Optimal Control of Switching Linear Systems

Ali Benmerzouga


A solution to the control of switching linear systems with input constraints was given in Benmerzouga (1997) for both the conventional enumeration approach and the new approach. The solution given there turned out to be not unique. The main objective in this work is to determine the optimal control sequences {Ui(k) ,  i = 1,..., Mk = 0, 1, ...,  N -1} which transfer the system from a given initial state  X0  to a specific target state  XT  (or to be as close as possible) by using the same discrete time solution obtained in Benmerzouga (1997) and minimizing a running cost-to-go function. By using the dynamic programming technique, the optimal solution is found for both approaches given in Benmerzouga (1997). The computational complexity of the modified algorithm is also given.




Controllability; Bilinear Systems; Dynamic Programming; Switching Linear Systems; Optimization.

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DOI: http://dx.doi.org/10.24200/squjs.vol9iss0pp41-51


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