2021/03/26 by Berk Altın, Altın, Berk, Ricardo G. Sanfelice +1
Computer Science · Engineering · #Advanced Control Systems Optimization #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.2103.14276
openalex publication_date 2021/03/26 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
The sequential compactness afforded hybrid systems under mild regularity constraints guarantee outer/upper semicontinuous dependence of solutions on initial conditions and perturbations. For reachable sets of hybrid systems, this property leads to upper semicontinuous dependence with respect to initial conditions, time, and perturbations. Motivated by these results, we define a counterpart to sequential compactness and show that it leads to lower semicontinuous dependence of solutions on initial conditions and perturbations. In the sequel, it is shown that under appropriate assumptions, reachable sets of systems possessing this novel property depend lower semicontinuously on initial conditions, time, and perturbations. When those assumptions fail, continuous approximations of reachable sets turn out to be still possible. Necessary and sufficient conditions for the introduced property are given by a combination of geometric constraints, regularity assumptions, and tangentiality conditions. Further applications to simulations and optimal control of hybrid systems are discussed.