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This work deals with the problem of partial asymptotic null controllability for constrained systems governed by semi-linear evolution equations, where the linear part generates a strongly continuous compact semigroup on Hilbert spaces. This consists of driven only a desired part of the system's state to the origin, taking into account mixed state-input constraints. We give sufficient conditions for the existence of appropriate control laws to ensure partial asymptotic null controllability. The explicit expression of such controls is given as strongly-weakly continuous selections of a set-valued map which is defined through a certain practical tangential condition. Application to semilinear parabolic partial differential equations is treated in order to illustrate the results established. [ABSTRACT FROM AUTHOR]

This paper is devoted to the problem of partial asymptotic null-controllability of control systems governed by ordinary differential equations, subjected to possibly mixed state-input constraints. Using Lyapunov functions within the framework of viability theory, feedback controls are designed in such a way a part of system's state can be driven to the origin asymptotically, taking into account the mixed constraints. By using Michael selection theorem, the existence of such controls is proved, in the case of convex constraints, and their expressions are given as continuous selections of an appropriate constructed multifunction. Finally, two examples are processed numerically in order to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]