Nonlinear <svg     style="vertical-align:-4.47127pt;width:36.412498px;" id="M1" height="20.262501" version="1.1" viewBox="0 0 36.412498 20.262501" width="36.412498"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.022,-0,0,-.022,.062,14.638)"><path id="x1D43B" d="M865 650q-1 -4 -4 -14t-4 -14q-62 -5 -77 -19.5t-29 -82.5l-74 -394q-12 -61 -0.5 -77t75.5 -21l-6 -28h-273l8 28q64 5 82 21t29 76l36 198h-380l-37 -197q-11 -64 0.5 -78.5t79.5 -19.5l-6 -28h-268l6 28q60 6 75.5 21.5t26.5 76.5l75 394q13 66 2 81.5t-77 20.5l8 28
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			<g transform="matrix(.016,-0,0,-.016,19.725,20.012)"><path id="x221E" d="M983 225q0 -112 -67 -174.5t-150 -62.5q-91 0 -154.5 43.5t-113.5 129.5q-49 -85 -104 -129t-138 -44q-98 0 -158.5 66t-60.5 154q0 59 21 106.5t54.5 75.5t70.5 43t73 15q90 0 152.5 -43.5t112.5 -128.5q48 84 104.5 128t140.5 44q93 0 155 -65t62 -158zM478 196
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</svg> Optimal Control Scheme for an Underwater Vehicle with Regional Function Formulation

<table> The desired lawnmower trajectory where “<svg height="8.5" id="M124" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 10.1 8.5" width="10.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,8.438)"><path d="M528 54l-36 -38l-198 201l-198 -201l-36 38l197 200l-197 201l36 38l198 -202l198 202l36 -38l-197 -201z" id="xD7"></path></g>
</svg>” marks the initial position of the AUV.</table>

Journal of Applied Mathematics

fig2

Figure 2

Figure 2: Nonlinear <svg     style="vertical-align:-4.47127pt;width:36.412498px;" id="M1" height="20.262501" version="1.1" viewBox="0 0 36.412498 20.262501" width="36.412498"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
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</svg> Optimal Control Scheme for an Underwater Vehicle with Regional Function Formulation 

Journal of Applied Mathematics

Nonlinear Optimal Control Scheme for an Underwater Vehicle with Regional Function Formulation

Figure 2