Dynamic systems state, disturbances and noises set-valued estimation under conditions of incomplete information

The paper considers the problem of set-valued dynamic systems state estimation under conditions of uncertainty, when the sets of disturbances and noises possible values are known and statistical information about them is absent or cannot be obtained. An algorithm for feasible set polyhedral approximation is described, when the sets of possible values of disturbances and noises are polyhedra. The algorithm is based on the implicit description of the information set with linear equations and inequalities systems and solving a number of linear programming problems. Methods for increasing the estimation accuracy by taking into account additional information about disturbances and noises models are considered. Set-valued estimation of the dynamical system state vector is described when the disturbances are given as a system of functions with unknown coefficients. In this case, due to the use of information that the coefficients are constant, the dynamic system state estimates are more accurate than in the case when the disturbances are known up to a set of possible values. A numerical example is presented to demonstrate the algorithm performance. Aim. The aim of the research is to develop dynamic system state, disturbance and noises set-valued estimation algorithms. Research methods. Methods of optimization theory, filtering, linear algebra, MATLAB software package were used in the work. Results. Dynamic system state estimation algorithm was described. The algorithm takes into account additional information about disturbances and noises models. A method of feasible set polyhedral approximation is described, which makes it possible to obtain a set-valued estimate of a state vector, a vector of disturbances and noises, and an evolution of reachable sets. It can be used in the adaptive estimation and control algorithms development. The algorithm for set-valued estimation of the system state vector and coefficients in the disturbance decomposition as a system of given functions is developed. Conclusion. An algorithm for feasible set polyhedral approximation was described.The numerical example was performed and the analysis of the estimateswas presented.