Constructive Nonlinear Control

Constructive Nonlinear Control presents a broad repertoire of constructive nonlinear designs not available in other works by widening the class of systems and design tools. Several streams of nonlinear control theory are merged and directed towards a constructive solution of the feedback stabilization problem. Analysis, geometric and asymptotic concepts are assembled as design tools for a wide variety of nonlinear phenomena and structures. Geometry serves as a guide for the construction of design procedures whilst analysis provides the robustness which geometry lacks. New recursive designs remove earlier restrictions on feedback passivation. Recursive Lyapunov designs for feedback, feedforward and interlaced structures result in feedback systems with optimality properties and stability margins. The design-oriented approach will make this work a valuable tool for all those who have an interest in control theory.

1 Introduction.- 1.1 Passivity, Optimality, and Stability.- 1.2 Feedback Passivation.- 1.3 Cascade Designs.- 1.4 Lyapunov Constructions.- 1.5 Recursive Designs.- 1.6 Book Style and Notation.- 2 Passivity Concepts as Design Tools.- 2.1 Dissipativity and Passivity.- 2.2 Interconnections of Passive Systems.- 2.3 Lyapunov Stability and Passivity.- 2.4 Feedback Passivity.- 2.5 Summary.- 2.6 Notes and References.- 3 Stability Margins and Optimality.- 3.1 Stability Margins for Linear Systems.- 3.2 Input Uncertainties.- 3.3 Optimality, Stability, and Passivity.- 3.4 Stability Margins of Optimal Systems.- 3.5 Inverse Optimal Design.- 3.6 Summary.- 3.7 Notes and References.- 4 Cascade Designs.- 4.1 Cascade Systems.- 4.2 Partial-State Feedback Designs.- 4.3 Feedback Passivation of Cascades.- 4.4 Designs for the TORA System.- 4.5 Output Peaking: an Obstacle to Global Stabilization.- 4.6 Summary.- 4.7 Notes and References.- 5 Construction of Lyapunov functions.- 5.1 Composite Lyapunov functions for cascade systems.- 5.2 Lyapunov Construction with a Cross-Term.- 5.3 Relaxed Constructions.- 5.4 Stabilization of Augmented Cascades.- 5.5 Lyapunov functions for adaptive control.- 5.6 Summary.- 5.7 Notes and references.- 6 Recursive designs.- 6.1 Backstepping.- 6.2 Forwarding.- 6.3 Interlaced Systems.- 6.4 Summary and Perspectives.- 6.5 Notes and References.- A Basic geometric concepts.- A.1 Relative Degree.- A.2 Normal Form.- A.3 The Zero Dynamics.- A.4 Right-Invertibility.- A.5 Geometric properties.- B Proofs of Theorems 3.18 and 4.35.- B.1 Proof of Theorem 3.18.- B.2 Proof of Theorem 4.35.