Efficient learning from adaptive control under sufficient excitation

Abstract

Summary Parameter convergence is desirable in adaptive control as it enhances the overall stability and robustness properties of the closed‐loop system. In existing online historical data (OHD)–driven parameter learning schemes, all OHD are exploited to update parameter estimates such that parameter convergence is guaranteed under a sufficient excitation (SE) condition which is strictly weaker than the classical persistent excitation condition. Nevertheless, the exploitation of all OHD not only results in possible unbounded adaptation but also loses the flexibility of handling slowly time‐varying uncertainties. This paper presents an efficient OHD‐driven parameter learning scheme for adaptive control, where a variable forgetting factor is specifically designed and is equipped with an estimation error feedback such that exponential parameter convergence is achieved under the SE condition without the aforesaid drawbacks. The proposed parameter learning scheme is incorporated with direct adaptive control to construct an OHD‐based composite learning control strategy. Numerical results have verified the effectiveness of the proposed approach.

Composite learning adaptive backstepping control using neural networks with compact supports

“…The reference output x d is generated by where x c = ∕3 at t ∈ [5, 10] ∪ [35,40] seconds, x c = − ∕3 at t ∈ [15,20] ∪ [45,50] seconds, and x c = 0 for other time. It is clear that the x d generated by the aforementioned model includes two tasks that are the same, and it does not satisfy the partial PE condition in Lemma 2.…”

“…26 However, in the existing NNLC methods, the necessity that the trajectory of NN inputs is recurrent is still stringent in practice, and the parameter convergence rate highly depends on PE levels, which generally gives rise to a slow parameter convergence speed. [31][32][33][34][35][36][37] The difference of the composite learning compared with the composite adaptation is that online historical data are employed to construct prediction errors so that closed-loop exponential stability is ensured by an interval excitation (IE) condition, which greatly relaxes the PE condition. [28][29][30] Motivated by the composite adaptation, an emerging composite learning technique was proposed to achieve parameter convergence in adaptive control at the absence of PE.…”

“…[31][32][33][34][35][36][37] The difference of the composite learning compared with the composite adaptation is that online historical data are employed to construct prediction errors so that closed-loop exponential stability is ensured by an interval excitation (IE) condition, which greatly relaxes the PE condition. The IE condition for parameter convergence in the composite learning was relaxed to be a condition of sufficient excitation in the work of Pan et al 35 In the work of Pan and Yu, 36 a composite learning control approach was developed for a general class of robotic arms. In the work of Pan and Yu, 32 the approach of Pan et al 31 was extended to a class of strict-feedback nonlinear systems with mismatched parametric uncertainties via command filtered backstepping.…”

“…In the work of Pan and Yu, 32 the approach of Pan et al 31 was extended to a class of strict-feedback nonlinear systems with mismatched parametric uncertainties via command filtered backstepping. However, the approaches of Pan and Yu 36 and Guo et al 37 are specifically designed for robotic systems; the time derivatives of plant states are needed to be estimated in the works of Pan et al, 32,33 and the extension of the integral transformation in other works 31,34,35 to the case with mismatched uncertainties is infeasible. The IE condition for parameter convergence in the composite learning was relaxed to be a condition of sufficient excitation in the work of Pan et al 35 In the work of Pan and Yu, 36 a composite learning control approach was developed for a general class of robotic arms.…”

On parameter convergence in least squares identification and adaptive control

“…Remark Composite learning achieves exponential parameter convergence in adaptive control without the deficiencies of the concurrent learning in Remark , rather than gradient‐based estimation laws, is developed to guarantee exponential parameter convergence; (ii) the indirect adaptive scheme , rather than direct adaptive schemes, is applied to update in the control law ; and (iii) the usage of is not necessary due to the interval integral action in and the integral transformation.…”