Based on adaptive dynamic programming(ADP),the fixed-point tracking control problem is solved by a value iteration(VI) algorithm. First, a class of discrete-time(DT)nonlinear system with disturbance is considered. Sec...Based on adaptive dynamic programming(ADP),the fixed-point tracking control problem is solved by a value iteration(VI) algorithm. First, a class of discrete-time(DT)nonlinear system with disturbance is considered. Second, the convergence of a VI algorithm is given. It is proven that the iterative cost function precisely converges to the optimal value,and the control input and disturbance input also converges to the optimal values. Third, a novel analysis pertaining to the range of the discount factor is presented, where the cost function serves as a Lyapunov function. Finally, neural networks(NNs) are employed to approximate the cost function, the control law, and the disturbance law. Simulation examples are given to illustrate the effective performance of the proposed method.展开更多
Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f（p∑i=1xi＋q∑j=1yj＋2d∑k=1zk/2）=p∑i=1f（xi）＋q∑j=1f（yj）＋2d∑k=1f（zk...Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f（p∑i=1xi＋q∑j=1yj＋2d∑k=1zk/2）=p∑i=1f（xi）＋q∑j=1f（yj）＋2d∑k=1f（zk）,where p, q, d are integers greater than 1, in non-Archimedean normed spaces.展开更多
In this work, we investigate the following fourth-order delay differential equation of boundary value problem with p-Laplacian(Φp(u))(t) + a(t)f(t, u(t- τ), u(t)) = 0, 0 < t < 1;u(0) = u(0) = 0, u(1) = αu(η)...In this work, we investigate the following fourth-order delay differential equation of boundary value problem with p-Laplacian(Φp(u))(t) + a(t)f(t, u(t- τ), u(t)) = 0, 0 < t < 1;u(0) = u(0) = 0, u(1) = αu(η);u(t) = 0,- τ≤ t ≤ 0.By using Schauder fixed-point theorem, some sufficient conditions are obtained which guarantee the fourth-order delay differential equation of boundary value problem with p-Laplacian has at least one positive solution. Some corresponding examples are presented to illustrate the application of our main results.展开更多
基金supported in part by the National Natural Science Foundation of China(61873300,61722312)in part by the Fundamental Research Funds for the Central Universities(FRF-GF-17-B45)
文摘Based on adaptive dynamic programming(ADP),the fixed-point tracking control problem is solved by a value iteration(VI) algorithm. First, a class of discrete-time(DT)nonlinear system with disturbance is considered. Second, the convergence of a VI algorithm is given. It is proven that the iterative cost function precisely converges to the optimal value,and the control input and disturbance input also converges to the optimal values. Third, a novel analysis pertaining to the range of the discount factor is presented, where the cost function serves as a Lyapunov function. Finally, neural networks(NNs) are employed to approximate the cost function, the control law, and the disturbance law. Simulation examples are given to illustrate the effective performance of the proposed method.
文摘Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation 2f（p∑i=1xi＋q∑j=1yj＋2d∑k=1zk/2）=p∑i=1f（xi）＋q∑j=1f（yj）＋2d∑k=1f（zk）,where p, q, d are integers greater than 1, in non-Archimedean normed spaces.
基金Foundation item： Supported by the National Natural Science Foundation of China（10801001） Supported by the Natural Science Foundation of Anhui Province（1208085MA13, KJ2009A005Z）
文摘In this work, we investigate the following fourth-order delay differential equation of boundary value problem with p-Laplacian(Φp(u))(t) + a(t)f(t, u(t- τ), u(t)) = 0, 0 < t < 1;u(0) = u(0) = 0, u(1) = αu(η);u(t) = 0,- τ≤ t ≤ 0.By using Schauder fixed-point theorem, some sufficient conditions are obtained which guarantee the fourth-order delay differential equation of boundary value problem with p-Laplacian has at least one positive solution. Some corresponding examples are presented to illustrate the application of our main results.
