Viability, the solution set, and fixed point approximation of hybrid systems

On the least restrictive control for collision avoidance of two unicycles

“…Also, since ' r50 we cannot have sinðf À y=2Þ ¼ 0: The first and third formulas are thus well defined and satisfy (9), by using sðxÞ > 2: Finally, the zero dot products appear as discussed above, and also coincide with condition (9).…”

“…So far we have shown that at any point x 2 @D n c \ W \ S c ; at least three out of the four vector fields satisfy condition (9). The remaining cases are complicated to verify analytically.…”

A Viability Problem for Control Affine Systems with Application to Collision Avoidance

“…Since s * (x(t)) is a continuous function of t, t 1 > 0. We cannot have i ∈ I * (x(t 1 )), where i corresponds to u 1 = v i ; 45th IEEE CDC, San Diego, USA, Dec. [13][14][15]2006 FrIP3.9…”

“…In ¬W , we will see the viability kernel is simply S c , so u p is only used in ∂S c ∩¬W . However, the system naturally remains viable in S c ∩ ¬W , 45th IEEE CDC, San Diego, USA, Dec. [13][14][15]2006 FrIP3.9…”

“…A characterization of the viability kernel is given. Recent, relevant work both on theory and numerical approaches to finding viability kernels are [5], [4], [10], [11], [14], [16], [17]. However, the specific class of viability problem treated here has not yet been investigated.…”