Proximal Aiming Control via State Constraint Removal for Linear Continuous-time Systems with State and Input Constraints

In this paper, the S-constrained controllability to a target set Sigma is studied for linear continuous-time systems with state and input constraints. A proximal aiming controller design scheme is presented, which involves a certain modification of the original dynamics. The modified dynamics in effect provide state constraint removal. Both a feasible near-set of initial states associated with the proposed feedback scheme and a procedure for obtaining the modified dynamics are also developed. The novel feature of the proposed discontinuous feedback control law is that it can steer the system state back to the interior of state constraint set S as quickly as possible when state arrives at (or near) the boundary of S. A numerical example is also given to illustrate the effectiveness of the design scheme.