Stabilization of nonlinear systems using receding-horizon control schemes : a parametrized approach for fast systems /
While conceptually elegant, the generic formulations of nonlinear model predictive control are not ready to use for the stabilization of fast systems. Dr. Alamir presents a successful approach to this problem based on a co-operation between structural considerations and on-line optimization. The bal...
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London :
Springer,
c2006
|
| Series: | Lecture notes in control and information sciences ;
339 Lecture notes in control and information sciences ; 339 Lecture notes in control and information sciences 339 |
| Subjects: |
Table of Contents:
- Cover
- Contents
- Part I: Generic Framework
- 1 Definitions and Notation
- 1.1 System-Related Definitions
- 1.2 Open-Loop-Control-Related Definitions
- 1.3 Open-Loop-Trajectories-Related Definitions
- 1.4 Further Notation
- 2 The Receding-Horizon State Feedback
- 2.1 The Strategy Most Commonly Used by Humans
- 2.2 The Ingredients of a Receding-Horizon Control Scheme
- 2.3 The Receding-Horizon State Feedback
- 2.4 Existence of Solutions
- 2.5 The Stability Issue
- 3 Stabilizing Schemes with Final Equality Constraint on the State
- 3.1 Some Assumptions and Preliminary Results
- 3.2 Fixed Prediction Horizon Formulations with Final Equality Constraint on the State
- 4 Stabilizing Formulations with Free Prediction Horizon and No Final Constraint on the State
- 4.1 Preliminary Results
- 4.2 A Contractive Free Prediction Horizon Formulation for Use in a Hybrid Scheme
- 4.3 A Contractive Self-Contained Free Final-Horizon Formulation
- 4.4 Generalization
- 5 General Stabilizing Formulations for Trivial Parametrization
- 5.1 Introduction
- 5.2 Definitions and Notation
- 5.3 Sufficient Conditions for Asymptotic Stability
- 5.4 A Quick Survey of Existing Stabilizing Formulations
- 5.5 Inverse Optimality
- 5.6 Current Issues: Distributing the Optimization over Real Time
- 6 Limit Cycles Stabilizing Receding-Horizon Formulation for a Class of Hybrid Nonlinear Systems
- 6.1 Problem Statement
- 6.2 Recall on Partial Feedback Linearization
- 6.3 The Proposed Receding-Horizon Feedback Scheme
- 6.4 Illustrative Examples
- 6.5 Conclusion
- 7 Generic Design of Dynamic State Feedback Using Receding-Horizon Schemes
- 7.1 Intuitive Presentation of the Main Idea
- 7.2 Rigorous Statement of the Dynamic State Feedback
- 7.3 Conclusion
- Part II: Application Examples
- Introduction to Part II
- 8 Swing-Up Mechanical Systems
- 8.1 Swing-Up and Stabilization of a Twin-Pendulum System
- 8.2 Swing-Up and Stabilization of a Reaction-Wheel Pendulum Under Constraints
- 8.3 Swing-Up and Stabilization of an Inverted Pendulum on a Cart
- 8.4 Swing-Up and Stabilization of a Double Inverted Pendulum on a Cart
- 8.5 Conclusion
- 9 Minimum-Time Constrained Stabilization of Nonholonomic Systems
- 9.1 Stabilisation of Nonholonomic Systems in Chained Form
- 9.2 Stabilisation of a Class of Nonholonomic Systems: Application to the Snakeboard Example
- 10 Stabilization of a Rigid Satellite in Failure Mode
- 10.1 The Model of a Satellite in Failure Mode
- 10.2 Designing Efficiently Computable Steering Trajectories
- 10.3 Numerical Experiments
- 10.4 State Feedback Definition
- 10.5 Closed-Loop Simulations
- 10.6 Conclusion
- 11 Receding-Horizon Solution to the Minimum-Interception-Time Problem
- 11.1 System Modelling and Problem Statement
- 11.2 Intuitive Presentation of the Controller Design
- 11.3 Explicit Definition of the Feedback Law
- 11.4 Simulation Results
- 11.5 Conclusion
- 12 Constrained Stabilization of a PVTOL Aircraft
- 12.1 The Model of the PVTOL Aircraft
- 12.2 Generation of Admissible Open-Loop Steering Trajectories
- 12
- 1 Definitions and notation
- 2. The receding-horizon state feedback
- 3. Stabilizing schemes with final equality constraint on the state
- 4. Stabilizing formulations with free prediction horizon and no final constraint on the state
- 5. General stabilizing formulations for trivial parametrization
- 6. Limit cycles stabilizing receding-horizon formulation for a class of hybrid nonlinear systems
- 7. Generic design of dynamic state feedback using receding-horizon schemes
- 8. Swing-up mechanical systems
- 9. Minimum-time constrained stabilization of nonholonomic systems
- 10. Stabilization of a rigid satellite in failure mode
- 11. Receding-horizon solution to the minimum-interception-time problem
- 12. Constrained stabilization of a PVTOL aircraft
- 13. Limit cycle stabilizing receding-horizon controller for the planar biped RABBIT.