A new adaptive law for robust adaptation without persistent excitation

Hybrid Adaptive Flight Control with Model Inversion Adaptation

“…where Γ = Γ ⊤ > 0 ∈ R m×m is an adaptive gain matrix, μ > 0 ∈ R is an e-modification parameter (Narendra & Annaswamy, 1987), . is a Frobenius norm, and P = P ⊤ > 0 ∈ R 6×6 solves the Lyapunov equation…”

“…For each failure emulation, each pilot was asked to provide Cooper-Harper Ratings (CHR) for a series of flight tasks, which included large amplitude attitude capture tasks and cross-wind approach and landing tasks. Seven adaptive control methods were selected for the piloted study that include e-modification (Narendra & Annaswamy, 1987), hybrid adaptive control (Nguyen et al, 2006), optimal control modification (Nguyen et al, 2008), metric-driven adaptive control using bounded linear stability method (Nguyen et al, 2007), L 1 adaptive control (Cao & Hovakimyan, 2008), adaptive loop recovery , and composite adaptive control (Lavretsky, 2009). This is by no means an exhaustive list of new advanced adaptive control methods that have been developed in the past few years, but this list provides an The study generally confirms that adaptive control can clearly provide significant benefits to improve aircraft flight control performance in adverse flight conditions.…”

Variable neural networks for adaptive control of nonlinear systems

“…The tracking error vector and the weight error vectors, respectively, are defined as (33) (34) (35) where and are the estimated weight vectors. From (1), it can be shown that (36) Hence, from (33)- (36), the dynamical expression of the tracking error is (37) One approach to this problem is to take the control input satisfying (38) where the vector makes the following matrix stable:…”

“…Using (37), the derivative of the Lyapunov function with respect to time is given by (41) where the vector is the th row of the matrix , i.e., . Since is a constant vector, we have that , similarly,…”

“…In the presence of a modeling error , to ensure the stability of the system, a lot of algorithms, e.g., the fixed or switching -modification [16], [17], -modification [37], and the dead-zone methods [38], [52], can be applied to modify the above standard adaptation laws.…”