  This paper focuses on developing a new paradigm motivated by investigating
the consensus problem of networked Lagrangian systems with time-varying delay
and switching topologies. We present adaptive controllers with piecewise
continuous or arbitrary times differentiable control torques for realizing
consensus of Lagrangian systems, extending the results in the literature. This
specific study motivates the formulation of a new paradigm referred to as
forwardstepping, which is shown to be a systematic tool for solving various
nonlinear control problems. One distinctive point associated with
forwardstepping is that the order of the reference dynamics is typically
specified to be equal to or higher than that of the original nonlinear system,
and the reference dynamics and the nonlinear system are governed by a
differential/dynamic-cascaded structure. The order invariance or increment of
the specified reference dynamics with respect to the nonlinear system and their
differential/dynamic-cascaded structure expands significantly the design
freedom and thus facilitates the seeking of solutions to many nonlinear control
problems which would otherwise often be intractable.
