Geodesic
Computational algorithm for optimal control of an object with distributed parameters in a nonsmooth area of final states
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 4, pp. 41-51

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We propose the effective computational algorithm for solving boundary-value problems of time-optimal and maximum accuracy control with a minimax estimation of the deviation of the final trajectory from a given state. The problem is reduced to a nonconvex nonlinear programming problem. The proposed algorithm takes into account the non-convex nature of the problem of nonlinear programming, provides a search in the "ravines" zone, performs a search quite efficiently under conditions of increased dimension of the definition domain of the optimized functional, and provides the required accuracy of the solution. Due to the transformation of the multidimensional non-convex nonlinear programming problem to the problem of minimizing a smooth monotonically decreasing function of one variable, the algorithm significantly reduces the computational complexity of solving boundary-value problems of optimal speed and maximum accuracy with a minimax estimate of the deviation of the final trajectory from a given state. We give an example of the solution of the test optimal control problem for induction heating of a cylindrical billet.
Keywords: distributed parameters, boundary-value problem, optimality criterion, search procedure, local minimum, global minimum. 
@article{VYURU_2019_12_4_a2,
     author = {M. Yu. Livshits and A. V. Nenashev and Yu. E. Pleshivtseva},
     title = {Computational algorithm for optimal control of an object with distributed parameters in a nonsmooth area of final states},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {41--51},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2019_12_4_a2/}
}
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M. Yu. Livshits; A. V. Nenashev; Yu. E. Pleshivtseva. Computational algorithm for optimal control of an object with distributed parameters in a nonsmooth area of final states. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 4, pp. 41-51. http://geodesic.mathdoc.fr/item/VYURU_2019_12_4_a2/