Abstract
SummaryThe ability to learn is crucial for neural network (NN) control as it is able to enhance the overall stability and robustness of control systems. In this study, a composite learning control strategy is proposed for a class of strict‐feedback nonlinear systems with mismatched uncertainties, where raised‐cosine radial basis function NNs with compact supports are applied to approximate system uncertainties. Both online historical data and instantaneous data are utilized to update NN weights. Practical exponential stability of the closed‐loop system is established under a weak excitation condition termed interval excitation. The proposed approach ensures fast parameter convergence, implying an exact estimation of plant uncertainties, without the trajectory of NN inputs being recurrent and the time derivation of plant states. The raised‐cosine radial basis function NNs applied not only reduces computational cost but also facilitates the exact determination of a subregressor activated along any trajectory of NN inputs so that the interval excitation condition is verifiable. Numerical results have verified validity and superiority of the proposed approach.
Highlights
One of the successful stories of applying machine learning to intelligent control is neural network (NN)-based adaptive control (NNAC) [1]
A more practical persistent excitation (PE) condition based on radial basis function (RBF)NNs shows that any recurrent trajectory of NN inputs that stays within a regular lattice leads to a partial PE condition [21]
Remark 2 : Another advantage of applying raised-cosine radial basis function (RCRBF)-NNs is that the subregressor Φζi(xi) activated along any given trajectory x(t) can be exactly determined due to the compact support of RCRBFs such that the interval excitation (IE) condition in Definition 1 is verifiable by checking the minimal singular value of Θi(t) in (14) and the time Tei that satisfies the IE condition is obtainable
Summary
One of the successful stories of applying machine learning to intelligent control is neural network (NN)-based adaptive control (NNAC) [1]. A model reference composite learning control method was presented for a class of nonlinear systems with matched parametric uncertainties in [31], where the time derivation of plant states is eliminated by using an integral transformation. An NN composite learning control (NNCLC) strategy is presented for the class of strict-feedback nonlinear systems in [29], where raised-cosine RBF (RCRBF)-NNs are used to approximate plant uncertainties. Compared with existing NNLC approaches, the attractive feature of our approach is that fast parameter convergence in NNs, implying exact learning of plant uncertainties, is guaranteed without the trajectory of NN inputs being recurrent. R, R+ and Rn denote the spaces of real numbers, positive real numbers and real n-vectors, respectively, L∞ is the space of bounded signals, x is the Euclidean norm of x, min{·}, max{·} and sup{·} are the operators of minimum, maximum and supremum, respectively, tanh(x) is a hyperbolic tangent function, Ωc := {x| x ≤ c} is the ball of radius c, and Ck represents the space of functions for which all k-order derivatives exist and are continuous, where c ∈ R+, x ∈ R, x ∈ Rn, and n and k are positive integers
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