Abstract
AbstractThe guaranteed approach to a description of uncertainties in control problems is developed and is based on an approximation of sets to which uncertain vectors belong by means of optimal ellipsoids. Optimal and suboptimal algebraic operations with ellipsoids (sum, intersection) are presented. By means of these operations, differential equations are obtained which describe the evolution of ellipsoids which provide external and internal bounds on the attainable sets for linear controlled systems. The developed theory is generalized for non‐linear systems and is applied to obtain bounds in optimal control problems and differential games and to obtain minimax filtering in systems with incomplete information. Some examples are also given.
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