In Search for Global Optima in Nonlinear Optimal Control Problems

R. Luus (Canada)


Optimal singular control; Iterative dynamic program ming; Global optimization, Homotopic continuation


In solving optimal control problems numerically, the number of time stages and the size of the time stages are important. Generally, the use of a larger number of time stages beyond about 40 yields a more refined control policy, but only a very slight improve ment in the performance index. However, in some cases, a totally different highly oscillatory control pol icy results, giving a substantial improvement in the performance index. This aspect of optimal control is illustrated by two examples. The first one involves generalizing the singular optimal control problem in troduced in 1980 by Yeo, by introducing a parameter into the nonlinear term. When this parameter is in creased beyond its nominal value of 0.0005 to 0.0025, the oscillatory behavior becomes more complex and the improvement over the nonoscillatory control pol icy is increased from 0.3% to 1.2%. When this para meter is reduced, the improvement of the oscillatory control policy is decreased, and the optimal control policy is more difficult to obtain, unless the informa tion for larger values of is used. The second example is a fed-batch reactor where it is shown that spikes, where the control is switched to its upper bound for very short periods of time, in the control policy can improve the performance index.

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