Robust adaptive parameter estimator design for a multi-sinusoidal signal with fixed-time stability and guaranteed prescribed performance boundary of estimation error

Concurrent Learning-Based Two-Stage Predefined-Time System Identification

“…Therefore, it can be concluded from ( 39) and (40) that ∥ Θ(t)∥ ∈ S holds for all t ≥ T. Remark 4. According to Theorem 1, system (1) can be identified exactly before T without NNAE compared with previous studies [17,27,28], where estimation error exists after the desired convergence times. In addition, system (1) can be identified with some error under NNAE according to Theorem 2, but the steady estimation error region S can be adjusted to be arbitrarily small by decreasing ε, i.e., by establishing enough neural basis functions for system modeling.…”

“…A predefined-time identification algorithm provides an exact time when the estimation of an unknown system is available for controllers. Several parameter estimation algorithms with the predefined-time property were studied based on prescribed performance control [27,28], where the convergence times of estimation errors are explicit design parameters in performance functions. The estimation errors in [27,28] can be restricted into arbitrary small regions, but they may not be eliminated entirely after the provided predefined times without considering modeling errors.…”

“…(2) The identification accuracy is much improved theoretically. Compared with traditional fixed-time and predefined-time estimators [17,27,28], it is proven that the estimation error converges to zero exactly, rather than zero nearby, without NNAEs after the predefined settling time.…”

“…(3) The identification algorithm takes effect under an easier finite-rank condition rather than the restrictive infinite PE condition compared with traditional finite-time and fixed-time identification studies [11][12][13][14]27,28], enhancing the practicality of the proposed approach. Notation 1.…”

Command filter‐based finite‐time adaptive tracking control for MIMO dynamic systems with external disturbances and prescribed performance constraints

“…Additionally, for a class of hydraulic systems, unknown system states and matched and mismatched uncertainties were handled simultaneously by using PPC technology [44]. In Hossein's work [45], not only multisinusoidal signals were considered but also prescribed performance of the estimation error was converged to their true values in a predefined time by using prescribed constraints. However, most of the results developed were only applicable to single‐input single‐output (SISO) systems, where the interconnections between different subsystems were not considered.…”