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

<table class="table-group" id="tab7"><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="M190" 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="M191" 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="M192" 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="M193" 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="M194" 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="M195" 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="M196" 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="M197" 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="M198" 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="M199" 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="M200" 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="M201" 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="M202" 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="M203" 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="11.1" id="M204" 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="M205" 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">3</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 27.475px;"><svg height="11.1" id="M206" 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">1</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="12.503" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">0</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 27.475px;"><svg height="10.9125" id="M207" 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">1</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="12.503" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">0</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 19.6625px;"><svg height="11.1" id="M208" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 19.6625 11.1" width="19.6625" 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">5</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>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 19.6625px;"><svg height="11.0375" id="M209" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 19.6625 11.0375" width="19.6625" 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">6</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 7.9375px;"><svg height="11.1" id="M210" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 7.9375 11.1" width="7.9375" 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">5</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 7.9375px;"><svg height="10.9125" id="M211" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 7.9375 10.9125" width="7.9375" 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>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 19.6625px;"><svg height="11.0375" id="M212" style="vertical-align:-0.27588pt" version="1.1" viewbox="0 0 19.6625 11.0375" width="19.6625" 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,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">9</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>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 19.6625px;"><svg height="10.9125" id="M213" 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">7</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>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 19.6625px;"><svg height="10.9125" id="M214" 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">3</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 19.6625px;"><svg height="10.9125" id="M215" 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">2</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 27.475px;"><svg height="10.9125" id="M216" 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">1</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="12.503" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">0</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center"><span style="width: 27.475px;"><svg height="11.1" id="M217" 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">1</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="12.503" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">0</tspan>
</text>
</g>
</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

tab7

Table 7

Table 7: Adaptive Control of a Two-Item Inventory Model with Unknown Demand Rate Coefficients 