Continuously operated autonomous processes governed by hereditary state equations are c;onsidered. The problem of improving of the optimal steady-state solution by periodic variations of control and state variables is discussed. A new formulation of the periodic hereditary control problem exploiting the heredity shift operator is presented, and its advantages are pointed out. This problem is solved iteratively by descent methods using variable metric ideas and implemented with the help of the

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... thematica system. The proposed approach is illustrated by a simple example of ecological hereditary system. Keywords Hereditary autonomous process, periodic control problem, heredity shift operator, descent method, Mathematica system. J. Doležal et al. (eds.), System Modelling and Optimization