A motion correction of stochastic evolutionary systems with uncertainties

Abstract

In this paper, evolutionary control systems in Hilbert space are considered, which subject to random and uncertain disturbances. The state of the system is unknown, but there is an equation of measurement in discrete instants. The initial state and uncertain disturbances are restricted by joint integral constraints. According to measurements, the best linear minimax estimate is calculated. The preliminary aim of control consists in minimization of the terminal criterion that equals to expectation of the squared final state. We suggest some statements of the problem based on the separation of control and observation processes. The optimal instants of transition from estimation to control are found on the base of the theory of optimal stopping. The approach is applied to systems with the deviation of time of retarded and neutral types. It can be applied to parabolic and hyperbolic partial differential equations as well. An example with numerical results is given.In this paper, evolutionary control systems in Hilbert space are considered, which subject to random and uncertain disturbances. The state of the system is unknown, but there is an equation of measurement in discrete instants. The initial state and uncertain disturbances are restricted by joint integral constraints. According to measurements, the best linear minimax estimate is calculated. The preliminary aim of control consists in minimization of the terminal criterion that equals to expectation of the squared final state. We suggest some statements of the problem based on the separation of control and observation processes. The optimal instants of transition from estimation to control are found on the base of the theory of optimal stopping. The approach is applied to systems with the deviation of time of retarded and neutral types. It can be applied to parabolic and hyperbolic partial differential equations as well. An example with numerical results is given.