Finite-time adaptive tracking control for unknown nonlinear systems with a novel barrier Lyapunov function

Finite‐time tracking control for nonaffine nonlinear pure‐feedback systems with a prescribed performance

“…Remark To reflect the advantages of Definition 2 and its difference from Definition 1, we make the following statement. The first two conditions in Definition 2 are same as ones in the settling‐time performance function 28‐31 . However, the third condition to the performance function in References 28‐31 is that , and for all with the positive constants and T .…”

“…Such a control scheme is developed to the general affine nonlinear strict‐feedback systems 26 and then the nonaffine nonlinear pure‐feedback systems 27 . To achieve the desired convergence accuracy with a settling convergence time, the settling‐time performance function was brought into the affine nonlinear strict‐feedback systems 28‐30 and then the nonaffine nonlinear pure‐feedback system 31 . Although the settling‐time performance function can determine the settling convergence time of the system, the control law is still the integer power control and the stability analysis is based on the asymptotic stability theory, which is irrelevant to the classic finite‐time stability.…”

Practical finite‐time sampled‐data output consensus for a class of nonlinear multiagent systems via output feedback

“…It should be emphasized that all the aforementioned fruits 20‐30 merely following their interests for the asymptotic control researches, and for finite‐time control which processes higher engineering control efficiency, none of the aforementioned results 20‐30 were considered. However, for many practical industrial nonlinear systems, such as the boiler water temperature automatic control system 31 and the fluid control system, 32 the water temperature and the liquid storage in open flume are necessary to reach the set temperature and the water level in finite time, respectively, therefore the broad application of finite‐time control in industrial fields has stimulated the development of the related theoretical researches (see the related works 33‐37 ). Finite‐time fault‐tolerant control algorithms were offered in References 33 and 34 for the nonlinear systems, and adaptive finite‐time tracking control was realized in Reference 35 for the uncertain strict‐feedback nonlinear system with full state constraints.…”

“…However, for many practical industrial nonlinear systems, such as the boiler water temperature automatic control system 31 and the fluid control system, 32 the water temperature and the liquid storage in open flume are necessary to reach the set temperature and the water level in finite time, respectively, therefore the broad application of finite‐time control in industrial fields has stimulated the development of the related theoretical researches (see the related works 33‐37 ). Finite‐time fault‐tolerant control algorithms were offered in References 33 and 34 for the nonlinear systems, and adaptive finite‐time tracking control was realized in Reference 35 for the uncertain strict‐feedback nonlinear system with full state constraints. Fuzzy logic systems were utilized in Reference 36 to tackle the finite‐time adaptive fuzzy control problem of the multi‐input and multi‐output (MIMO) nonlinear nonstrict feedback system, and such fuzzy logic systems were also extended in Reference 37 to address the stochastically finite‐time control problem of the uncertain stochastic nonlinear system in nontriangular form.…”

“…In addition, the aforementioned finite‐time control literature 33‐37 for nonlinear systems were further extended to the finite‐time consensus researches for nonlinear multiagent systems, for instance, see References 38‐41. The finite‐time consensus investigation was concerned in Reference 38 for the nonlinear multiagent system, and the practical finite‐time consensus was explored in Reference 39 for the second‐order heterogeneous switched nonlinear multiagent system.…”