  This paper proposes a composite adaptive control architecture using dual
adaptation scheme for dynamical systems comprising time-varying uncertain
parameters. While majority of the adaptive control schemes in literature
address the case of constant parameters, recent research has conceptualized
improved adaptive control techniques for time-varying systems with rigorous
stability proofs. The proposed work is an effort towards a similar direction,
where a novel dual adaptation mechanism is introduced to efficiently tackle the
time-varying nature of the parameters. Projection and $\sigma$-modification
algorithms are strategically combined using congelation of variables to claim a
global result for the tracking error space. While the classical adaptive
systems demand a restrictive condition of persistence of excitation (PE) for
accurate parameter estimation, the proposed work relies on a milder condition,
called initial excitation (IE) for the same. A rigorous Lyapunov stability
analysis is carried out to establish uniformly ultimately bounded (UUB)
stability of the closed-loop system. Further it is analytically shown that the
proposed work can recover the performance of previously designed IE-based
adaptive controller in case of time invariant systems.
