Nonlinear grey-box identification

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Table of contents

1 General Introduction 
1.1 The European Shell Eco-Marathon
1.1.1 Categories of participation
1.1.2 The Shell Eco-Marathon around the world
1.2 The EcoMotionTeam
1.3 Motivation of the work
1.4 Outline
2 The Low Consumption Vir’volt Electric Vehicle 
2.1 Introduction
2.2 The Vir’volt prototype
2.2.1 Electric vehicle dynamics
2.2.2 Parameter identification
2.2.2.1 Nonlinear grey-box identification
2.2.2.2 Parameter estimation
2.3 Low consumption driving strategy
2.3.1 Energetic considerations
2.3.2 Optimization problem
2.3.2.1 Constraints of the Optimality problem
2.3.2.2 The Multi-phase Optimality problem
2.4 Nonlinear discrete-time model
2.5 Real-time tracking of the optimal driving strategy
2.5.1 Linearised model
2.5.2 Linear Parametric Varying model
2.6 Benchmark
2.7 Conclusions
3 Tracking Model Predictive Control 
3.1 Introduction
3.2 Preliminaries
3.2.1 Polytopic constraints
3.2.2 Problem formulation
3.3 Design of the invariant terminal set
3.4 MPC-based tracking with time-invariant constraints: an academic example
3.4.1 Computation of the terminal invariant set
3.4.2 Closed loop response
3.5 MPC-based tracking with time-invariant constraints: application to the Vir’volt vehicle
3.6 Conclusions
4 Tracking under time-varying polytopic constraints 
4.1 Introduction
4.2 Preliminaries
4.3 Homothetic transformation of the invariant set
4.3.1 Principle of the homothetic transformation
4.3.2 Computation of the homothetic factor
4.4 MPC with homothetic transformation of the invariant set
4.5 MPC-based tracking with time-varying constraints: an academic example
4.5.1 Problem statement
4.5.2 Results
4.5.3 Computational resources
4.6 MPC-based tracking with time-varying constraints: application to the Vir’volt vehicle
4.6.1 Results
4.7 Conclusions
5 Real-time Robust Model Predictive Control for LPV systems 
5.1 Introduction
5.2 Problem formulation
5.3 Robust constrained MPC for LPV systems
5.3.1 Explicit MPC for LPV systems with off-line computation of LMIs
5.3.1.1 Asymptotically stable invariant ellipsoids
5.3.1.2 The explicit MPC algorithm
5.4 Robust MPC for LPV systems: application to the Vir’volt vehicle
5.4.1 Robust MPC for LPV systems with on-line computation of LMIs
5.4.2 Explicit MPC for LPV systems with off-line computation of LMIs
5.4.3 Comparison of the fully on-line MPC and explicit MPC .
5.5 MPC for LPV systems with Parameter dependent Lyapunov function
5.6 Explicit MPC using the PDLF
5.6.1 The asymptotically stable invariant set
5.6.2 Algorithm of the explicit MPC based on PDLF
5.7 Robust MPC for LPV systems with PDLF: application to the Vir’volt vehicle
5.7.1 Robust MPC with PDLF with on-line computation of LMIs
5.7.2 Explicit MPC for LPV using PDLF
5.7.3 Comparison of fully on-line MPC based on PDLF and explicit MPC based on PDLF
5.8 Explicit MPC for LPV using PDLF: application to the benchmark
5.9 Conclusions
6 Robust adaptive real-time control based on an on-off driving srategy 
6.1 Introduction
6.2 Parameter identification
6.2.1 Problem formulation
6.2.2 Identification of parameter a
6.2.2.1 Algorithm of the off-line identification
6.2.3 Identification of parameters b and c
6.3 Low consumption driving strategy
6.3.1 Problem formulation
6.3.2 Former results
6.3.3 Periodic low consumption driving strategy
6.4 Robust adaptive real-time control based on an on-off driving strategy: application to the Vir’volt vehicle
6.4.1 Off-line identification of the parameter a
6.4.2 On-line adaptative real-time control
6.5 Conclusions
7 General conclusions and Perspectives 
A Rotterdam’s Ahoy circuit 
B Proofs of Chapter 5 
B.1 Schur complement
B.2 Proof of equation (5.27)
B.3 Proof of equation (5.28)
B.4 Proof of equation (5.31)
B.5 Proof of equation (5.32)
C Proofs of Chapter 6 179
C.1 Proof of equation (6.13)
References