Recursive functions of context free languages (Ⅱ)——Validity of CFPRF and CFRF definitions

In this paper we proved that the function class CFRF and its proper subclass CFPRF are respectively the partial recursive functions and primitive recursive functions of context free languages (CFLs). Also we discussed the relation between them and recursive functions defined on other domains . It is indicated that the functions of natural numbers and/or symbol strings (words) are functions of CFLs. Several frequently used primitive recursive functions on words were given, including logical connectives, conditional expressions. Also the powerful operators (bounded maximization and minimization operators) for constructing primitive recursive functions were defined. Two important nontrivial algorithms, the characteristic function of arbitrary CFL and the parse function of CFL sentences were constructed. Based on them, the method for extending or restricting function domain was described.     

Pattern Matching Compilation of Functions Defined in Context—Free Languages

LFC is a functional language based on recursive functions defined in context-free languages.In this paper,a new pattern matching algorithm for LFC is presented,which can represent a sequence of patterns as an integer by an encoding method.It is a rather simple method and produces efficient case-expressions for pattern matching definitions of LFC.The algorithm can also be used for other functional languages,but for nested patterns it may become complicated and further studies are needed.     

A Type of Triangular Ball Surface and its Properties

A new type of bivariate generalized Ball basis function on a triangle is presented for free-form surface design.Some properties of the basis function are given,then degree elevation,recursive evaluation and some other properties of the generalized Ball surfaces are also derived.It is shown that the proposed recursive evaluation algorithm is more efficient than those of the old surfaces.     

A new self-learning optimal control laws for a class of discrete-time nonlinear systems based on ESN architecture

A novel self-learning optimal control method for a class of discrete-time nonlinear systems is proposed based on iteration adaptive dynamic programming(ADP)algorithm.It is proven that the iteration costate functions converge to the optimal one,and a detailed convergence analysis of the iteration ADP algorithm is given.Furthermore,echo state network(ESN)architecture is used as the approximator of the costate function for each iteration.To ensure the reliability of the ESN approximator,the ESN mean square training error is constrained in the satisfactory range.Two simulation examples are given to demonstrate that the proposed control method has a fast response speed due to the special structure and the fast training process.     

H_∞ controller synthesis of piecewise discrete time linear systems

This paper presents an H∞ controller design method for pieccwise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ perfomiance and the controller can be obtained by solving a set of bilinear lnatrLx inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global qnadnmc Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.     

Convergence analysis of an incremental approach to online inverse reinforcement learning

Interest in inverse reinforcement learning (IRL) has recently increased,that is,interest in the problem of recovering the reward function underlying a Markov decision process (MDP) given the dynamics of the system and the behavior of an expert.This paper deals with an incremental approach to online IRL.First,the convergence property of the incremental method for the IRL problem was investigated,and the bounds of both the mistake number during the learning process and regret were provided by using a detailed proof.Then an online algorithm based on incremental error correcting was derived to deal with the IRL problem.The key idea is to add an increment to the current reward estimate each time an action mismatch occurs.This leads to an estimate that approaches a target optimal value.The proposed method was tested in a driving simulation experiment and found to be able to efficiently recover an adequate reward function.     

Control synthesis for a class of nonlinear systems based on partition of unity

A partition-of-unity-based approach is proposed to derive an approximate model for a class of nonlinear systems. The precision of the approximate model is analyzed by using the modulus of continuity of continuous functions. The system stability of the approximate model is analyzed by using Lyapunov stability theory. A design algorithm for constructing tracking controllers with tracking performance related to tracking error is given based on the approximate model and the partition of unity method.     

An approach for ergonomic design of mouse wheel

A new method for ergonomic design of a computer mouse is proposed in this paper.In the method,the movements of joints and tip of the forefinger during operating a mouse was captured by a high-speed video camera.The captured videos were analyzed and an algorithm was developed to decide the size and location of the mouse wheel according to ergonomic principles.The algorithm was then coded in a software package with Visual C++ and OpenGL languages.Results of the calculation and simulation agreed well with those of the experiments.The software can also be used for shape design of mouse body,buttons and their layouts.     

Efficient approach and application of the Green’s functions in spatial domain in multilayered media

Based on the dipole source method, all components of the Green＇s functions in spectral domain are restructured concisely by four basis functions, and in terms of the two-level discrete complex image method （DCIM） with the high order Sommerfeld identities, an efficient algorithm for closed-form Green＇s functions in spatial domain in multilayered media is presented. This new work enjoys the advantages of the surface wave pole extraction directly carried out by the generalized integral path without troubles of that all components of Green＇s function in spectral domain should be reformed respectively in transmission line network analogy, and then the Green＇s functions for mixed-potential integral equation （MPIE） analysis in both near-field and far-field in multilayered media are obtained. In addition, the curl operator for coupled field in MPIE is avoided conveniently. It is especially applicable and useful to characterize the electromagnetic scattering by, and radiation in the presence of, the electrically large 3-D objects in multilayered media. The numerical results of the S-parameters of a microstrip periodic bandgap （PBG） filter, the radar cross section （RCS） of a large microstrip antenna array, the characteristics of scattering, and radiation from the three-dimensional （3-D） targets in multilayered media are obtained, to demonstrate better effectiveness and accuracy of this technique.     

Counting and Topological Order

The counting method is a simple and efficient method for processing linear recursive datalog queries.Its time complexity is bounded by O(n,e)where n and e denote the numbers the numbers of nodes and edges,respectively,in the graph representing the input.relations.In this paper,the concepts of heritage appearance function and heritage selection function are introduced,and an evaluation algorithm based on the computation of such functions in topological order is developed .This new algorithm requires only linear time in the case of non-cyclic data.     

Stabilization of a class of discrete-time switched systems via observer-based output feedback

In this paper, observer-based static output feedback control problem for discrete-time uncertain switched systems is investigated under an arbitrary switching rule. The main method used in this note is combining switched Lyapunov function (SLF) method with Finsler’s Lemma. Based on linear matrix inequality (LMI) a less conservative stability condition is established and this condition allows extra degree of freedom for stability analysis. Finally, a simulation example is given to illustrate the efficiency of the result.     

基于神经网络的预测模型中输入变量的选择

It is important to select input variables when the neural network forecasting model is proposed. In this pa-per, by using the autocorrelation function on input variables sets selection for neural network forecasting model, a systemic and scienti[ic method for input variables sets selection is put forward. FFT is adopted to accomplish the speediness calculation, which enhances the maneuverability of this approach. A forecasting example is given, whos eresult indicates that the method is effective.     

Moving least-squares approximations for linearly-solvable stochastic optimal control problems

Nonlinear stochastic optimal control problems are fundamental in control theory.A general class of such problems can be reduced to computing the principal eigenfunction of a linear operator.Here,we describe a new method for finding this eigenfunction using a moving least-squares function approximation.We use efficient iterative solvers that do not require matrix factorization,thereby allowing us to handle large numbers of basis functions.The bases are evaluated at collocation states that change over iterations of the algorithm,so as to provide higher resolution at the regions of state space that are visited more often.The shape of the bases is automatically defined given the collocation states,in a way that avoids gaps in the coverage.Numerical results on test problems are provided.     

Attribute reduction theory of concept lattice based on decision formal contexts

The theory of concept lattices is an efficient tool for knowledge representation and knowledge discovery, and is applied to many fields successfully. One focus of knowledge discovery is knowledge reduction. Based on the reduction theory of classical formal context, this paper proposes the definition of decision formal context and its reduction theory, which extends the reduction theory of concept lattices. In this paper, strong consistence and weak consistence of decision formal context are defined respectively. For strongly consistent decision formal context, the judgment theorems of consistent sets are examined, and approaches to reduction are given. For weakly consistent decision formal context, implication mapping is defined, and its reduction is studied. Finally, the relation between reducts of weakly consistent decision formal context and reducts of implication mapping is discussed.     

An equivalent linearization method for nonlinear Van der Pol oscillator subjected to random vibration using orthogonal functions

This paper deals with the idea of the orthogonal functions in the equivalent linearization of the nonlinear systems. Block Pulse (BP) function gives effective tools to approximate complex problems. The aim of this work is on using properties of the BP function as an orthogonal function in process of linearization. The BP functions have been used to propose an equivalent linearization method in the time domain to determine the unknown linearization coefficients. The accuracy of the proposed method compared with the other equivalent linearization approaches, including the regulation linearization and the dual criterion linearization methods. This study exploited the nonlinear Van der Pol oscillator system under stationary random excitation to demonstrate the feasibility of the proposed method. The validity of the analytical method is verified by applying different values of nonlinearity and intensity of excitation. Besides, by comparing the mean square responses and frequency response functions of the linearized systems for a wide range of nonlinearity depicted the present method is in agreement with other methods.     

New Results on Global Synchronization of Chua's Circuit

Some new results on global exponential synchronization and global synchronization for Chua's circuit are derived by means of Lyapunov functions and some other mathematic methods, which improve the existing results in the literatures. A strict and complete proof of the result is also given as a complement to the relevant literature where the proof was incomplete. The paper offers some new approaches for studying chaos synchronization for Chua's circuit.     

Proving total correctness and generating preconditions for loop programs via symbolic-numeric computation methods

We present a symbolic-numeric hybrid method, based on sum-of-squares （SOS） relaxation and rational vec- tor recovery, to compute inequality invariants and ranking functions for proving total correctness and generating pre- conditions for programs. The SOS relaxation method is used to compute approximate invariants and approximate rank- ing functions with floating point coefficients. Then Gauss- Newton refinement and rational vector recovery are applied to approximate polynomials to obtain candidate polynomials with rational coefficients, which exactly satisfy the conditions of invariants and ranking functions. In the end, several exam- ples are given to show the effectiveness of our method.     

Gain-scheduled L-one control for linear parameter-varying systems with parameter-dependent delays

This paper deals with the problem of gain-scheduled L-one control for linear parameter-varying (LPV) systems with parameter-dependent delays. The attention is focused on the design of a gain-scheduled L-one controller that guarantees being an asymptotically stable closed-loop system and satisfying peak-to-peak performance constraints for LPV systems with respect to all amplitude-bounded input signals. In particular, concentrating on the delay-dependent case, we utilize parameter-dependent Lyapunov functions (PDLF) to establish peak-to-peak performance criteria for the first time where there exists a coupling between a Lyapunov function matrix and system matrices. By introducing a slack matrix, the decoupling for the parameter-dependent time-delay LPV system is realized. In this way, the sufficient conditions for the existence of a gain-scheduled L-one controller are proposed in terms of the Lyapunov stability theory and the linear matrix inequality (LMI) method. Based on approximate basis function and the gridding technique, the corresponding controller design is cast into a feasible solution problem of the finite parameter linear matrix inequalities. A numerical example is given to show the effectiveness of the proposed approach.     

H_∞ controller synthesis of piecewise discrete time linear systems

This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ performance and the controller can be obtained by solving a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.