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.
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