By Cornelius T Leondes
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Extra info for Control and dynamic systems : advances in theory and applications ; 10
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  obtained excellent convergence properties in their orbit transfer problems. Moyer and Pinkham  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).
Control and dynamic systems : advances in theory and applications ; 10 by Cornelius T Leondes