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SUMMARYIn this paper, we consider the linear-quadratic control problem with an inequality constraint on the control variable. We derive the feedback form of the optimal control by the agency of the unconstrained linearquadratic control systems.

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In this paper, we consider the linear‐quadratic control problem with an inequality constraint on the control variable. We derive the feedback form of the optimal control by the agency of the unconstrained linear‐quadratic control systems. Copyright © 2001 John Wiley & Sons, Ltd.

Functions that are invariant with respect to the tetrahedral and cubic symmetries are determined. These invariant mappings are applied to serve as the density functions for automatic generation of the colorful images with such symmetries in three dimensional space from a dynamical system's point of view.