In some industrial processes the control transients are accompanied by thermal transients which produce damaging thermal stresses in parts of the apparatus. The steam turbine start-up may be cited as an example of such a process. The need arises to schedule the control transients so that the resulting damage be minimized while the requirements of the process are met. This problem is analyzed in the case when the measure of damage is the maximum value of the thermal stress transient at a given location and the admissible controls are constrained by two time-dependent limits. The system is assumed to be linear and time invariant with thermal stress selected at critical locations. The solution of the minimax problem is obtained for systems whose impulse response function of thermal stress satisfies certain conditions common in thermoelastic problems. The proof of the method of solution and an example of application are also given.

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