  Firstly, a new state feedback model reference adaptive control approach is
developed for uncertain systems with gain scheduled reference models in a
multi-input multi-output (MIMO) setting. Specifically, adaptive state feedback
for output tracking control problem of MIMO nonlinear systems is studied and
gain scheduled reference model system is used for generating desired state
trajectories. Using convex optimization tools, a common Lyapunov matrix is
computed for multiple linearizations near equilibrium and non-equilibrium
points of the nonlinear closed loop gain scheduled reference system. This
approach guarantees stability of the closed-loop gain scheduled system.
Adaptive state feedback control scheme is then developed, and its stability is
proven. The resulting closed-loop system is shown to have bounded solutions
with bounded tracking error, with the proposed stable gain scheduled reference
model. Secondly, the developed control approach is improved for systems with
constraints on the control inputs. The resulting closed-loop system is shown to
have bounded solutions with bounded tracking error. Sufficient conditions for
ultimate boundedness of the closed-loop system are derived. A semi-global
stability result is proved with respect to the level of saturation for
open-loop unstable plants while the stability result is shown to be global for
open-loop stable plants. Thirdly, a decentralized adaptive state feedback
control architecture is developed and its stability is proved. Specifically,
the resulting closed-loop system is shown to have bounded solutions with
bounded tracking error for all the subsystems with the proposed stable gain
scheduled reference model. Simulation results are presented for each control
architecture.
