Recent Advances in Model Predictive Control: Theory, Algorithms, and Applications (Lecture Notes in Control and Information Sciences, 485)

✍ Scribed by Timm Faulwasser (editor), Matthias A. Müller (editor), Karl Worthmann (editor)

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 250
• Category: Library

✦ Synopsis

This book focuses on distributed and economic Model Predictive Control (MPC) with applications in different fields. MPC is one of the most successful advanced control methodologies due to the simplicity of the basic idea (measure the current state, predict and optimize the future behavior of the plant to determine an input signal, and repeat this procedure ad infinitum) and its capability to deal with constrained nonlinear multi-input multi-output systems. While the basic idea is simple, the rigorous analysis of the MPC closed loop can be quite involved. Here, distributed means that either the computation is distributed to meet real-time requirements for (very) large-scale systems or that distributed agents act autonomously while being coupled via the constraints and/or the control objective. In the latter case, communication is necessary to maintain feasibility or to recover system-wide optimal performance. The term economic refers to general control tasks and, thus, goes beyond the typically predominant control objective of set-point stabilization. Here, recently developed concepts like (strict) dissipativity of optimal control problems or turnpike properties play a crucial role.

The book collects research and survey articles on recent ideas and it provides perspectives on current trends in nonlinear model predictive control. Indeed, the book is the outcome of a series of six workshops funded by the German Research Foundation (DFG) involving early-stage career scientists from different countries and from leading European industry stakeholders.

✦ Table of Contents

Preface
Contents
1 Predictive Path Following Control Without Terminal Constraints
1.1 Introduction
1.2 Preliminaries and Problem Statement
1.2.1 Path-Following Problems
1.2.2 Model Predictive Path Following (MPFC)
1.3 MPC Stability and Performance Bounds
1.4 Cost Controllabiltiy for Differentially Flat Systems
1.4.1 Existence of Feasible Motions for Flat Systems
1.4.2 Construction of a Growth Function
1.5 Example–2-DoF Robot
1.5.1 Cost Controllability: Growth Function
1.5.2 Stabilizing Prediction Horizon Length
1.5.3 Simulation Results
1.6 Summary and Conclusions
References
2 Dissipativity in Economic Model Predictive Control: Beyond Steady-State Optimality
2.1 Introduction
2.2 Setup
2.3 Dissipativity
2.4 Optimal Steady-State Operation
2.5 Optimal Periodic Operation
2.6 General Optimal Operating Conditions
2.7 Computation of Storage Functions
2.8 Time-Varying Case
2.9 Conclusions
References
3 Primal or Dual Terminal Constraints in Economic MPC? Comparison and Insights
3.1 The Dissipativity Route to Optimal Control and MPC
3.2 Economic MPC Revisited
3.2.1 Dissipativity-Based Stability Results
3.3 Comparison
3.3.1 Discrete-Time Euler–Lagrange Equations
3.3.2 Primal Feasibility and Boundary Conditions of the NCO
3.3.3 Invariance of barx Under EMPC
3.3.4 Bounds on the Stabilizing Horizon Length
3.4 Simulation Example
3.5 Summary and Outlook
References
4 Multi-level Iterations for Economic Nonlinear Model Predictive Control
4.1 Introduction
4.2 Direct Optimal Control in Economic Nonlinear MPC
4.3 The Extended Multi-level Iteration Scheme
4.3.1 Predictor–Corrector Path-Following Methods
4.3.2 Real-Time Iterations
4.4 Finding New Linearization Points
4.4.1 The Advanced Step Real-Time Iteration
4.5 Hessian Approximations
4.5.1 Hessian Update Formulae
4.5.2 Relative Cost of Exact Hessian Computation in Direct Multiple Shooting
4.6 A Tutorial Example
4.6.1 Convergence Rates
4.6.2 Generalized Tangential Predictors
4.6.3 Path-Following
4.7 Wind Turbine Control Example
4.7.1 The Optimal Control Problem
4.7.2 Simulation Results
4.8 Summary
References
5 On Closed-Loop Dynamics of ADMM-Based MPC
5.1 Specific Notation
5.2 Background on ADMM-based MPC for Linear Systems
5.3 An Augmented Model for the Closed-Loop Dynamics
5.4 Linear Dynamics Around the Augmented Origin
5.5 Positive Invariance Around the Augmented Origin
5.6 Cost-to-Go Around the Augmented Origin
5.7 Design Parameters of the Real-Time ADMM
5.8 Numerical Benchmark
5.9 Conclusions and Outlook
References
6 Distributed Optimization and Control with ALADIN
6.1 Introduction
6.1.1 Brief Literature Overview
6.1.2 On the road between ADMM and SQP
6.1.3 Why ALADIN?
6.2 Problem Formulation
6.2.1 Consensus Constraints
6.2.2 Inequality Constraints and Hidden Variables
6.3 Augmented Lagrangian Based Alternating Direction Inexact Newton (ALADIN) Method
6.3.1 Termination Conditions
6.3.2 Derivative-Free Variants
6.3.3 Inequality Constraint Variants
6.3.4 Implementation Details
6.4 Convergence Analysis
6.4.1 Local Convergence Results
6.4.2 Global Convergence Results
6.5 Numerical Implementation and Examples
6.5.1 Tutorial Example
6.5.2 Model Predictive Control
6.6 Conclusions
References
7 Model Predictive Control for the Internet of Things
7.1 Introduction
7.2 MPC for Interconnected Systems
7.2.1 Interconnected Systems
7.2.2 Centralized Versus Distributed Versus Decentralized Model Predictive Control
7.3 Challenges for Distributed MPC in the Internet of Things
7.3.1 Using Low-Power Wide Area Networks for Control
7.4 Temperature Control of a Smart Building
7.5 Results
7.5.1 Value of Communication
7.5.2 Embedded Decentralized Control with Limited Communication
7.6 Conclusion
References
8 Hybrid Gaussian Process Modeling Applied to Economic Stochastic Model Predictive Control of Batch Processes
8.1 Introduction
8.2 Problem Formulation
8.3 Solution Approach
8.3.1 Gaussian Process Hybrid Model Training
8.3.2 Hybrid Gaussian Process Model Predictive Control Formulation
8.3.3 Closed-Loop Monte Carlo Sample
8.3.4 Constraint Tightening Using Monte Carlo Samples
8.3.5 Algorithm
8.4 Case Study
8.4.1 Semi-batch Bioreactor Model
8.4.2 Problem Setup
8.4.3 Implementation and Initial Dataset Generation
8.5 Results and Discussions
8.6 Conclusions
References
9 Collision Avoidance for Mobile Robots Based on an Occupancy Grid
9.1 Introduction
9.1.1 The Burden of Communication
9.1.2 Lifting Communication Burden with Quantization
9.1.3 Non-cooperative Control and Communication
9.1.4 Occupancy Grid
9.2 Problem Setting
9.3 Prediction Coherence and Differential Updates
9.4 Bounding Box Constraint Formulation
9.5 DMPC with Decreasing Bounding Box Constraints
9.6 Conclusion
References