Preserving stability/performance when facing an unknown time-delay

A gradient-based parameter identification method for time-delay chaotic systems

“…Our parameter identification problem can be stated as follows: Given system (12) with initial conditions (13), choose the unknown quantities ζ 1 , ζ 2 and τ to minimize the objective function…”

“…On the other hand, although gradientbased optimization techniques have excellent local searching capabilities, they have yet to be fully exploited to solve the parameter identification problem for time-delay chaotic systems. In addition, the existing identification methods for nonlinear time-delay systems (see [12][13][14][15][16][17]) are not suitable for chaotic systems, as such systems typically contain nonlinear terms with more than one unknown delay/parameter.…”

Delay identification in time-delay systems using variable structure observers

“…Another (single) delay estimation technique can be found in [7] where the present signal u = u(t) and its delayed value, denoted by v(t) = u(t − h) are supposed to be known and their derivative to be bounded as follows: 0 < α ≤ . u(t) ≤ β.…”

“…The adaptive control of delay systems is not so much developed either [2,12,35] and the delay is generally assumed to be known. As noted in [7], the on-line delay estimation has a longstanding issue in signal processing: these applications [7,32] however assume that both the present signal u = u(t) and its delayed value u(t − h) are known and their derivative to be bounded as follows: 0 < α ≤ . u(t) ≤ β.…”

A novel online adaptive time delay identification technique

“…Zhou and Frank [8] developed an approach based on a modified tracking filter for time delay identification for a class of nonlinear autoregressive processes with exogenous inputs. Diop et al [9] utilized an on-line estimation scheme based on least squares algorithm to identify time delay while providing exponential stability. In [10], So presented an unbiased impulse response estimation approach for time delay identification between signals received at two spatially separated sensors.…”