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Among the pending problems of control synthesis under set-membership uncertainty lies the case when the bounds on the disturbances and the controls are generated by dierent types of inequalities. This paper presents a scheme of designing strategies of nonlinear target control synthesis under joint quadratic and hard bounds on the controls and hard bounds on the disturbances. The techniques are based on a combination of dynamic programming methods with techniques introduced by N. N. Krasovski and L. S. Pontryagin.