and Simulations -- 5.5 The ARZ PDE Model with Parameter Uncertainty -- Scaling the States -- Observer Canonical Form -- 5.6 Parametric Model and Parameter Estimation -- 5.7 Filter-Based Observer Design -- 5.8 Adaptive Output-Feedback Control Design -- 5.9 Lyapunov Stability Analysis -- L2 Boundedness -- Convergence -- 5.10 Numerical Simulation -- 5.11 Notes and References -- 6 Event-Triggered Control of ARZ Model. |
6.1 Event-Triggered Control and Its Role in Controlled Traffic -- 6.2 VSL Full-State Feedback Control Design -- 6.3 Event-Triggered Strategies for Boundary Control -- Static Triggering Condition -- Dynamic Triggering Condition -- 6.4 Absence of the Zeno Phenomenon -- Static Triggering Condition -- Dynamic Triggering Condition -- 6.5 Stability Results -- Static Triggering Condition -- Dynamic Triggering Condition -- 6.6 Numerical Simulations -- 6.7 Notes and References -- 7 Comparison of Backstepping with Reinforcement Learning -- 7.1 From (Model-Based) Adaptive Control to (Less Model-Based) Reinforcement Learning -- Adaptive Backstepping -- Relative Merits of RL and Adaptive Backstepping -- Learning Characteristics of RL and Adaptive Backstepping -- Reliance on Full-State Measurement -- Is RL Learning the Backstepping Feedback Law? -- Comparison of RL with Proportional-Integral Controllers -- 7.2 RL Control Approach -- 7.3 Boundary Control Problem Reformulation -- ARZ PDE Traffic Model -- Boundary Control Design -- Setpoint Control -- PDE Backstepping Control -- P Control -- PI Control -- 7.4 Control of ARZ Model by Reinforcement Learning -- Boundary Control of PDE as a MDP -- Value |
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Function and Q-Function -- Actor-Critic -- Critic -- Actor -- Proximal Policy Optimization -- 7.5 Comparative Simulation Study -- Simulation Configuration -- Comparative Study with Full Knowledge of System Dynamics -- Learning Process of RL Controllers -- State Evolution, Reward, and Control Inputs -- Other Performance Measures -- Comparison Study with Partial Knowledge of System -- Scenario 1 of Lighter In-Domain Traffic -- Scenario 2 of Denser In-Domain Traffic -- 7.6 Notes and References -- Comparative Assessment of RL and Backstepping -- RL Versus Extremum Seeking -- Possible Advances with RL -- Code Availability -- Part II Advanced Backstepping for Traffic Flows. |
8 Two-Lane Traffic Control -- 8.1 Modeling and Controlling Two Lanes: By Four PDEs and Two VSL Inputs -- 8.2 Two-Lane Traffic ARZ Model -- Driver's Preference Over Two Lanes -- VSL Control of Linearized Two-Lane ARZ Model -- 8.3 Full-State Feedback Control Design -- 8.4 Collocated Observer and Output-Feedback Control -- Collocated Observer Design -- Output-Feedback Controller -- 8.5 Numerical Simulation -- Output-Feedback Stabilization and Performance -- Different Traffic Scenarios, One-Lane Backstepping and PI Controllers -- 8.6 Notes and References -- 9 Two-Class Traffic Control -- 9.1 Diverse Driver and Vehicle Classes: Additional PDEs Controlled by a Single Input -- 9.2 Two-Class ARZ Traffic Model -- Linearized Two-Class PDE Model -- Free/Congested Regime Analysis of Two-Class Traffic -- 9.3 Boundary Control Design Model -- 9.4 Full-State Feedback Control -- 9.5 Anti-collocated Boundary Observer Design -- 9.6 Output-Feedback Control Design -- 9.7 Numerical Simulation -- Performance Indices -- 9.8 Notes and References -- 10 Control of Two Cascaded Freeway Segments -- 10.1 Taking the ARZ Control Design Beyond a Single Freeway Segment -- 10.2 Possible Control Configurations for a Cascade of Freeway Segments -- Macroscopic Modeling of a Cascade of Freeway Segments -- Boundary Control of a Cascade of Freeway Segments -- 10.3 ARZ PDE Model of a Cascade of Freeway Segments -- Actuated Boundary at Two Different Locations -- Congested Steady States ps: [/EMC pdfmark [/Subtype /Span /ActualText (left parenthesis rho 1 Superscript star Baseline comma v 1 Superscript star Baseline comma rho 2 Superscript star Baseline comma v 2 Superscript star Baseline right parenthesis) /StPNE pdfmark [/StBMC pdfmark(ρ1,v1,ρ2,v2)ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- Linearized Model in the Riemann Coordinates -- 10.4 State Feedback Control Designs. |
Feedback Law U0(t) with Flow Rate Control from x=0 -- Feedback Law UL(t) with Flow Rate Control from x=L -- 10.5 Boundary Observer Designs -- Observer with Measurement Y0(t) at x=0 -- Observer with Measurement at Outlet -- 10.6 Output-Feedback Laws -- 10.7 Robustness to Input Delays -- 10.8 Simulation Results -- Output-Feedback Stabilization -- Robustness to Delays -- Comparison with PI Controllers -- 10.9 Notes and References -- 11 Estimation of Freeway Diverge Flows -- 11.1 Traffic Flow Estimation Beyond a Single Road Segment -- 11.2 PDE Model of One Incoming and Two Outgoing Roads -- 11.3 Linearized Model in the Riemann Coordinates -- 11.4 Boundary Observer Design -- 11.5 Robustness to Disturbance and Noise -- 11.6 Notes and References -- 12 Control Under Routing-Induced Instability -- 12.1 ARZ Model with Routing Feedback -- 12.2 Feedback Design for the Linearized System -- 12.3 Closed-Loop Stability -- 12.4 Existence of Solutions to Kernel Equations -- 12.5 Notes and References -- 13 Bilateral Regulation of Moving Shock Position -- 13.1 Delay-Compensating Predictors for PDE-ODE Models of Traffic Shock Movement -- 13.2 Moving Shockwave Model -- 13.3 State-Dependent |
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PDE-ODE Model -- 13.4 Predictor-Based Control Design -- From Coupled PDE-ODE to Delay System Representation -- Predictor-Based Backstepping Transformation -- 13.5 Lyapunov Analysis -- 13.6 Numerical Simulation -- 13.7 Notes and References -- 14 Extremum Seeking for Flow Maximization at Downstream Bottleneck -- 14.1 Bottleneck: Unknown Fundamental Diagram and Maximizing the Flow -- 14.2 Lane-Drop Bottleneck Control Problem -- Lane-Drop Bottleneck Model -- Linearized Reference Error System -- 14.3 Online Optimization by Extremum Seeking Control -- 14.4 Stability Analysis (Averaging, Backstepping, and Lyapunov) -- Closed-Loop System -- Average System -- Backstepping Transformation. |
Lyapunov Functional. |
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