  State and input constraints are ubiquitous in all engineering systems. In
this article, we derive adaptive controllers for uncertain linear systems under
pre-specified state and input constraints. Several modifications of the model
reference adaptive control (MRAC) framework have been proposed to address input
constraints in uncertain linear systems. Considering the infeasibility of
arbitrary reference trajectories, reference modification has been implemented
in the case of input constraints in literature. The resulting conditions on the
reference and input signals are difficult to verify online. Similar results on
state and input constraints together have also been proposed, albeit resulting
in more complex and unverifiable conditions on the control. The primary
objective of this article is therefore to account for state and input
constraints in uncertain linear systems by providing easily verifiable
conditions on the control and reference. A combination of reference
modification and barrier Lyapunov methods in adaptive control are employed to
arrive at these results.
