Sensitivity of Automatic Control Systems

Although it arose much earlier in a variety of contexts, sensitivity theory became an independent branch of science in the sixties. Since then, researchers from around the world have continued to make great strides in both the theory and its applications. However, much of the work of Russian scientific schools and specialists remain unknown in the West.
Sensitivity of Control Systems summarizes the results of the authors and their disciples in sensitivity theory, addressing the basic notions of the theory and the problem of selecting technical parameters of systems. The authors formulate problems for actual technical systems and their models, and establish relations between sensitivity theory and classical stability problems. They offer a significant, general theory for investigating the sensitivity of boundary problems and use elements of this theory for sensitivity analysis of solutions to nonlinear programming and variational calculus problems, as well as oscillatory processes. The book also presents general investigation methods for discontinuous systems, including those described by operator models.
Full of powerful new methods and results, this book offers a unique opportunity for those in theoretical investigation and in the design, testing, and exploitation of various control systems to explore the work of Russia's leading researchers in sensitivity theory. Furthermore, its techniques for parametric perturbation investigation, Sensitivity of Control Systems will prove useful in fields outside of control theory, including oscillation theory, motion dynamics, and mathematical economy.

Efim Rozenwass, Rafael Yusupov

Preface Parametric Models State Variables and Control System Parameters Parametric Models of Control Systems Sensitivity Functions and their Applications Finite-Dimensional Continuous Systems Finite-Dimensional Continuous Systems Depending on a Parameter Second Lyapunov's Method in Sensitivity Theory Sensitivity on Infinite Time Intervals Sensitivity Analysis of Self-Oscillating Systems in the Time Domain Sensitivity of Non-Autonomous Systems Sensitivity of Solutions of Boundary Value Problems Finite-Dimensional Discontinuous Systems Sensitivity Equations for Finite Dimensional Discontinuous Systems Sensitivity Equations for Relay Systems Sensitivity Equations for Pulse and Relay-Pulse Systems Discontinuous Systems Given by Operator Models Operator Parametric Models of Control Systems Operator Models of Discontinuous Systems Sensitivity of Operator Models Sensitivity Equations of Relay and Pulse Systems Non-Time Characteristics Sensitivity of Transfer Function and Frequency Response of Linear Systems Sensitivity of Zeros and Poles Sensitivity of Eigenvalues and Eigenvectors of Linear Time Invariant Control Systems Sensitivity of Integral Quality Indices Indirect Characteristics of Sensitivity Functions Sensitivity Invariants Sensitivity Invariants of Time Characteristics Root and Transfer Function Sensitivity Invariants Sensitivity Invariants of Frequency Responses Sensitivity Invariants of Integral Estimates Sensitivity Invariants for Gyroscopic Systems Sensitivity of Mathematical Programming Sensitivity of Linear Programming Problems Sensitivity of Optimal Solutions of Non-Linear Programming Problems Sensitivity of a Simplest Variational Problem Sensitivity of Variational Problems with Flexible Boundaries and Corner Points Sensitivity of Variational Problems on Conditional Extremum Applied Sensitivity Problems Direct and Inverse Problems of Sensitivity Theory Identification of Dynamic Systems Distribution of Parameter Tolerance Synthesis of Insensitive Systems Numerical Solution of Sensitivity Equations