Adaptive Control of Nonlinear Discrete-Time Systems by Using OS-ELM Neural Networks

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="267609.fig.005a" src="https://static.hindawi.com/articles/aaa/volume-2014/267609/figures/267609.fig.005a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b><svg height="15.0875" id="M223" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 56.924999 15.0875" width="56.924999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> random input</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="267609.fig.005b" src="https://static.hindawi.com/articles/aaa/volume-2014/267609/figures/267609.fig.005b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b><svg height="15.0875" id="M224" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 46.950001 15.0875" width="46.950001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,14.103,12.138)"><path d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" id="x2C"></path></g><g transform="matrix(.017,-0,0,-.017,20.801,12.138)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
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</svg> random input</td></tr></table></td></tr></table>

<table>OS-ELM control results with different initial training samples.</table>

Abstract and Applied Analysis

fig5

Figure 5

Figure 5: Adaptive Control of Nonlinear Discrete-Time Systems by Using OS-ELM Neural Networks 