Geodesic
Resource consumption optimal and quasi-optimal controls for dynamic systems
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 166-249

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A numerical method of solving the problem on minimization of consumption resources for dynamic systems is proposed. The method is based on developing finite control translating a linear system in the fixed time from an initial state to a desired final state and allowing the structure of resource consumption optimal control to be calculated. The technique is given for an initial approximation to be specified an iterative algorithm of calculating the optimal control is considered. The system of linear algebraic equations is obtained that relates the increments of initial conditions for an adjoint system to the increments of phase coordinates about a given final state. A calculating algorithm is offered. The calculating process with sequence of the controls is proved to converge to the resource consumption optimal control. The radius of local convergence is found, its quadratic rate being determined. The results of modeling and calculating are presented. The method is generalized to disturbed dynamic systems. The features of real-time control are considered. An approximate method of solving the problem on minimization of resource consumption is proposed, estimation of closeness between the approximate and the optimal solutions being obtained with the technique to reduce their discrepancy. One more iterative algorithm using an approximate solution as initial one is considered for the problem in question to be solved.
Keywords: optimal control, finite control, resource consumption, linear system, phase trajectory, swit-ching moment, adjoint system, iteration, disturbance, real time, estimation of close-ness.
Mots-clés : quasi-optimal control, variation, convergence, approximal solution 
@article{SEMR_2010_7_a17,
     author = {V. M. Aleksandrov},
     title = {Resource consumption optimal and quasi-optimal controls for dynamic systems},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {166--249},
     publisher = {mathdoc},
     volume = {7},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2010_7_a17/}
}
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V. M. Aleksandrov. Resource consumption optimal and quasi-optimal controls for dynamic systems. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 166-249. http://geodesic.mathdoc.fr/item/SEMR_2010_7_a17/