2017/06/01 by Monica Motta, Motta, Monica, Caterina Sartori +1
Biochemistry, Genetics and Molecular Biology · Engineering · #Microbial metabolism and enzyme function #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1706.00229
We consider a nonlinear control system depending on two controls u and v, with dynamics affine in the (unbounded) derivative of u, and v appearing initially only in the drift term. Recently, motivated by applications to optimization problems lacking coercivity, [1] proposed a notion of generalized solution x for this system, called \it limit solution, associated to measurable u and v, and with u of possibly unbounded variation in [0,T]. As shown in [1], when u and x have bounded variation, such a solution (called in this case BV simple limit solution) coincides with the most used graph completion solution (see e.g. [6]). This correspondence has been extended in [24] to BVloc u and trajectories (with bounded variation just on any [0,t] with t