Further advancements on the output-feedback global continuous control for the finite-time and exponential stabilisation of bounded-input mechanical systems: desired conservative-force compensation and experiments

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

“…The remaining tests were added as a suggestion from an anonymous reviewer. In particular, Test 3 aims to show a profit over counting on the finite-time convergence criterion stated through (18) with respect to that obtained through homogeneity in the regulation cases from the works by Zamora-Gómez et al 12,15 -namely a 1 ∈ (0, 1), a 2 = a 1 and a 3 = (1 + a 1 )∕2-which happens to be a very particular case included in (18). Finally, Test 4 shows the closed-loop system performance when a 1 and a 2 take a common low value.…”

“…This has been so for every type of systems to which the works on finite-time continuous control have been addressed to. As for mechanical or Euler-Lagrange systems, solutions to various formulations of finite-time continuous control problems have been developed, addressing both regulation 1,[8][9][10][11][12][13][14][15] and tracking. 16 Among these works, some have been developed disregarding input constraints 1,8,9,11,13 and others under the consideration of constrained inputs.…”

“…16 Among these works, some have been developed disregarding input constraints 1,8,9,11,13 and others under the consideration of constrained inputs. 10,12,[14][15][16] Furthermore, among those devoted to regulation, some of them have developed state-feedback approaches 1,[8][9][10][11]14 and others have proposed output-feedback controllers. 12,13,15 But the problem of output-feedback finite-time tracking continuous control still needs attention to be paid to.…”

“…10,12,[14][15][16] Furthermore, among those devoted to regulation, some of them have developed state-feedback approaches 1,[8][9][10][11]14 and others have proposed output-feedback controllers. 12,13,15 But the problem of output-feedback finite-time tracking continuous control still needs attention to be paid to. In particular, controllers (with overall continuous structure) that solve such a problem under input constraints are still missing in the literature.…”

“…19 Such a simplicity, together with the coherence of such a (passivity-based) design perspective with the nature of the considered type of systems, has inspired proposals developed in the regulation case. 12,15 These have been further supported through (a particular notion of) homogeneity (more precisely, through local homogeneity 20 which has made it possible to deal with input constraints).…”