On the Suboptimal Solution of the Speed-In-Action Problem for a Linear Discrete System in the Case of Asymmetric Control Constraints

The paper considers a linear discrete system with bounded control. The speed-in-action problem is solved for the system, that is, it is required to construct a control process that transfers the system from the initial state to the origin in a minimum number of steps. If the set of acceptable control values has a superellipse structure, then the problem of calculating optimal control can be reduced to solving a system of algebraic equations. A superellipsoidal approximation method has been developed for sets of arbitrary structure, and the case of asymmetric sets has been considered. Examples are given.

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