By Astrom K.J., Wittenmark B.
Compatible for complex undergraduates and graduate scholars, this evaluation introduces theoretical and sensible elements of adaptive keep an eye on. It provides a superb standpoint on ideas and an lively wisdom of key methods, supplying a well-developed feel of whilst to exploit adaptive thoughts and while different equipment are extra acceptable. 1995 version.
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Tomlab Optimization Inc, Pullman, Washington 87. Sauer CG (1989) Midas—mission design and analysis software for the optimization of ballistic interplanetary trajectories. J Astronaut Sci 37(3):251–259 88. Schwartz A (1996) Theory and implementation of numerical methods based on runge-kutta integration for solving optimal control problems. PhD thesis, Department of Electrical Engineering, University of California, Berkeley 89. Schwartz A, Polak E (1996) Consistent approximations for optimal control problems based on runge-kutta integration.
46. 47. 48. 49. 50. 19 Bryson AE, Ho Y-C (1975) Applied optimal control. Hemisphere Publishing, New York Butcher JC (1964) Implicit runge-kutta processes. Math Comput 18(85):50–64 Butcher JC (2008) Numerical methods for ordinary differential equations. Wiley, New York Byrd RH, Nocedal J, Waltz RA (2006) Knitro: an integrated package for nonlinear optimization. In: Large scale nonlinear optimization. Springer, Berlin, pp 35–59 Coverstone-Carroll VL, Hartmann JW, Mason WJ (2000) Optimal multi-objective low-thrust spacecraft trajectories.
S − 1). 35) In the context of trajectory optimization, local collocation has been employed using one of two categories of discretization: Runge-Kutta methods and orthogonal collocation methods. Nearly all Runge-Kutta methods used are implicit [31–36, 49, 69, 88, 89] because the stability properties of implicit Runge-Kutta methods are better than those of explicit methods. The seminal work on orthogonal collocation methods in trajectory optimization is due to Reddien , where Legendre-Gauss points were used together with cubic splines.