GENERALIZED SOLUTIONS OF IMPULSIVE CONTROL SYSTEMS AND REACHABLE SETS

  • Published : 2000.02.01

Abstract

This paper is concerned with the impulsive Cauchy problem (equation omitted) where u is a possibly discontinuous vector-valued function and f, $g_{i}$ : $IR^{n}$ -> $IR^{n}$ are suitably smooth functions. We show that the input-output map is Lipschitz continuous and investigate compactness of reachable sets.

Keywords

References

  1. Lecture Notes on the Mathematical Theory A.Bressan
  2. Rend. Sem. Mat. Univ. Padova v.78 On Differential Systems with Impulsive Controls
  3. Nonsmooth analysis and geometric in deterministic optimal control
  4. Boll. Un. Mat. Ital., Series B v.3 On Differential Systems with Vector-Valued Impulsive Controls A. Bressan;F.Rampazzo
  5. J. Optim. Theory Apply. v.71 Impulsive Control Systems with Commutative Vector Fields
  6. Journal of optimization theory and applications v.81 no.3 Impulsive Control Systems without Commutativity Assumptions
  7. Journal of dynamical and control systems v.3 no.2 Impulsive On Mappings of Bounded Variation V.V.Chistyakov
  8. Differential and Integral Equations v.4 On Systems of Ordinary Differential Equations with Measure as Controls G. Dal Maso;F.Rampazzo
  9. Differential Inclusion in Nonsmooth Mechanical problems M.D.P.Monteiro
  10. Optimal Impulsive Controls with a Contraint on Total Variation F. Rampazzo
  11. SIAM Journal on Control,Series A v.3 Optimal Control Theory for Nonlinear Differential Equations Containing Measures W.W.Schmaedeke
  12. Journal of KMS v.34 Generalized Solutions of Impulsive Control Systems Corresponding to Controls C.E. Shin
  13. Rend. Sem. Mat. Univ. Padova Generalized Solutions of Time Dependent Impulsive Control Systems C.E.Shin;Ryu,J.H
  14. Annals of Probability v.6 On the Gap between Deterministic and Stochastic Ordinary Differential Equations H.J. Sussmann