Adaptive Control of a Two-Item Inventory Model with Unknown Demand Rate Coefficients

<table class="table-group" id="tab9"><tr><td><table class="table"><tr><td class="thead-hr" colspan="15"><hr/></td></tr><tr><td align="left">Parameter</td><td align="center"><span style="width: 19.25px;"><svg height="14.475" id="M248" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 19.25 14.475" width="19.25" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.475)">
<g transform="translate(72,-60.42)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜃</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.9,60.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">1</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 19.25px;"><svg height="14.475" id="M249" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 19.25 14.475" width="19.25" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.475)">
<g transform="translate(72,-60.42)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜃</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.9,60.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">2</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 19.5375px;"><svg height="10.925" id="M250" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 19.5375 10.925" width="19.5375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.925)">
<g transform="translate(72,-63.26)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑎</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.67,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">2</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 19.5375px;"><svg height="10.925" id="M251" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 19.5375 10.925" width="19.5375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.925)">
<g transform="translate(72,-63.26)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑎</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.67,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">1</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 14.8125px;"><svg height="16.0875" id="M252" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 14.8125 16.0875" width="14.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.0875)">
<g transform="translate(72,-59.13)">
<g>
<path d="m -71.95,70.71 6.88,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<text transform="matrix(1,0,0,-1,-71.95,62.31)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑥</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.07,59.18)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 14.8125px;"><svg height="16.0875" id="M253" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 14.8125 16.0875" width="14.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.0875)">
<g transform="translate(72,-59.13)">
<g>
<path d="m -71.95,70.71 6.88,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<text transform="matrix(1,0,0,-1,-71.95,62.31)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑥</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.07,59.18)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 14.6875px;"><svg height="14.475" id="M254" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 14.6875 14.475" width="14.6875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.475)">
<g transform="translate(72,-60.42)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑘</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.17,60.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 14.6875px;"><svg height="14.475" id="M255" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 14.6875 14.475" width="14.6875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.475)">
<g transform="translate(72,-60.42)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑘</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.17,60.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 17.3125px;"><svg height="10.925" id="M256" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 17.3125 10.925" width="17.3125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.925)">
<g transform="translate(72,-63.26)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑚</tspan>
</text>
<text transform="matrix(1,0,0,-1,-63.07,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 17.3125px;"><svg height="10.925" id="M257" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 17.3125 10.925" width="17.3125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.925)">
<g transform="translate(72,-63.26)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑚</tspan>
</text>
<text transform="matrix(1,0,0,-1,-63.07,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 13.7875px;"><svg height="14.475" id="M258" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 13.7875 14.475" width="13.7875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.475)">
<g transform="translate(72,-60.42)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜃</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.9,60.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 13.7875px;"><svg height="14.475" id="M259" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 13.7875 14.475" width="13.7875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.475)">
<g transform="translate(72,-60.42)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜃</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.9,60.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 14.5375px;"><svg height="14.475" id="M260" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 14.5375 14.475" width="14.5375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.475)">
<g transform="translate(72,-60.42)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑑</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.3,60.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 14.5375px;"><svg height="14.475" id="M261" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 14.5375 14.475" width="14.5375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.475)">
<g transform="translate(72,-60.42)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑑</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.3,60.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
</g>
</g>
</svg></span></td></tr><tr><td align="left" colspan="15"><hr/></td></tr><tr><td align="left">Value</td><td align="center"><span style="width: 27.475px;"><svg height="10.9125" id="M262" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 27.475 10.9125" width="27.475" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">8</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 27.475px;"><svg height="11.0375" id="M263" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 27.475 11.0375" width="27.475" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0375)">
<g transform="translate(72,-63.17)">
<text transform="matrix(1,0,0,-1,-71.95,63.4)">
<tspan style="font-size: 12.50px; " x="0" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">6</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 15.75px;"><svg height="10.9125" id="M264" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 15.75 10.9125" width="15.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">0</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 15.75px;"><svg height="11.1" id="M265" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 15.75 11.1" width="15.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1)">
<g transform="translate(72,-63.12)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">5</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 7.9375px;"><svg height="10.6875" id="M266" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 7.9375 10.6875" width="7.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6875)">
<g transform="translate(72,-63.45)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">2</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 7.9375px;"><svg height="10.6875" id="M267" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 7.9375 10.6875" width="7.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6875)">
<g transform="translate(72,-63.45)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">1</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 15.75px;"><svg height="10.9125" id="M268" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 15.75 10.9125" width="15.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">0</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 15.75px;"><svg height="11.1" id="M269" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 15.75 11.1" width="15.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1)">
<g transform="translate(72,-63.12)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">5</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 15.75px;"><svg height="11.1" id="M270" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 15.75 11.1" width="15.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1)">
<g transform="translate(72,-63.12)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">5</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 15.75px;"><svg height="10.9125" id="M271" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 15.75 10.9125" width="15.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">0</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 27.475px;"><svg height="11.1" id="M272" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 27.475 11.1" width="27.475" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1)">
<g transform="translate(72,-63.12)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">5</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 19.6625px;"><svg height="10.9125" id="M273" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 19.6625 10.9125" width="19.6625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">1</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 15.75px;"><svg height="10.9125" id="M274" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 15.75 10.9125" width="15.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">0</tspan>
</text>
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</g>
</svg></span></td><td align="center"><span style="width: 15.75px;"><svg height="10.9125" id="M275" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 15.75 10.9125" width="15.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">0</tspan>
</text>
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</g>
</svg></span></td></tr><tr class="table-tr"><td colspan="15"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Journal of Applied Mathematics

tab9

Table 9

Table 9: Adaptive Control of a Two-Item Inventory Model with Unknown Demand Rate Coefficients 