On the Linear Quadratic Minimum-fuel Problem

H. Benazza and N. El Alami (Morocco)


Minimum-Fuel, Hamilton-Jacobi-Bellman, Riccati, Dc motor.


E.I.Verriest and F.L.Lewis have presented in [1] a new method to approach the minimum-time control of linear continuous-time systems avoiding the Bang-Bang control. Their method relied on the optimization of a cost includ ing time energy and precisions terms. Then, N.Elalami and N.Znaidi [2], extended these results to the discrete-time linear systems. The objective of this work is to propose an approach for minimum fuel problem where the term of consumption is increased by an energetic term in order to avoid Bang-off-Bang control and singular intervals. Using the Hamilton-Jacobi-Bellman(HJB) equation we are able to provide a convenient solution to the problem of minimal consumption that uses the Riccati matrix.

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