Analytical design of optimal controllers in the class of logic‐dynamic (hybrid) systems

The classical problem of analytical design of the optimal controllers which was stated and solved by A.M. Letov for continuous linear systems was considered for the class of logicdynamic (hybrid) systems. Equations to determine the optimal feedback control were derived on basis of the sufficient optimality conditions. In distinction to classical case, the optimal positional control is realized by the piecewise‐linear controller with the piecewise‐quadratic Bellman function. In contrast to the continuous, discrete or discrete‐continuous systems, the optimal processes of logic‐dynamic systems, can have multiple switchings in the logic block, thus hindering the optimal control design. Therefore it was suggested to consider a simplified problem where the logic‐dynamic system is replaced by a discrete‐continuous system admitting instantaneous multiple switchings of the discrete part. The resulting control for the logic‐dynamic system becomes suboptimal. Application of the optimality and suboptimality conditions was demonstrated by way of several examples.