By C. T. Leonides
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Additional resources for Advances in Algorithms and Computational Techniques in Dynamic Systems Control, Part 1 of 3
85) Now the new problem is to estimate the vector z(k) given by the first equation of system (80) with measurements given by (81) and (85). «- HjCk, k + 1) v(k) • Equation of the Observer For the new system given by the equations (86) ALGORITHMS AND COMPUTATIONAL TECHNIQUES 41 Z(k + 1) = A n (k, k + l)z(k) + A12(k, k + l) yi (k) + B 1 (k,k+l)u(k^ 1 (k) za(k) = Ha(k,k+l)z(k) + 4a(k) we will write the equation of the observer following the procedures in Refs. [145, 146]: z(k + 1) = KjOOÍOO + K2(k)za(k) + K3(k)[B1(k, k + l)u(k) + A12(k, k + DyjCk)], where Ku K2, and K3 are (n - Γ) x (n - /)-, (n - /) x (/ + q)-, and (n - /) x (n - /)dimensional matrices of unknown observer coefficients, respectively.
J. McLANE, Asymptotic stability of linear autonomous systems with state-dependent noise. IEEE Trans. Autom. Control AC-14, 752-753 (1969). P. J. McLANE, Linear optimal stochastic control using instantaneous output feedback. Int. J. Control 13(2), 383-396 (1971). P. J. McLANE, Optimal stochastic control of linear systems with state-dependent and control-dependent disturbances. IEEE Trans. Autom. Control AC-16(6), 793-798 (1971). 50 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49.
PANOSSIAN E[ßo(k^oT(j)] = 3(k)okj. 6) 0, (46) is the Ü! x n2 null matrix A(k) 0 7) Φ00 = 2 Λ1ι 1 4 X11 2 0(k) and r(k) = B(k) r(k) 8) x(0) is deterministic (for convenience). We note that ôkj is the Kronecker delta operator. The scalar index of performance for the above control system is defined by the following quadratic cost functional: N-l J(u) = EÍxT(n)Fx(N) + ^Σ [xV)Q(k)x(k) + uV)R(k)u(k)], 2 2k=o (47) where F and Q are positive-semidefinite and R positive-definite matrices of appropriate dimensions.
Advances in Algorithms and Computational Techniques in Dynamic Systems Control, Part 1 of 3 by C. T. Leonides