Method for the Synthesis of Adaptive Algorithms for Estimating the Parameters of Dynamic Systems Based on the Decomposition Principle and the Joint Maximum Methodology

A method of synthesis of a filter for estimating the state of dynamic systems of Kalman type with an adaptive model built on the basis of the principle of decomposition of the system using kinematic relations from the condition of constancy of motion invariants has been developed. The structure of the model is determined from the condition of the maximum function of the generalized power up to a nonlinear synthesizing function that determines the rate of dissipation and, accordingly, the degree of structural adaptation. The resulting model has an explicit relation with the gradient of the estimation error functional, which makes it possible to adapt to the intensity of regular and random influences and can be used to construct a filter for estimating the state of the Kalman structure. On the basis of the developed method, a discrete algorithm is obtained and its comparative analysis with the classical Kalman filter is carried out.

One-dimensional self-consistent kinetic models as Vlasov equation solutions

One-dimensional self-consistent kinetic models may describe some states of intense charged particle beams. In the collisionless approximation, which is appropriate for the short current pulse duration, the kinetic distribution function may be built as a function of the motion integrals. Two situations are considered corresponding to the wide charged particle flux with the sharp front and to the sheet continuous beam freely propagating in space. In both cases, one-dimensional Vlasov equation solutions are shown to exist, which are based on algebraic functions of the motion invariants.