The synthesis of the observer (27) is reduced [18] to determining the observer gain coefficients [G.sub.i] by minimization of the error vector of the recovery of the

state vector x(t) of the initial system (25) and maximization of the same norm of the error vector along the plant uncertainty vector [eta](t) and the vector of external signal influences [omega](t), which also corresponds to the worst case disturbance.

where: x is a PS

state vector; z is a vector of measurements; h(x) is a vector of functions (also nonlinear), representing dependence of measured quantities from the

state vector x; R is a diagonal matrix of measurement covariances.

The EKF process (4) and output (5) models are driven by the nonlinear, differentiable vector functions, f( x ) and g( x ), where [x.sub.k+1] is the unknown system

state vector at time index k+1, [y.sub.k] depicts the observation or output vector, [u.sub.k] is the control vector and the random variables [w.sub.k] and [v.sub.k] (6) represent the process and measurement additive, zero-mean noise samples.

This paper considers a solution to the problem of development of the effective accommodation system for faults caused by errors in the sensor, which measure the position of output shaft of gear and by changing the value of viscous friction coefficient in electric servo actuators of the UMs described by mathematical model including differential equations with nonlinearity and variable parameters and not fully known

state vector.

In this paper, an outline of the

state vector, state prediction f(x), and observation functions h(x) for each measurement update is discussed.

where [x.sub.j](t) = [[[x.sub.j1](t), [x.sub.j2](t), ..., [x.sub.jn](t)].sup.T] is the

state vector of system (2).

In attitude estimation, the quaternion can be used as the

state vector. The accelerometer-magnetometer combination can be used for measurement model.

In this paper, the receding horizon UFIR (RHUFIR) filters using only known means of

state vector components at starting points of sliding windows are suggested.

In Figure 2, these are

state vectors (t + 1) and (t).

The traditional KNN algorithm includes five procedures: data acquisition and input,

state vector construction, pattern library establishment, K value calibration, and prediction based on weighted average functions.

where [m.sup.b] is the

state vector before update and the superscript b refers to background; B is the covariance matrix of [m.sup.b]; [d.sup.obs] is the observed responses; d = f(m) is the dynamic vector composed of simulated responses obtained by running a reservoir simulator f for the

state vector m; and R is the covariance matrix of observation error.

In order to make the process fully automated, two user-defined inputs are required: (i) the clutch

state vector s and (ii) the state priority vector sp.