Kokotovic P., Khalil H.K., O’Reilly J. Singular Perturbation Methods in Control: Analysis and Design

Philadelphia: Academic Press, 1999. — 388 p. — (Society for Industrial and Applied Mathematics).Singular perturbations and time-scale techniques were introduced to control engineering in the late 1960s and have since become common tools for the modeling, analysis and design of control systems. The 1986 edition of this book, reprinted here in its original form, provides the theoretical foundation for representative control applications. Its bibliography includes more than 400 references. Their number has been steadily growing since the 1986 publication of the book.
Recent publications show a significant diversification in control applications of singular perturbation techniques. Most current developments can be divided in three groups. The first group comprises the use of singular perturbations in new control problems. One of these stresses the geometric ("slow manifold") aspect of two-time-scale systems and provides, via high-gain feedback, an interpretation of the important concept of zero dynamics. Multi-time-scale behavior is also analyzed in high-gain observers, which are employed for semiglobal stabilization of nonlinear systems. A singular perturbation analysis reveals the dangers of large magnitude transients ("peaking") in high-gain feedback systems and serves as a basis for low-gain/high-gain designs in which such undesirable transients are avoided. Singularly perturbed H^ control systems have also been studied, including H w estimators with small noise. The second group of new results encompasses extensions and refinements of earlier theoretical concepts. More general singularly perturbed optimal control problems have been solved with a broader definition of the reduced (slow) problem based on averaging. New results have been obtained on stability of singularly perturbed systems with the help of the recently introduced concept of input-to-state stability. Analytical tools for multi-time-scale analysis of Markovian systems have been advanced.
The third group of new results includes diverse problem-specific applications. For robotic manipulators, the slow manifold approach has been employed to separately design the slow (rigid system) dynamics and the fast (flexible) transients. Electric machines and power systems have been an area of major applications of multi-time methods for aggregate (reduced order) modeling and transient stability studies. Singular perturbations are continuing to be among the frequently used tools in chemical kinetics and flight dynamics. A new application area for multi-time-scale methods are models of manufacturing systems. While these new developments go beyond the topics covered in this book, they are still based on the methodology described here, which continues to be their common starting point.Preface to the Classics Edition Preface
Time-scale modeling
ntroduction
The Standard Singular Perturbation Model
Time-Scale Properties of the Standard Model
Case Study 3.1: Two-Time-Scale PID Control
Slow and Fast Manifolds
Construction of Approximate Models
From Nonstandard to Standard Forms
Case Studies in Scaling
Case Study 7.1: Dimensionless E in the DC-Motor Model
Case Study 7.2: Parameter Scaling in an Airplane Model
Case Study 7.3: State Scaling in a Voltage Regulator
Exercises
Notes and References
Linear time-invariant systemsThe Block-Triangular Forms
Eigenvalue Properties
The Bloci -Dlagonal Form; Eigenspace Properties
Validation of Approximate Models
Controllability and Observability
Frequency-Domain Models
Exercises
Notes and References
Linear feedback controlComposite State-Feedback Control
Eigenvalue Assignment
Near-Optimal Regulators
A Corrected Linear-Quadratic Design
High-Gain Feedback
Robust Output-Feedback Design
Exercises
Notes and References
Stochastic linear filtering and controlSlow-Fast Decomposition in the Presence of White-Noise Inputs
The Steady-State Kalman-Bucy Filter
The Steady-State LOG Controller
An Aircraft Autopilot Case Study
Corrected LOG Design and the Choice of the Decoupling Transformation
Scaled White-Noise Inputs
Exercises
Notes and References
Linear time-varying systemsSlowly Varying Systems
Decoupling Transformation
Uniform Asymptotic Stability
Stability of a Linear Adaptive System
State Approximations
Controllability
Observability
Exercises
Notes and References
Optimal controlBoundary Layers In Optimal Control
The Reduced Problem
Near-Optimal Linear Control
Nonlinear and Constrained Control
Cheap Control and Singular Arcs
Exercises
Notes and References
Nonlinear systemsStability Analysis: Autonomous Systems
Case Study: Stability of a Synchronous Machine
Case Study: Robustness of an Adaptive System
Stability Analysis: Nonautonomous Systems
Composite Feedback Control
Near-Optimal Feedback Design
Exercises
Notes and ReferencesReferences added in proof
Appendix A Approximation of singularly perturbed systems driven by white noise
Appendix B