Analysis and design engineering systems by Henry M. Paynter PDF

System Theory

By Henry M. Paynter

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2). 37) also form a conditionally Gaussian vector with respect to the entire observation process y(t) = [y1 (t), y2 (t)], since x2 (t) is Gaussian and the observation process components y1 (t) and y2 (t) are uncorrelated. 3), and, therefore, the following considerations are applicable. 39), is equal to zero, because the process x(t) − m(t) is conditionally Gaussian. 40) b(t)bT (t) − P(t)AT (t)(B(t)BT (t))−1 A(t)P(t))dt, with the initial condition P(t0 ) = E[(x(t0 ) − m(t0 )(x(t0 ) − m(t0 )T | FtY0 ].

5 (Fig. 4). 51). 26. 54). Discussion The simulation results show that the values of the estimate calculated by using the obtained optimal filter for a quadratic-linear state with unmeasured linear part over linear observations are noticeably closer to the real values of the reference variable than the values of the estimate given by the conventional extended Kalman-Bucy filter. 47) itself is unstable and the nonlinear component x1 (t) goes to infinity for a finite time. On the contrary, the conventionally designed extended Kalman-Bucy estimates diverge from the real values.

J In the simulation process, the initial conditions at t = 0 are equal to zero for the state variables Cm1 , . . 5 for the estimates m1 (t), . . , m10 (t), to 1 for the diagonal entries of the variance matrix, and to zero for its other entries. For the purpose of testing the obtained filter, the system parameter values are all set to 1: V = 1; d Δm1 /dt = 1; KL1 = 1; K11 = 1; K21 = 1; K31 = 1; K32 = 1; d Δm2 /dt = 1; d Δm3 /dt = 1; d Δm∗ /dt = 1; KL2 = 1; KL3 = 1; K12 = 1; K13 = 1; K22 = 1; Kd = 1; Kt1 = 1; Kt2 = 1; Kt3 = 1; θ = 1.

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Analysis and design engineering systems by Henry M. Paynter

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