On the Integrated Learning of English and Law

This paper centers on the integrated learning of English and law in China.Firstly,it outlines the importance of English in the solution of the ever increasing legal disputes between China and the outside world,which inevitably involves an integrated learning of English and law.Secondly,it points out that the content of legal English reflects a combination of legal knowledge and English skills.Thirdly,it expounds on the difficulties that Chinese English majors are facing in the process of learning English and law simultaneously and furnishes some practical suggestions.

Learning the continuous-time optimal decision law from discrete-time rewards

The concept of reward is fundamental in reinforcement learning with a wide range of applications in natural and social sciences.Seeking an interpretable reward for decision-making that largely shapes the system's behavior has always been a challenge in reinforcement learning.In this work,we explore a discrete-time reward for reinforcement learning in continuous time and action spaces that represent many phenomena captured by applying physical laws.We find that the discrete-time reward leads to the extraction of the unique continuous-time decision law and improved computational efficiency by dropping the integrator operator that appears in classical results with integral rewards.We apply this finding to solve output-feedback design problems in power systems.The results reveal that our approach removes an intermediate stage of identifying dynamical models.Our work suggests that the discrete-time reward is efficient in search of the desired decision law,which provides a computational tool to understand and modify the behavior of large-scale engineering systems using the optimal learned decision.

An Exploration on Adaptive Iterative Learning Control for a Class of Commensurate High-order Uncertain Nonlinear Fractional Order Systems

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.

Exponential Continuous Non-Parametric Neural Identifier With Predefined Convergence Velocity

This paper addresses the design of an exponential function-based learning law for artificial neural networks(ANNs)with continuous dynamics.The ANN structure is used to obtain a non-parametric model of systems with uncertainties,which are described by a set of nonlinear ordinary differential equations.Two novel adaptive algorithms with predefined exponential convergence rate adjust the weights of the ANN.The first algorithm includes an adaptive gain depending on the identification error which accelerated the convergence of the weights and promotes a faster convergence between the states of the uncertain system and the trajectories of the neural identifier.The second approach uses a time-dependent sigmoidal gain that forces the convergence of the identification error to an invariant set characterized by an ellipsoid.The generalized volume of this ellipsoid depends on the upper bounds of uncertainties,perturbations and modeling errors.The application of the invariant ellipsoid method yields to obtain an algorithm to reduce the volume of the convergence region for the identification error.Both adaptive algorithms are derived from the application of a non-standard exponential dependent function and an associated controlled Lyapunov function.Numerical examples demonstrate the improvements enforced by the algorithms introduced in this study by comparing the convergence settings concerning classical schemes with non-exponential continuous learning methods.The proposed identifiers overcome the results of the classical identifier achieving a faster convergence to an invariant set of smaller dimensions.

L_2-L_∞ learning of dynamic neural networks

This paper proposes an y2-y∞ learning law as a new learning method for dynamic neural networks with external disturbance. Based on linear matrix inequality （LMI） formulation, the y2-y∞ learning law is presented to not only guarantee asymptotical stability of dynamic neural networks but also reduce the effect of external disturbance to an y2-y∞ induced norm constraint. It is shown that the design of the y2-y∞ learning law for such neural networks can be achieved by solving LMIs, which can be easily facilitated by using some standard numerical packages. A numerical example is presented to demonstrate the validity of the proposed learning law.

ON THE DESIGN OF A NEURO-FUZZY CONTROLLER–APPLICATION TO THE CONTROL OF A BIOREACTOR

This paper presents a new methodological approach for the synthesis ofa neuro-fuzzy controller, using an on-line learning procedure. A simple algebraic formulation of a Sugeno fuzzy inference system that ensures a coherent universe of discourse, making easy its interpretation by a human being, is proposed and implemented in the case of the control of a bioreactor, which is considered as a complex non linear process.

A novel D-type iterative learning control design for antilinear systems

In this paper,a novel D-type iterative learning control(ILC)law is proposed for discrete-time antilinear systems.This D-type control law is different from the previous linear(nonlinear)D-type ILC law.The main feature is that we take the conjugate of the(t+1)-th error to construct the proposed controller.The convergence proofs are given for their corresponding ILC schemes.