An Offline Formulation of MPC for LPV Systems Using Linear Matrix Inequalities

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="786351.fig.003a" src="https://static.hindawi.com/articles/jam/volume-2014/786351/figures/786351.fig.003a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Two sequences of ellipsoids corresponding to <svg height="18.65" id="M243" style="vertical-align:-4.77652pt" version="1.1" viewbox="0 0 18.237499 18.65" width="18.237499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.4)"><path d="M716 28l-8 -28h-254l8 28q55 5 66 17.5t5 47.5l-30 145h-232l-74 -138q-21 -43 -11 -54.5t72 -17.5l-6 -28h-235l8 28q53 7 73.5 21t53.5 70l319 540l33 8q6 -43 33 -176l80 -381q10 -49 26.5 -63t72.5 -19zM495 281l-49 264h-2l-149 -264h200z" id="x1D434"></path></g>
<g transform="matrix(.012,-0,0,-.012,12.525,15.475)"><path d="M394 607q0 -25 -15.5 -43t-39.5 -18q-19 0 -32 13t-13 35t16 41.5t40 19.5q20 0 32 -13.5t12 -34.5zM360 349l-57 -283q-38 -188 -122 -263q-72 -64 -114 -64q-16 0 -30 10.5t-14 22.5q0 24 21 45q15 13 26 6q30 -20 54 -20q41 0 65 95q37 147 86 415q6 34 6.5 42.5
t-5.5 11.5q-18 0 -79 -54l-14 25q48 48 96.5 79t71.5 31q29 0 9 -99z" id="x1D457"></path></g>
</svg></td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="786351.fig.003b" src="https://static.hindawi.com/articles/jam/volume-2014/786351/figures/786351.fig.003b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>A sequence of positively invariant sets</td></tr></table></td></tr></table>

<table>The ellipsoids computed offline in Example <a href="https://static.hindawi.com/articles/jam/volume-2014/786351/figures/#ex4.2">2</a> (a) two sequences of ellipsoids corresponding to <svg height="18.65" id="M242" style="vertical-align:-4.77652pt" version="1.1" viewbox="0 0 18.237499 18.65" width="18.237499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.4)"><path d="M716 28l-8 -28h-254l8 28q55 5 66 17.5t5 47.5l-30 145h-232l-74 -138q-21 -43 -11 -54.5t72 -17.5l-6 -28h-235l8 28q53 7 73.5 21t53.5 70l319 540l33 8q6 -43 33 -176l80 -381q10 -49 26.5 -63t72.5 -19zM495 281l-49 264h-2l-149 -264h200z" id="x1D434"></path></g>
<g transform="matrix(.012,-0,0,-.012,12.525,15.475)"><path d="M394 607q0 -25 -15.5 -43t-39.5 -18q-19 0 -32 13t-13 35t16 41.5t40 19.5q20 0 32 -13.5t12 -34.5zM360 349l-57 -283q-38 -188 -122 -263q-72 -64 -114 -64q-16 0 -30 10.5t-14 22.5q0 24 21 45q15 13 26 6q30 -20 54 -20q41 0 65 95q37 147 86 415q6 34 6.5 42.5
t-5.5 11.5q-18 0 -79 -54l-14 25q48 48 96.5 79t71.5 31q29 0 9 -99z" id="x1D457"></path></g>
</svg> and (b) a sequence of positively invariant sets.</table>

Journal of Applied Mathematics

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Figure 3

Figure 3: An Offline Formulation of MPC for LPV Systems Using Linear Matrix Inequalities 