Geodesic
Optimal control of linear systems under uncertainty
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 3, pp. 56-72

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The problem of optimal control of a linear dynamical system under set-membership uncertainty is studied: it is required to steer the system to the terminal set with a guarantee and to maximize the guaranteed value of the quality criterion. The sets of the initial and current preposteriori distributions of the states of the dynamical system are introduced; they are used to determine a positional solution of the problem of optimal preposteriori observation with the help of inaccurate measurements of input and output signals of the observation object by two measuring devices. The obtained solution is used for determining a positional solution of the optimal control problem under uncertainty. Depending on the amount of the information used, optimal closable and closed loops are determined. The method of quasi-implementation of optimal loops by means of optimal estimator and regulator producing real-time control actions is described. The results are illustrated by examples.
Keywords: set-membership uncertainty, preposteriori distribution, width of a set, optimal preposteriori observation, optimal control of a linear dynamical system, optimal closable and closed loops, optimal estimator and regulator. 
@article{TIMM_2009_15_3_a4,
     author = {R. Gabasov and F. M. Kirillova and E. I. Poyasok},
     title = {Optimal control of linear systems under uncertainty},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {56--72},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2009_15_3_a4/}
}
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R. Gabasov; F. M. Kirillova; E. I. Poyasok. Optimal control of linear systems under uncertainty. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 3, pp. 56-72. http://geodesic.mathdoc.fr/item/TIMM_2009_15_3_a4/