Journal of Mathematical Sciences

, Volume 199, Issue 6, pp 646–653 | Cite as

The Canonical Theory of the Impulse Process Optimality

  • V. A. Dykhta
  • O.N. Samsonyuk


The paper is devoted to the development of the canonical theory of the Hamilton–Jacobi optimality for nonlinear dynamical systems with controls of the vector measure type and with trajectories of bounded variation. Infinitesimal conditions of the strong and weak monotonicity of continuous Lyapunov-type functions with respect to the impulsive dynamical system are formulated. Necessary and sufficient conditions of the global optimality for the problem of the optimal impulsive control with general end restrictions are represented. The conditions include the sets of weak and strong monotone Lyapunov-type functions and are based on the reduction of the original problem of the optimal impulsive control a finite-dimensional optimization problem on an estimated set of connectable points.


Canonical Theory Impulsive Control Impulsive System Weak Monotonicity Connectable Point 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institute of System Dynamics and Control Theory, SB RAS, Russia; Institute of MathematicsEconomics and Informatics of Irkutsk State UniversityIrkutskRussia

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