Probability-Weighted Optimal Control for Nonlinear Stochastic Vibrating Systems with Random Time Delay

<div>The sample time history of displacement <svg height="11.8174pt" id="M191" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 14.402 11.8174" width="14.402pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M699 368C699 549 574 666 407 666C186 666 23 488 23 277C23 113 129 -3 288 -13L307 -26C431 -111 501 -139 533 -147C559 -154 613 -163 658 -164L666 -141C597 -111 507 -66 430 -11L416 -1C580 42 699 190 699 368ZM601 371C601 227 518 54 381 22L354 40L278 24C175 47 120 145 120 269C120 451 235 631 398 631C540 631 601 521 601 371Z" id="g113-82"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.321,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path></g></svg> for controlled system compared with uncontrolled system.</div>

Shock and Vibration

fig6

Figure 6

Figure 6: Probability-Weighted Optimal Control for Nonlinear Stochastic Vibrating Systems with Random Time Delay 