Output‐feedback finite‐time and exponential tracking continuous control for mechanical systems with constrained inputs

An output‐feedback finite‐time/exponential tracking continuous control scheme for mechanical systems with constrained inputs is proposed. The developed controller has a velocity‐free saturating‐proportional saturating‐derivative type structure, inducing damping through a dirty‐derivative based auxiliary dynamics. Special well‐defined functions that coat the error correction actions of the control scheme give the required shaping for the concerned type of convergence and input saturation avoidance. The type of convergence is determined through the choice on the values of specific control parameters. Differently to similar previous approaches for state‐feedback tracking or output‐feedback regulation, the control parameters that determine the trajectory convergence are not restricted to satisfy a fixed equivalence relation but rather a wider comparative one. This expands the spectrum of finite‐time convergent trajectories that may be induced, and further gives the option of an additional (unconventional) type of exponential stability (in addition to the conventional one). The closed‐loop analysis is supported through suitable strict Lyapunov functions. Experimental tests on a 3‐degree‐of‐freedom robot manipulator further support the contributed result.