Adaptive fuzzy finite‐time optimal control for switched nonlinear systems

Abstract

Summary This article addresses the adaptive fuzzy finite‐time control problem for a class of switched nonlinear systems whose powers are positive odd rational numbers and vary with the switching signal. The fuzzy logic systems (FLSs) are used to approximate the unknown nonlinearities of the controlled systems, and then by combining backstepping control algorithm with adding a power integrator technique, an adaptive finite‐time controller is designed. By modifying and optimizing the relevant design parameters of the proposed adaptive finite‐time controller, a novel adaptive finite‐time optimal control approach is developed. The proposed two adaptive finite‐time optimal control schemes can guarantee semi‐globally practically finite‐time stability of the closed‐loop system. Moreover, the adaptive finite‐time optimal controller can also achieve optimized performance in relation to the cost functional. Finally, a simulation example is given to illustrate the effectiveness of the proposed two adaptive finite‐time control strategies.

Finite‐time adaptive stabilization and H∞$$ {H}_{\infty } $$ control for a class of nonlinear Hamiltonian singular systems with parametric perturbations

“…The finite-time adaptive H ∞ control of NHSS ( 30) is specifically formulated as follows. A given disturbance attenuation level 𝛾 > 0 for NHSS (30), design an adaptive control law…”

“…where Λ(x) is the same as that in (30), the remaining parameters are in common with those in (22), and g…”

“…The finite-time control scheme will enable the system to obtain better transient performance and anti-disturbance performance, so investigating finite-time stabilization has received extensive attention. [26][27][28][29][30] In order to achieve the finite-time attitude stabilization of the spacecraft without angular velocity measurement, an output feedback control law is proposed in Reference 26. In Reference 27, the output feedback controller for the nonlinear time-delay system with p-normal form is designed by the recursive design method and ensures finite-time stability.…”

Adaptive finite‐time fault‐tolerant control for interconnected nonlinear systems

“…It is worth mentioning that the finite‐time control not only has the above two characteristics but also has a faster converge speed for states to equilibrium. On account of these significant properties, finite‐time control methods along with nonlinearity have been obtained in References 12‐21. The state feedback control strategies of strict and nonstrict feedback systems using adaptive finite‐time/fixed‐time control technique were investigated in References 16‐19, respectively.…”

“…On account of these significant properties, finite‐time control methods along with nonlinearity have been obtained in References 12‐21. The state feedback control strategies of strict and nonstrict feedback systems using adaptive finite‐time/fixed‐time control technique were investigated in References 16‐19, respectively. Subsequently, the works in References 20,21 extended state feedback to output feedback control, and the problem of the adaptive finite‐time SISO and MIMO nonlinear systems with unavailable states were further studied.…”