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...
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| Format: | Book |
| Language: | English |
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London :
Springer,
c2006
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| 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: |
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| 100 | 1 | |a Alamir, Mazen |0 http://viaf.org/viaf/60238416 | |
| 100 | 1 | |a Alamir, Mazen | |
| 245 | 1 | 0 | |a Stabilization of nonlinear systems using receding-horizon control schemes : |b a parametrized approach for fast systems / |c Mazen Alamir |
| 260 | |a London : |b Springer, |c c2006 | ||
| 300 | |a xvii, 308 p. : |b ill. ; |c 24 cm | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a unmediated |b n |2 rdamedia | ||
| 338 | |a volume |b nc |2 rdacarrier | ||
| 440 | 0 | |a Lecture notes in control and information sciences ; |v 339 | |
| 490 | 1 | |a Lecture notes in control and information sciences ; |v 339 | |
| 504 | |a Includes bibliographical references (p. [301]-306) and index | ||
| 505 | 0 | |a 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 | |
| 505 | 0 | 0 | |g 1 |t Definitions and notation -- |g 2. |t The receding-horizon state feedback -- |g 3. |t Stabilizing schemes with final equality constraint on the state -- |g 4. |t Stabilizing formulations with free prediction horizon and no final constraint on the state -- |g 5. |t General stabilizing formulations for trivial parametrization -- |g 6. |t Limit cycles stabilizing receding-horizon formulation for a class of hybrid nonlinear systems -- |g 7. |t Generic design of dynamic state feedback using receding-horizon schemes -- |g 8. |t Swing-up mechanical systems -- |g 9. |t Minimum-time constrained stabilization of nonholonomic systems -- |g 10. |t Stabilization of a rigid satellite in failure mode -- |g 11. |t Receding-horizon solution to the minimum-interception-time problem -- |g 12. |t Constrained stabilization of a PVTOL aircraft -- |g 13. |t Limit cycle stabilizing receding-horizon controller for the planar biped RABBIT. |
| 520 | |a 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 balance between structural and optimization aspects of the method is dependent on the system being considered so the many examples aim to transmit a mode of thought rather than a ready-to-use recipe; they include: - double inverted pendulum; - non-holonomic systems in chained form; - snake board; - missile in intercept mission; - polymerization reactor; - walking robot; - under-actuated satellite in failure mode. In addition, the basic stability results under receding horizon control schemes are revisited using a sampled-time, low-dimensional control parameterization that is mandatory for fast computation and some novel formulations are proposed which offer promising directions for future research | ||
| 530 | |a Also available online via the World Wide Web; access restricted to licensed sites/users | ||
| 596 | |a 31 | ||
| 650 | 0 | |a Automatic control |x Mathematical models | |
| 650 | 0 | |a Nonlinear control theory | |
| 650 | 7 | |a Automatic control |x Mathematical models |2 fast | |
| 650 | 7 | |a Nonlinear control theory |2 fast | |
| 776 | |w (OCoLC)262691387 | ||
| 830 | 0 | |a Lecture notes in control and information sciences ; |v 339 | |
| 830 | 0 | |a Lecture notes in control and information sciences |v 339 | |
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