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Matrix criterion robust linear quadratic control problem. (English) Zbl 0629.93080

The paper deals with dynamical systems which may be modelled, for different operating points/conditions (o.p.c.), by N linear-invariant stochastic systems (input and output additive stochastic disturbances are considered) and with the robust design of a single constant linear output controller in order to achieve satisfactory performance over the set of o.p.c. by using a matrix-valued quadratic performance index (at each o.p.c. a vector-valued one is defined). Some problems related to Pareto- minimal solutions are studied (e.g. Soland scalarization, Fritz John conditions of optimality, existence of Pareto-solutions). In order to design a Pareto-minimal controller an efficient numerical method based on a minimax problem formulation is developed. Finally, an illustrative example is given.
Reviewer: M.Voicu

MSC:

93E20 Optimal stochastic control
49K45 Optimality conditions for problems involving randomness
58E17 Multiobjective variational problems, Pareto optimality, applications to economics, etc.
90C31 Sensitivity, stability, parametric optimization
49K35 Optimality conditions for minimax problems
93C05 Linear systems in control theory
93E25 Computational methods in stochastic control (MSC2010)
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