Impulsive Control in Continuous and Discrete-Continuous Systems

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.- 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.- 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.