ROBUST INPUT POLICIES FOR BATCH REACTORS UNDER PARAMETRIC UNCERTAINTY

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Abstract
Batch-reactor input profiles are normally obtained under the assumption of knowledge of a parametric model. When this assumption does not hold, parameter deviation from the nominal value can severely impair performance of the nominal optimization. The minimax optimization offers an allernative that accounts for parameteric uncertainty, but its inherent worst-case assumption degrades its performance near the nominal parameter value compared to that of the nominal optimization. This work presents a new optimization procedure that offers robustness similar to the minimax optimization while retaining nominal performance similar to the nominal optimization. Given a probability distribution for the uncertain process parameters from a previous identification step, the method optimizes the expectation of cost function for the entire parameter space instead of optimizing the cost function for the expectation of the parameters. In this way increased robustness towards uncertain or time-varying parameters is obtained without unduly compromising the nominal performance. Since evaluation of the proposed objective function involves numerical integration, an efficient strategy is presented for obtaining its exact gradient indirectly, thereby rendering the method numerically reliable and computationally attractive, and less demanding than the minimax approach, in general. For the special case where the nominal parameter value is assigned probability one, the method reduces to the well-known control vector iteration procedure, a numerical optimization strategy based on Pontryagin's maximum principle. Two examples demonstrate the advantage of the new method over the conventional approaches, namely, nominal optimization, minimax approach and local-sensitivity-based approach.