OPTIMAL CONTROL OF HYDROSYSTEMS

Transcription

1 OPTIMAL CONTROL OF HYDROSYSTEMS Larry W. Mays Arizona State University Tempe, Arizona MARCEL DEKKER, INC. NEW YORK BASEL HONG KONG

2 Preface Hi PART I. BASIC CONCEPTS FOR OPTIMAL CONTROL Chapter 1 Systems Theory and Optimal Control Classifications of Systems Concepts of Systems Definition of Optimal Control Problems 8 References 10 Chapter 2 Introduction to Hydrosystems Problems Optimization of Hydrosystems Groundwater Management Systems Real-Time Operation of River-Reservoir Systems for Flood Control Reservoir System Operation for Water Supply Water Distribution System Operation Freshwater Inflows to Bays and Estuaries Sediment Control in Rivers and Reservoirs Soil Aquifer Treatment Systems General Problem Formulation 30 References 37 V«

3 Vlll Chapter 3 Nonlinear Optimization Methods Matrix Algebra for Nonlinear Programming Unconstrained Nonlinear Programming Constrained Optimization: Optimality Conditions Constrained Nonlinear Optimization: Generalized Reduced Gradient (GRG) Method Constrained Nonlinear Optimization: Penalty Function Methods The Augmented Lagrangian Method Solution of Discrete-Time Optimal Control Problems 62 Appendix: Computer Software 68 References 69 PART II. APPLICATIONS BASED ON MATHEMATICAL PROGRAMMING Chapter 4 Groundwater Management Systems Problem Identification Problem Formulation Problem Solution Application 86 Appendix: Computation of Basis Matrix Elements 88 References 94 Chapter 5 Real-Time Operation of River-Reservoir Systems Problem Identification Problem Formulation Problem Solution Application 116 Appendix A: Solution of Simulation Model 121 Appendix B: Computation of Basis Matrix Elements 124 References 128 Chapter 6 Water Distribution System Operation Problem Identification Problem Formulation Problem Solution 135

4 ix Chapter 6.4 Application Appendix A: Simulation Model Appendix B: Computation of Basis Elements References 7 Freshwater Inflows to Estuaries Problem Identification Problem Formulation Problem Solution Application Appendix A: HYD-SAL Simulation Models Appendix B: Derivation of Deterministic Equivalent of Chance Constraints Based on Regression Equations References PART III. APPLICATIONS BASED ON OPTIMAL CONTROL PROCEDURES Chapter 8 Optimal Control by Feedback Control Methods Dynamic Programming Feedback Method of Optimal Control for Linear Systems Groundwater Management Problems Feedback Method of Optimal Control for Nonlinear Systems 201 References 205 Chapter 9 Differential Dynamic Programming Differential Dynamic Programming Algorithm Convergence of Unconstrained DDP Multireservoir Operation Optimal Control of Groundwater Hydraulics Groundwater Reclamation Models 221 Appendix: Derivation of Coefficients for Quadratic 225 References 230 Chapter 10 Estuarine Management Model Using SALQR Problem Formulation Problem Solution Example Application 245 References 252

5 X Chapter 11 Sediment Control in Rivers and Reservoirs Problem Identification Problem Formulation Problem Solution Example Application to Agua Fria River 265 Appendix: Hyperbolic Penalty Function for the Violation of Storage Constraint 273 References 275 Chapter 12 Optimal Operation of Soil Aquifer Treatment Systems Using SALQR Problem Identification Problem Formulation Problem Solution Application Examples 286 Appendix: Derivative Calculations 298 References 299 Chapter 13 Real-Time Optimal Control: Linear Quadratic Feedback for Lumped Systems Introduction Discrete-Time, Linear, Quadratic Regulator (LQR) Discrete-Time, Linear, Quadratic Tracker (LQT) General, Discrete-Time, Stochastic, Linear, Quadratic, Optimal Control for Estuarine Management Analytical Feedback Control Law for General, Discrete-Time, Stochastic, Linear, Quadratic, Optimal Control for Estuarine Management Application of Stochastic, Linear, Quadratic Feedback Optimal Control to Water Resources Engineering Parameter Estimation for Lumped-Parameter System Applications to Estuary Management 322 References 328

6 XI Chapter 14 Stochastic Optimal Control for Estuarine Management Introduction Stochastic Optimal Control for a Distributed- Parameter System Parameter Estimation with Uncertainty Analysis Application to Estuary Management 349 References 360 Index 365