A solution to the decentralized adaptive stabilization problem

Stability analysis of decentralized adaptive backstepping control systems with actuator failures

“…The design parameters are chosen as κ i = [4,4] T , i = 1, 2, c 1 1 = c 1 2 = 2, c 2 1 = c 2 2 = 1, l 1 1 = l 2 1 = 1 1 2 = l 2 2 = 0.001, Γ 1 = Γ 2 = 0.1. The outputs and control inputs of both subsystems for both cases with and without actuator failure are given in Figures 1-4.…”

“…However, the tradeoff between simplicity in design and difficulty in analysis of the overall system by applying this technique results in a limited results with rigorous analysis. In [1][2][3][4][5], several results were reported on global stability and steady state tracking obtained by using conventional adaptive approach. Backstepping [6] was firstly adopted in decentralized adaptive control in [7], where the restriction on subsystem relative degrees was relaxed.…”

Decentralized adaptive output feedback control via input/output inversion

“…Gavel and Siljak (1989) proposed an alternative high-gain approach for a class of large-scale systems composed of subsystems with matched uncertainties that relaxed some of the restrictive assumptions of Ioannou (1986). Applying Morse's dynamic certainty equivalence principle, Ortega and Herrera (1993) removed the restriction on subsystem relative degrees. Wen (1994) achieved the same result using integrator backstepping.…”

Adaptive backstepping control of uncertain systems with actuator failures and subsystem interactions

“…Adaptive control is one of the most promising tools to accommodate uncertainties, it is also widely adopted in developing decentralized control methods. Based on conventional adaptive approach, several results on global stability and steady state tracking were reported, see for examples [80][81][82][83][84][85][86]. In [80], a class of linear inter-connected system with bounded external disturbances, unmodeled interactions and singular perturbations are considered.…”

“…Thus the obtained results with rigorous analysis are still limited. Based on conventional adaptive approach, several results on global stability and steady state tracking were reported, see for examples [81,[85][86][87]110,111]. However, transient performance is not ensured and non-adjustable by changing design parameters due to the methods used.…”