Impulsive Control in Continuous and Discrete-Continuous Systems

Impulsive Control in Continuous and Discrete-Continuous Systems is an up-to-date introduction to the theory of impulsive control in nonlinear systems. This is a new branch of the Optimal Control Theory, which is tightly connected to the Theory of Hybrid Systems. The text introduces the reader to the...

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Bibliographic Details
Main Authors: Miller, Boris M., Rubinovich, Evgeny Y. (Author)
Format: eBook
Published: New York, NY Springer US 2003, 2003
Edition:1st ed. 2003
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 5 Optimal control problems within the class of generalized solutions
  • 5.1 Statement of the optimal control problems with phase constraints
  • 5.2 Existence of the optimal generalized solution
  • 5.3 Optimal control problems for DCS with ordinary and impulse controls
  • 5.4 Optimal generalized solutions in nonlinear hybrid systems
  • 6 Optimality conditions in control problems within the class of generalized solutions
  • 6.1 Introduction
  • 6.2 Generalized maximum principle
  • 6.3 Applications of generalized maximum principle
  • 6.4 Generalized maximum principle in linear-convex problems
  • 7 Observation control problems in discrete-continuous stochastic systems
  • 7.1 Statement of the problem
  • 7.2 Generalized solutions in observation control problems
  • 7.3 Convex properties of observation control problems
  • 7.4 Examples of observation control problems
  • 7.5 Observation control problem with constrained number of the observation instants
  • 1 Introduction
  • 1.1 Concept of discrete-continuous (hybrid) system and some typical problems
  • 1.2 Robust and non-robust discrete-continuous systems
  • 1.3 The structure of the book
  • 2 Discrete-continuous systems with impulse control
  • 2.1 Definition of impulsive control and the system solution
  • 2.2 Stability (robustness) conditions for systems with impulse control
  • 2.3 Generalized solutions of systems with impulse control and their representations
  • 3 Optimal impulse control problem with restricted number of impulses
  • 3.1 Introduction and the problem statement
  • 3.2 Auxiliary optimal control problem
  • 3.3 Necessary and sufficient optimality conditions
  • 4 Representation of generalized solutions via differential equations with measures
  • 4.1 Generalized solutions of nonlinear differential equations
  • 4.2 Generalized solutions of differential equations with affine dependence on unbounded controls
  • 8 Appendix. Differential equations with measures
  • 8.1 Auxiliary results
  • 8.2 Linear differential equations with a measure
  • 8.3 Nonlinear differential equations with a measure