This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commens...This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance.To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control(ILC), a new boundary layer function is proposed by employing MittagLeffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function(CEF)containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.展开更多
Node order is one of the most important factors in learning the structure of a Bayesian network(BN)for probabilistic reasoning.To improve the BN structure learning,we propose a node order learning algorithmbased on th...Node order is one of the most important factors in learning the structure of a Bayesian network(BN)for probabilistic reasoning.To improve the BN structure learning,we propose a node order learning algorithmbased on the frequently used Bayesian information criterion(BIC)score function.The algorithm dramatically reduces the space of node order and makes the results of BN learning more stable and effective.Specifically,we first find the most dependent node for each individual node,prove analytically that the dependencies are undirected,and then construct undirected subgraphs UG.Secondly,the UG-is examined and connected into a single undirected graph UGC.The relation between the subgraph number and the node number is analyzed.Thirdly,we provide the rules of orienting directions for all edges in UGC,which converts it into a directed acyclic graph(DAG).Further,we rank the DAG’s topology order and describe the BIC-based node order learning algorithm.Its complexity analysis shows that the algorithm can be conducted in linear time with respect to the number of samples,and in polynomial time with respect to the number of variables.Finally,experimental results demonstrate significant performance improvement by comparing with other methods.展开更多
基金supported by the National Natural Science Foundation of China(60674090)Shandong Natural Science Foundation(ZR2017QF016)
文摘This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance.To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control(ILC), a new boundary layer function is proposed by employing MittagLeffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function(CEF)containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.
基金The work partially supported by the National Natural Science Foundation of China(Grant Nos.61432011,U1435212,61322211 and 61672332)the Postdoctoral Science Foundation of China(2016M591409)+1 种基金the Natural Science Foundation of Shanxi Province,China(201801D121115 and 2013011016-4)Research Project Supported by Shanxi Scholarship Council of China(2020-095).
文摘Node order is one of the most important factors in learning the structure of a Bayesian network(BN)for probabilistic reasoning.To improve the BN structure learning,we propose a node order learning algorithmbased on the frequently used Bayesian information criterion(BIC)score function.The algorithm dramatically reduces the space of node order and makes the results of BN learning more stable and effective.Specifically,we first find the most dependent node for each individual node,prove analytically that the dependencies are undirected,and then construct undirected subgraphs UG.Secondly,the UG-is examined and connected into a single undirected graph UGC.The relation between the subgraph number and the node number is analyzed.Thirdly,we provide the rules of orienting directions for all edges in UGC,which converts it into a directed acyclic graph(DAG).Further,we rank the DAG’s topology order and describe the BIC-based node order learning algorithm.Its complexity analysis shows that the algorithm can be conducted in linear time with respect to the number of samples,and in polynomial time with respect to the number of variables.Finally,experimental results demonstrate significant performance improvement by comparing with other methods.
