This paper deals with realizable adaptive algorithms of the nonlinear approximation with finite terms based on wavelets. We present a concrete algorithm by which we may find the required index set Am for the greedy al...This paper deals with realizable adaptive algorithms of the nonlinear approximation with finite terms based on wavelets. We present a concrete algorithm by which we may find the required index set Am for the greedy algorithm Gm^P（., Ψ）. This makes the greedy algorithm realize the near best approximation in practice. Moreover, we study the efficiency of the finite-term approximation of another Mgorithm introduced by Birge and Massart.展开更多
In this paper, the capability of neural networks and some approximation problens in system identification with neural networks are investigated. Some results are given: (i) For any function g ∈Llocp (R1) ∩S’ (R1) t...In this paper, the capability of neural networks and some approximation problens in system identification with neural networks are investigated. Some results are given: (i) For any function g ∈Llocp (R1) ∩S’ (R1) to be an Lp-Tauber-Wiener function, it is necessary and sufficient that g is not apolynomial; (ii) If g∈(Lp TW), then the set of is dense in Lp(K)’ (iii) It is proved that bycompositions of some functions of one variable, one can approximate continuous functional defined on compact Lp(K) and continuous operators from compact Lp1(K1) to LP2(K2). These results confirm the capability of neural networks in identifying dynamic systems.展开更多
This paper proposes an iterative learning control (ILC) algorithm with the purpose of controling the output of a linear stochastic system presented in state space form to track a desired realizable trajectory. It is p...This paper proposes an iterative learning control (ILC) algorithm with the purpose of controling the output of a linear stochastic system presented in state space form to track a desired realizable trajectory. It is proved that the algorithm converges to the optimal one a.s. under the condition that the product input-output coupling matrices are full-column rank in addition to some assumptions on noises. No other knowledge about system matrices and covariance matrices is required.展开更多
In this paper,the problem of identifying autoregressive-moving-average systems under random threshold binary-valued output measurements is considered.With the help of stochastic approximation algorithms with expanding...In this paper,the problem of identifying autoregressive-moving-average systems under random threshold binary-valued output measurements is considered.With the help of stochastic approximation algorithms with expanding truncations,the authors give the recursive estimates for the parameters of both the linear system and the binary sensor.Under reasonable conditions,all constructed estimates are proved to be convergent to the true values with probability one,and the convergence rates are also established.A simulation example is provided to justify the theoretical results.展开更多
In this work,the exponential approximation is used for the numerical simulation of a nonlinear SITR model as a system of differential equations that shows the dynamics of the new coronavirus(COVID-19).The SITR mathema...In this work,the exponential approximation is used for the numerical simulation of a nonlinear SITR model as a system of differential equations that shows the dynamics of the new coronavirus(COVID-19).The SITR mathematical model is divided into four classes using fractal parameters for COVID-19 dynamics,namely,susceptible(S),infected(I),treatment(T),and recovered(R).The main idea of the presented method is based on the matrix representations of the exponential functions and their derivatives using collocation points.To indicate the usefulness of this method,we employ it in some cases.For error analysis of the method,the residual of the solutions is reviewed.The reported examples show that the method is reasonably efficient and accurate.展开更多
The paper considers the adaptive regulation for the Hammerstein and Wiener systems with event-triggered observations.The authors adopt a direct approach,i.e.,without identifying the unknown parameters and functions wi...The paper considers the adaptive regulation for the Hammerstein and Wiener systems with event-triggered observations.The authors adopt a direct approach,i.e.,without identifying the unknown parameters and functions within the systems,adaptive regulators are directly designed based on the event-triggered observations on the regulation errors.The adaptive regulators belong to the stochastic approximation algorithms and under moderate assumptions,the authors prove that the adaptive regulators are optimal for both the Hammerstein and Wiener systems in the sense that the squared regulation errors are asymptotically minimized.The authors also testify the theoretical results through simulation studies.展开更多
基金the foundation under the program of"One Hundred Outstanding Young Chinese Scientists"of the Chinese Academy of Sciencesthe Graduate Innovation Foundation of the Chinese Academy of Sciences
文摘This paper deals with realizable adaptive algorithms of the nonlinear approximation with finite terms based on wavelets. We present a concrete algorithm by which we may find the required index set Am for the greedy algorithm Gm^P（., Ψ）. This makes the greedy algorithm realize the near best approximation in practice. Moreover, we study the efficiency of the finite-term approximation of another Mgorithm introduced by Birge and Massart.
基金Project supported by the Climbing Programme-National Key Project for Fundamental Research in China, Grant NSC 92092 and NSF 19371022
文摘In this paper, the capability of neural networks and some approximation problens in system identification with neural networks are investigated. Some results are given: (i) For any function g ∈Llocp (R1) ∩S’ (R1) to be an Lp-Tauber-Wiener function, it is necessary and sufficient that g is not apolynomial; (ii) If g∈(Lp TW), then the set of is dense in Lp(K)’ (iii) It is proved that bycompositions of some functions of one variable, one can approximate continuous functional defined on compact Lp(K) and continuous operators from compact Lp1(K1) to LP2(K2). These results confirm the capability of neural networks in identifying dynamic systems.
基金This work was supported by the National Natural Science Foundation of China by the Ministry of Science and Technology of China.
文摘This paper proposes an iterative learning control (ILC) algorithm with the purpose of controling the output of a linear stochastic system presented in state space form to track a desired realizable trajectory. It is proved that the algorithm converges to the optimal one a.s. under the condition that the product input-output coupling matrices are full-column rank in addition to some assumptions on noises. No other knowledge about system matrices and covariance matrices is required.
文摘In this paper,the problem of identifying autoregressive-moving-average systems under random threshold binary-valued output measurements is considered.With the help of stochastic approximation algorithms with expanding truncations,the authors give the recursive estimates for the parameters of both the linear system and the binary sensor.Under reasonable conditions,all constructed estimates are proved to be convergent to the true values with probability one,and the convergence rates are also established.A simulation example is provided to justify the theoretical results.
文摘In this work,the exponential approximation is used for the numerical simulation of a nonlinear SITR model as a system of differential equations that shows the dynamics of the new coronavirus(COVID-19).The SITR mathematical model is divided into four classes using fractal parameters for COVID-19 dynamics,namely,susceptible(S),infected(I),treatment(T),and recovered(R).The main idea of the presented method is based on the matrix representations of the exponential functions and their derivatives using collocation points.To indicate the usefulness of this method,we employ it in some cases.For error analysis of the method,the residual of the solutions is reviewed.The reported examples show that the method is reasonably efficient and accurate.
基金supported by the National Key Research and Development Program of China under Grant No.2018YFA0703800the Chinese Academy of Sciences(CAS)Project for Young Scientists in Basic Research under Grant No.YSBR-008the Strategic Priority Research Program of CAS under Grant No.XDA27000000。
文摘The paper considers the adaptive regulation for the Hammerstein and Wiener systems with event-triggered observations.The authors adopt a direct approach,i.e.,without identifying the unknown parameters and functions within the systems,adaptive regulators are directly designed based on the event-triggered observations on the regulation errors.The adaptive regulators belong to the stochastic approximation algorithms and under moderate assumptions,the authors prove that the adaptive regulators are optimal for both the Hammerstein and Wiener systems in the sense that the squared regulation errors are asymptotically minimized.The authors also testify the theoretical results through simulation studies.
