Stability and convergence of Euler’s method for state-constrained differential inclusions. (English) Zbl 1262.34021

Baier, Robert; Chahma, Ilyes Aïssa; Lempio, Frank

SIAM J. Optim. 18, No. 3, 1004-1026 (2007).

Summary: A discrete stability theorem for set-valued Euler’s method with state constraints is proved. This theorem is combined with known stability results for differential inclusions with so-called smooth state constraints. As a consequence, order of convergence equal to 1 is proved for set-valued Euler’s method, applied to state-constrained differential inclusions.

MSC:

34A60	Ordinary differential inclusions
34A45	Theoretical approximation of solutions to ordinary differential equations
49J15	Existence theories for optimal control problems involving ordinary differential equations
65L20	Stability and convergence of numerical methods for ordinary differential equations

Keywords:

Filippov theorem; set-valued Euler’s method; differential inclusions with state constraints; stability and convergence of discrete approximations