Robust estimation of state vector coordinates in the controlled helicopter motion problem

Abstract

The problem of finding H∞ – a observer of the state vector of a linear continuous non-stationary dynamical system with a semi-infinite time of functioning is considered. It is assumed that a mathematical model of a closed-loop linear continuous deterministic dynamical system with an optimal linear regulator, found as a result of minimization of the quadratic quality criterion, is known. For solving the state observer synthesis problem the reduction of the problem to a min-max optimal control problem is used. In this problem, the minimum of the quality criterion is sought by the observer’s gain matrix, and the maximum – by the external influence, measurement noise, and initial conditions. To solve this problem, the extension principle is applied and sufficient optimality conditions are obtained that requires the choice of auxiliary functions of the Krotov–Bellman type. As a result of the implementation of the procedure for choosing an auxiliary function and using the rules of matrix differentiation, relations for the synthesis of the observer and formulas for finding the best matrix of observer gains, as well as the laws for choosing the worst external influences and noise, were obtained. We find a solution to the problem of state vector coordinates estimation in the presence of limited external influences and disturbances in a linear model of the measuring system. As an example, the equations of motion of the Raptor-type helicopter are used.