A robust controller for bank to turn(BTT) missiles with aerodynamic fins and reaction jet control system(RCS) is developed based on nonlinear control dynamic models comprising couplings and aerodynamic uncertainties. ...A robust controller for bank to turn(BTT) missiles with aerodynamic fins and reaction jet control system(RCS) is developed based on nonlinear control dynamic models comprising couplings and aerodynamic uncertainties. The fixed time convergence theory is incorporated with the sliding mode control technique to ensure that the system tracks the desired command within uniform bounded time under different initial conditions. Unlike previous terminal sliding mode approaches, the bound of settling time is independent of the initial state, which means performance metrics like convergence rate can be predicted beforehand. To reduce the burden of control design in terms of robustness, extended state observer(ESO) is introduced for uncertainty estimation with the output substituted into the controller as feedforward compensation. Cascade control structure is employed with the proposed control law and therein the compound control signal is obtained.Afterwards, control inputs for two kinds of actuators are allocated on the basis of their inherent characteristics. Finally, a number of simulations are carried out and demonstrate the effectiveness of the designed controller.展开更多
Branched continued fractions are one of the multidimensional generalization of the continued fractions. Branched continued fractions with not equivalent variables are an analog of the regular C-fractions for multiple ...Branched continued fractions are one of the multidimensional generalization of the continued fractions. Branched continued fractions with not equivalent variables are an analog of the regular C-fractions for multiple power series. We consider 1-periodic branched continued fraction of the special form which is an analog fraction with not equivalent variables if the values of that variables are fixed. We establish an analog of the parabola theorem for that fraction and estimate truncation error bounds for that fractions at some restrictions. We also propose to use weight coefficients for obtaining different parabolic regions for the same fraction without any additional restriction for first element.展开更多
Support vector machines （SVMs） have been extensively studied and have shown remarkable success in many applications. A new family of twice continuously differentiable piecewise smooth functions are used to smooth th...Support vector machines （SVMs） have been extensively studied and have shown remarkable success in many applications. A new family of twice continuously differentiable piecewise smooth functions are used to smooth the objective function of uncon- strained SVMs. The three-order piecewise smooth support vector machine （TPWSSVMd） is proposed. The piecewise functions can get higher and higher approximation accuracy as required with the increase of parameter d. The global convergence proof of TPWSSVMd is given with the rough set theory. TPWSSVMd can efficiently handle large scale and high dimensional problems. Nu- merical results demonstrate TPWSSVMa has better classification performance and learning efficiency than other competitive base- lines.展开更多
In this paper,a bandwidth-adjustable extended state observer(ABESO)is proposed for the systems with measurement noise.It is known that increasing the bandwidth of the observer improves the tracking speed but tolerates...In this paper,a bandwidth-adjustable extended state observer(ABESO)is proposed for the systems with measurement noise.It is known that increasing the bandwidth of the observer improves the tracking speed but tolerates noise,which conflicts with observation accuracy.Therefore,we introduce a bandwidth scaling factor such that ABESO is formulated to a 2-degree-of-freedom system.The observer gain is determined and the bandwidth scaling factor adjusts the bandwidth according to the tracking error.When the tracking error decreases,the bandwidth decreases to suppress the noise,otherwise the bandwidth does not change.It is proven that the error dynamics are bounded and converge in finite time.The relationship between the upper bound of the estimation error and the scaling factor is given.When the scaling factor is less than 1,the ABESO has higher estimation accuracy than the linear extended state observer(LESO).Simulations of an uncertain nonlinear system with compound disturbances show that the proposed ABESO can successfully estimate the total disturbance in noisy environments.The mean error of total disturbance of ABESO is 15.28% lower than that of LESO.展开更多
In this research article,we interrogate two new modifications in inverse Weierstrass iterative method for estimating all roots of non-linear equation simultaneously.These modifications enables us to accelerate the con...In this research article,we interrogate two new modifications in inverse Weierstrass iterative method for estimating all roots of non-linear equation simultaneously.These modifications enables us to accelerate the convergence order of inverse Weierstrass method from 2 to 3.Convergence analysis proves that the orders of convergence of the two newly constructed inverse methods are 3.Using computer algebra system Mathematica,we find the lower bound of the convergence order and verify it theoretically.Dynamical planes of the inverse simultaneous methods and classical iterative methods are generated using MATLAB(R2011b),to present the global convergence properties of inverse simultaneous iterative methods as compared to classical methods.Some non-linear models are taken from Physics,Chemistry and engineering to demonstrate the performance and efficiency of the newly constructed methods.Computational CPU time,and residual graphs of the methods are provided to present the dominance behavior of our newly constructed methods as compared to existing inverse and classical simultaneous iterative methods in the literature.展开更多
Some properties of Sugeno measure are further discussed, which is a kind of typical nonadditive measure. The definitions and properties of gλ random variable and its distribution function, expected value, and varianc...Some properties of Sugeno measure are further discussed, which is a kind of typical nonadditive measure. The definitions and properties of gλ random variable and its distribution function, expected value, and variance are then presented. Markov inequality, Chebyshev＇s inequality and the Khinchine＇s Law of Large Numbers on Sugeno measure space are also proven. Furthermore, the concepts of empirical risk functional, expected risk functional and the strict consistency of ERM principle on Sugeno measure space are proposed. According to these properties and concepts, the key theorem of learning theory, the bounds on the rate of convergence of learning process and the relations between these bounds and capacity of the set of functions on Sugeno measure space are given.展开更多
Support vector machines （SVMs） have shown remarkable success in many applications. However, the non-smooth feature of objective function is a limitation in practical application of SVMs. To overcome this disadvantag...Support vector machines （SVMs） have shown remarkable success in many applications. However, the non-smooth feature of objective function is a limitation in practical application of SVMs. To overcome this disadvantage, a twice continuously differentiable piecewise-smooth function is constructed to smooth the objective function of unconstrained support vector machine （SVM）, and it issues a piecewise-smooth support vector machine （PWESSVM）. Comparing to the other smooth approximation functions, the smooth precision has an obvious improvement. The theoretical analysis shows PWESSVM is globally convergent. Numerical results and comparisons demonstrate the classification performance of our algorithm is better than other competitive baselines.展开更多
Alternating direction method of multipliers(ADMM)receives much attention in the recent years due to various demands from machine learning and big data related optimization.In 2013,Ouyang et al.extend the ADMM to the s...Alternating direction method of multipliers(ADMM)receives much attention in the recent years due to various demands from machine learning and big data related optimization.In 2013,Ouyang et al.extend the ADMM to the stochastic setting for solving some stochastic optimization problems,inspired by the structural risk minimization principle.In this paper,we consider a stochastic variant of symmetric ADMM,named symmetric stochastic linearized ADMM(SSL-ADMM).In particular,using the framework of variational inequality,we analyze the convergence properties of SSL-ADMM.Moreover,we show that,with high probability,SSL-ADMM has O((ln N)·N^(-1/2))constraint violation bound and objective error bound for convex problems,and has O((ln N)^(2)·N^(-1))constraint violation bound and objective error bound for strongly convex problems,where N is the iteration number.Symmetric ADMM can improve the algorithmic performance compared to classical ADMM,numerical experiments for statistical machine learning show that such an improvement is also present in the stochastic setting.展开更多
基金supported by the National Natural Science Foundation of China(11572036)
文摘A robust controller for bank to turn(BTT) missiles with aerodynamic fins and reaction jet control system(RCS) is developed based on nonlinear control dynamic models comprising couplings and aerodynamic uncertainties. The fixed time convergence theory is incorporated with the sliding mode control technique to ensure that the system tracks the desired command within uniform bounded time under different initial conditions. Unlike previous terminal sliding mode approaches, the bound of settling time is independent of the initial state, which means performance metrics like convergence rate can be predicted beforehand. To reduce the burden of control design in terms of robustness, extended state observer(ESO) is introduced for uncertainty estimation with the output substituted into the controller as feedforward compensation. Cascade control structure is employed with the proposed control law and therein the compound control signal is obtained.Afterwards, control inputs for two kinds of actuators are allocated on the basis of their inherent characteristics. Finally, a number of simulations are carried out and demonstrate the effectiveness of the designed controller.
文摘Branched continued fractions are one of the multidimensional generalization of the continued fractions. Branched continued fractions with not equivalent variables are an analog of the regular C-fractions for multiple power series. We consider 1-periodic branched continued fraction of the special form which is an analog fraction with not equivalent variables if the values of that variables are fixed. We establish an analog of the parabola theorem for that fraction and estimate truncation error bounds for that fractions at some restrictions. We also propose to use weight coefficients for obtaining different parabolic regions for the same fraction without any additional restriction for first element.
基金supported by the National Natural Science Foundation of China(6110016561100231+6 种基金5120530961472307)the Natural Science Foundation of Shaanxi Province(2012JQ80442014JM83132010JQ8004)the Foundation of Education Department of Shaanxi Province(2013JK1096)the New Star Team of Xi’an University of Posts and Telecommunications
文摘Support vector machines （SVMs） have been extensively studied and have shown remarkable success in many applications. A new family of twice continuously differentiable piecewise smooth functions are used to smooth the objective function of uncon- strained SVMs. The three-order piecewise smooth support vector machine （TPWSSVMd） is proposed. The piecewise functions can get higher and higher approximation accuracy as required with the increase of parameter d. The global convergence proof of TPWSSVMd is given with the rough set theory. TPWSSVMd can efficiently handle large scale and high dimensional problems. Nu- merical results demonstrate TPWSSVMa has better classification performance and learning efficiency than other competitive base- lines.
基金supported by the National Natural Science Foundation of China(61873126)。
文摘In this paper,a bandwidth-adjustable extended state observer(ABESO)is proposed for the systems with measurement noise.It is known that increasing the bandwidth of the observer improves the tracking speed but tolerates noise,which conflicts with observation accuracy.Therefore,we introduce a bandwidth scaling factor such that ABESO is formulated to a 2-degree-of-freedom system.The observer gain is determined and the bandwidth scaling factor adjusts the bandwidth according to the tracking error.When the tracking error decreases,the bandwidth decreases to suppress the noise,otherwise the bandwidth does not change.It is proven that the error dynamics are bounded and converge in finite time.The relationship between the upper bound of the estimation error and the scaling factor is given.When the scaling factor is less than 1,the ABESO has higher estimation accuracy than the linear extended state observer(LESO).Simulations of an uncertain nonlinear system with compound disturbances show that the proposed ABESO can successfully estimate the total disturbance in noisy environments.The mean error of total disturbance of ABESO is 15.28% lower than that of LESO.
文摘In this research article,we interrogate two new modifications in inverse Weierstrass iterative method for estimating all roots of non-linear equation simultaneously.These modifications enables us to accelerate the convergence order of inverse Weierstrass method from 2 to 3.Convergence analysis proves that the orders of convergence of the two newly constructed inverse methods are 3.Using computer algebra system Mathematica,we find the lower bound of the convergence order and verify it theoretically.Dynamical planes of the inverse simultaneous methods and classical iterative methods are generated using MATLAB(R2011b),to present the global convergence properties of inverse simultaneous iterative methods as compared to classical methods.Some non-linear models are taken from Physics,Chemistry and engineering to demonstrate the performance and efficiency of the newly constructed methods.Computational CPU time,and residual graphs of the methods are provided to present the dominance behavior of our newly constructed methods as compared to existing inverse and classical simultaneous iterative methods in the literature.
基金supported by the National Natural Science Foundation of China(Grant No.60573069)the Natural Science Foundation of Hebei Province(Grant No.F2004000129)+1 种基金the Key Scientific Research Project of Hebei Education Department(Grant No.2005001D)the Key Scientific and Technical Research Project of the Ministry of Education of China(Grant No.20602).
文摘Some properties of Sugeno measure are further discussed, which is a kind of typical nonadditive measure. The definitions and properties of gλ random variable and its distribution function, expected value, and variance are then presented. Markov inequality, Chebyshev＇s inequality and the Khinchine＇s Law of Large Numbers on Sugeno measure space are also proven. Furthermore, the concepts of empirical risk functional, expected risk functional and the strict consistency of ERM principle on Sugeno measure space are proposed. According to these properties and concepts, the key theorem of learning theory, the bounds on the rate of convergence of learning process and the relations between these bounds and capacity of the set of functions on Sugeno measure space are given.
基金supported by the National Natural Science Foundation of China (61100165, 61100231, 61105064, 51205309)the Natural Science Foundation of Shaanxi Province (2012JQ8044, 2011JM8003, 2010JQ8004)the Foundation of Education Department of Shanxi Province (2013JK1096)
文摘Support vector machines （SVMs） have shown remarkable success in many applications. However, the non-smooth feature of objective function is a limitation in practical application of SVMs. To overcome this disadvantage, a twice continuously differentiable piecewise-smooth function is constructed to smooth the objective function of unconstrained support vector machine （SVM）, and it issues a piecewise-smooth support vector machine （PWESSVM）. Comparing to the other smooth approximation functions, the smooth precision has an obvious improvement. The theoretical analysis shows PWESSVM is globally convergent. Numerical results and comparisons demonstrate the classification performance of our algorithm is better than other competitive baselines.
基金Supported by National Natural Science Foundation of China (61662036)。
文摘Alternating direction method of multipliers(ADMM)receives much attention in the recent years due to various demands from machine learning and big data related optimization.In 2013,Ouyang et al.extend the ADMM to the stochastic setting for solving some stochastic optimization problems,inspired by the structural risk minimization principle.In this paper,we consider a stochastic variant of symmetric ADMM,named symmetric stochastic linearized ADMM(SSL-ADMM).In particular,using the framework of variational inequality,we analyze the convergence properties of SSL-ADMM.Moreover,we show that,with high probability,SSL-ADMM has O((ln N)·N^(-1/2))constraint violation bound and objective error bound for convex problems,and has O((ln N)^(2)·N^(-1))constraint violation bound and objective error bound for strongly convex problems,where N is the iteration number.Symmetric ADMM can improve the algorithmic performance compared to classical ADMM,numerical experiments for statistical machine learning show that such an improvement is also present in the stochastic setting.
