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Earthquake Engineering Research - HKU Libraries - The University ...

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484<br />

solved for the Hamilton Jacobi-Bellman equation of the optimality condition, and the switching hyperplane is<br />

expressed by the following equation.<br />

S = F = X m lty'B T usm P (8)<br />

where P in (8 ) denotes the positive semi definite matrix which satisfies the following equations.<br />

(9)<br />

Sliding Mode Controller Design by Disturbance-Accommodating<br />

Here, we obtain the continuous sliding mode controller based on the switching hyperplane by disturbanceaccommodating<br />

bilinear control. <strong>The</strong> block diagram of the proposed control system is shown in Fig. 2. <strong>The</strong><br />

control law consits of the feedback link and the feedforward link.<br />

This control object is represented by the following bilinear equation.<br />

We assume an sliding mode is defined in n-dimensional state space as follows :<br />

(10)<br />

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