Techniques

Control and dynamic systems : advances in theory and - download pdf or read online

By Cornelius T Leondes

ISBN-10: 0120127105

ISBN-13: 9780120127108

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Extra info for Control and dynamic systems : advances in theory and applications ; 10

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General Multi-Point Boundary Value Problem The necessary conditions developed in Sections II, B and II, C comprise a discontinuous, multi-point boundary value problem. Previous work has shown that quasilinearization is a premixing technique for solving two point boundary value problems. In one of the earliest computer applications of quasilinearization, McGill and Kenneth [6] obtained excellent convergence properties in their orbit transfer problems. Moyer and Pinkham [11] compare the convergence properties of quasilinearization to those of gradient and second-order methods.

Extrapolate (or truncate) the terminal portion of this subarc to T k using the following relationship. a ( F Yk(Tk) - Yk (t k-1) + k-1 k-1) (t k - t k-1). Compute the discontinuity in Yk at Tkl (12)+). After computing Yk(Tk-1 + 2e), ~ 15 2 ) using equation continue the inte- gration of equation (118) from t = Tk-1 + 2e to t = Extrapolate (or truncate) the initial portion of the second 48 SUBOPTIMAL STRATEGIES USING QUASILINEARIZATION subarc to Tk as follows. Yk(Tk + 2e) = Yk(T kl + 2e) kali)(tk-1 + 2e)(Tk - +F t (153) 1) .

It is assumed that n of the initial values of U are specified. For a well posed problem, therefore, the sum of the dimensions of Wa for all a must equal N- n. The unknown corner and final times are implicitly determined by the Ya functions. In summary, there are N differential equations with n boundary conditions specified at the initial time and a total of N - n conditions specified at the corner and final times. These corner and final times are implicitly defined by the stopping conditions equation (109).

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Control and dynamic systems : advances in theory and applications ; 10 by Cornelius T Leondes


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