Analytic design of constraint automata

The paper is concerned with design of controls insuring that the dynamic system stays in a specified region of the state space or in the vicinity of that region with simultaneous minimization of the “generalized work” functional. It is shown that with conditions typical for that functional the constraining controls are independent of the optimizing ones and can be obtained separately. For a linear system of piecewise-linear constraint approximation the problem is solved in a general closed form. For the nonlinear problem an operational or iterative solution algorithm is recommended.