Abstract
This paper proposes an adaptive iterative learning control (AILC) method for uncertain nonlinear system with continuous nonlinearly input to solve different target tracking problem. The method uses the radial basis function neural network (RBFNN) to approximate every uncertain term in systems. A time-varying boundary layer, a typical convergent series are introduced to deal with initial state error and unknown bounds of errors, respectively. The conclusion is that the tracking error can converge to a very small area with the number of iterations increasing. All closed-loop signals are bounded on finite-time interval 0 , T . Finally, the simulation result of mass-spring mechanical system shows the correctness of the theory and validity of the method.
Highlights
Adaptive control is used to handle system control problem about uncertainties
Based on RBF neural network approximation, the paper [9] proposed adaptive iterative learning control (AILC) for nonlinear pure-feedback systems to solve the nonuniform target tracking problem. e uniform AILC frame for uncertain nonlinear system was proposed in the literature [10], by Lyapunov theory, and it could prove the convergence
There is no report from the literature for the AILC of nonlinear systems with continuous nonlinearly input and initial state error. is is a problem that needs to be solved urgently
Summary
E following definition and lemma are used in the controller design process. E approximation error can be arbitrarily decreased by increased NN node number Designing an AILC law uk(t) on [0, T] to make the output yk(t) following the target trajectory yr,k(t) is the control objective of this paper; that is to say, limk⟶∞‖yk(t) − yr,k(t)‖ ≤ ρ, where ρ is a very small positive number. E following functions zjφ,k are introduced to deal with initial state errors: zjφ,k zj,k − φj,k(t)satφjz,kj(,kt),. Φj,k(t) εj,ke− ηt, where zj,k and zjφ,k are variables of t, εj,k are sequences of convergent series, and the saturation function sat is given as follows: sat zj,k φj,k(t). E initial state errors must satisfy |zj,k(0)| εj,k for some known positive parameters εj,k, j 1, . Compared with the assumptions of the initial state in other articles, the assumptions in this paper are more relaxed and easy to be satisfied
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
