Couple-stress Effects Near an Interior Hole of an Infinite Elastic Plane Subjected to a Concentrated Force

Couple-stress solutions are obtained near the hole boundary of an infinite elastic plane subjected to a radial concentrated force at x = b, y = 0,under the restriction of r/b<-0.2 and b/l?;-10. Here r and l are the distance from the center of the hole to the point of interest and a characteristic length (couple-stress constant). At r = a, θ = ±π2, the stress ratio of the couple-stress solution to the classical one for the current problem is slightly lower than one of the Mindlin problem (1) for some values of v, except for v = 0.5 where they are equal. The dimensionless stress σ&#x0302;_θθ is found along the hole boundary.     

Incentive feedback Stackelberg strategy for stochastic systems with state-dependent noise

This paper designs an incentive strategy for a class of stochastic Stackelberg games in finite horizon and infinite horizon, respectively. The obtained incentive Stackelberg strategy works well in the sense that the leader will get his desired solution in the end. Different from the existing works, the state-dependent noise is considered in the design of the incentive Stackelberg strategy. Moreover, the mean-square stabilization can be guaranteed by the follower. The algorithm procedure is put forward to obtain effectively the incentive feedback Stackelberg strategy in infinite horizon. Finally, two examples are given to shed light on the effectiveness of the proposed algorithm procedure.     

A novel design method for optimal IIR system identification using opposition based harmony search algorithm

In this paper a population based evolutionary optimization methodology called Opposition based Harmony Search Algorithm (OHS) is applied for the optimization of system coefficients of adaptive infinite impulse response (IIR) system identification problem. The original Harmony Search (HS) algorithm is chosen as the parent one and opposition based approach is applied to it with an intention to exhibit accelerated near global convergence profile. During the initialization, for choosing the randomly generated population/solution opposite solutions are also considered and the fitter one is selected as apriori guess for having faster convergence profile. Each solution in Harmony Memory (HM) is generated on the basis of memory consideration rule, a pitch adjustment rule and a re-initialization process which gives the optimum result corresponding to the least error fitness in multidimensional search space. Incorporation of different control parameters in basic HS algorithm results in balancing of exploration and exploitation of search space. The proposed OHS based system identification approach has alleviated from inherent drawbacks of premature convergence and stagnation, unlike Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Differential Evolution (DE). The simulation results obtained for some well known benchmark examples justify the efficacy of the proposed OHS based system identification approach over GA, PSO and DE in terms of convergence speed, identifying the system plant coefficients and mean square error (MSE) fitness values produced for both same order and reduced order models of adaptive IIR filters.     

Nonlinear H∞ feedback control with integrator for polynomial discrete-time systems

This paper investigates the problem of designing a nonlinear _H∞$H_{\infty }$ feedback controller for polynomial discrete-time systems with and without polytopic uncertainties. The objective is to design a controller such that the ratio between the energy of the regulated outputs and the energy of the exogenous disturbance/inputs is minimized or guaranteed to be less or equal to a prescribed value. It is well known that the state dependant or parameter dependant Lyapunov function is always chosen for synthesizing polynomial discrete-time systems. This leads the solution to be nonconvex because the Lyapunov function and the controller matrix are coupled and therefore cannot be solved by semidefinite programming (SDP). Hence, in this paper, an integrator is proposed to be incorporated into the controller structure. In doing so, the coupling of Lyapunov function and controller matrix can be eliminated effectively. This somehow simplifies the numerical solution of the problem. Then, by using SOS decomposition approach, sufficient conditions for the existence of the proposed controller are provided in terms of solvability of the state-dependent linear matrix inequalities (SDLMIs) which can be solved by SDP. A tunnel diode circuit is used to demonstrate the effectiveness of this integrator approach.     

Finite and infinite horizon indefinite linear quadratic optimal control for discrete-time singular Markov jump systems

This paper concerns the indefinite linear quadratic (LQ) optimal control problem for discrete-time singular Markov jump systems (MJSs) with finite and infinite horizon, where the weight matrices for state and control of cost function are all indefinite. Firstly, the indefinite LQ problem for singular MJSs is equivalently transformed into indefinite LQ problem for MJSs under a series of equivalent transformations. Then, the sufficient and necessary condition is proposed for the solvability of finite horizon case, the optimal control and optimal cost value are given, and the resulting optimal closed-loop system is regular, casual. Next, some sufficient and necessary conditions are obtained to ensure the transformed equivalent LQ problem for MJSs to be definite one, which can guarantee the generalized algebraic Riccati equation with Markov jump has a unique semi-positive definite solution. Meanwhile, the optimal control and nonnegative optimal cost value in infinite horizon are acquired, and the resulting optimal closed-loop system is stochastically admissible. Finally, three examples are presented to illustrate the theoretical results.     

A continuous-time consensus algorithm using neurodynamic system for distributed time-varying optimization with inequality constraints

In this paper, a distributed time-varying convex optimization problem with inequality constraints is discussed based on neurodynamic system. The goal is to minimize the sum of agents’ local time-varying objective functions subject to some time-varying inequality constraints, each of which is known only to an individual agent. Here, the optimal solution is time-varying instead of constant. Under an undirected and connected graph, a distributed continuous-time consensus algorithm is designed by using neurodynamic system, signum functions and log-barrier penalty functions. The proposed algorithm can be understood through two parts: one part is used to reach consensus and the other is used to achieve gradient descent to track the optimal solution. Theoretical studies indicate that all agents will achieve consensus and the proposed algorithm can track the optimal solution of the time-varying convex problem. Two numerical examples are provided to validate the theoretical results.     

Optimal stabilization for differential systems with delays - Malkin’s approach

The paper considers a process controlled by a system of delayed differential equations. Under certain assumptions, a control function is determined such that the zero solution of the system is asymptotically stable and, for an arbitrary solution, the integral quality criterion with infinite upper limit exists and attains its minimum value in a given sense. To solve this problem, Malkin’s approach to ordinary differential systems is extended to delayed functional differential equations, and Lyapunov’s second method is applied. The results are illustrated by examples, and applied to some classes of delayed linear differential equations.     

A robust unscented transformation for uncertain moments

This paper proposes a robust version of the unscented transform (UT) for one-dimensional random variables. It is assumed that the moments are not exactly known, but are known to lie in intervals. In this scenario, the moment matching equations are reformulated as a system of polynomial equations and inequalities, and it is proposed to use the Chebychev center of the solution set as a robust UT. This method yields a parametrized polynomial optimization problem, which in spite of being NP-Hard, can be relaxed by some algorithms that are proposed in this paper.     

A state space approach to elasticity

The two-dimensional, plane stress problem of linear elasticity is analyzed within a state space framework. The medium considered is homogeneous and isotropic. Vlasov's mixed formulation of elasticity is used throughout. The field equations are derived in closed form, thus avoiding Vlasov's intermediate infinite series solution. Finally, all the properties of the transfer matrix are shown to follow directly from embedding the problem into a state space setting.     

Three Dimensional Electro-magnetic Field Diffusion in Multilayer Cylindrical Structures

The problem of the magnetic field diffusion through cylindrical structures is considered. An analytic solution is given for the problem of diffusion, through any number of resistive coaxial layers, of the three components of a quite general input vector magnetic field assigned on a boundary cylindrical surface. The limitations on the class of input functions (or more generally distributions) are the existence of the double space Fourier transform and the time Laplace transform; this makes the solution suitable for studying the transient-state behaviour in cylindrical structures of finite or infinite length.     

一种直觉模糊多属性群决策方法及其拓展运用

针对知识产权风险投资项目风险评估过程中的复杂模糊关系,提出一种直觉模糊多属性群决策问题求解的方法。首先,借助直觉模糊数,改进语言变量法和定量指标值转换公式,将专家关于指标的原始评价值全部标准化。而后,应用熵度量的新方法确定指标权重,并以专家对项目的了解程度衡量决策权力。进一步地,将TOPSIS引入群体评价。最后,经算例证明这种方法兼具可操作性和实用性,能得到可靠的评估结果,有利于风险投资者正确筛选项目。     

Moving horizon estimation for ARMAX processes with additive output noise

Auto-Regressive-Moving-Average with eXogenous input (ARMAX) models play an important role in control engineering for describing practical systems. However, ARMAX models can be non-realistic in many practical contexts because they do not consider the measurement errors on the output of the process. Due to the auto-regressive nature of ARMAX processes, a measurement error may affect multiple data entries, making the estimation problem very challenging. This problem can be solved by enhancing the ARMAX model with additive error terms on the output, and this paper develops a moving horizon estimator for such an extended ARMAX model. In the proposed method, measurement errors are modeled as nuisance variables and estimated simultaneously with the states. Identifiability was achieved by regularizing the least-squares cost with the ?₂-norm of the nuisance variables, which leads to an optimization problem that has an analytical solution. For the proposed estimator, convergence results are established and unbiasedness properties are also proved. Insights on how to select the tuning parameter in the cost function are provided. Because of the explicit modeling of output noise, the impact of a measurement error on multiple data entries can be estimated and reduced. Examples are given to demonstrate the effectiveness of the proposed estimator in dealing with additive output noise as well as outliers.     

The solution of boundary value problems by multiple Laplace transformations

By use of the multiple Laplace transform a partial differential equation and its associated boundary conditions characterizing a boundary value problem in n independent real variables can be transferred directly into an algebraic equation in n independent complex variables. This algebraic equation can be solved for the multiple transform of the solution of the boundary value problem. Multiple inversion of this transform then gives the desired solution. The general theory underlying such solution of boundary value problems in two and three independent variables is advanced in detail. Use of this theory is illustrated by solution of two specific problems.     

A hybrid approximation scheme for discretizing constrained quadratic optimal control problems

In this paper, a composite Chebyshev finite difference method for solving linear quadratic optimal control problems with inequality constraints on state and control variables is introduced. This method is an extension of Chebyshev finite difference scheme and is based on a hybrid of block-pulse functions and Chebyshev polynomials using the well known Chebyshev–Gauss–Lobatto nodes. The excellent properties of hybrid functions are used to convert optimal control problem into a mathematical programming problem whose solution is much more easier than the original one. Various types of optimal control problems are investigated to demonstrate the effectiveness of the proposed approximation scheme. The method is simple, easy to implement and provides very accurate results.     

Fault detection in finite frequency domain for networked control systems with missing measurements

This paper is concerned on the fault detection (FD) problem in finite frequency domain for networked control systems (NCSs) with missing measurements. By virtue of the stopping time, the considered NCSs are firstly modeled as Markov jumping systems (MJSs). The notion of finite frequency stochastic _H−$H_{-}$ index is then introduced to measure the sensitivity of the residuals. Taking into account a new sensor fault model, which is valid to express the failures of stuck, loss of effectiveness as well as outage ones, a novel FD scheme is developed with simultaneous consideration of sensitivity performance and attenuation performance in finite frequency domain, such that it is valid for all admissible sensor faults. In addition, new convex conditions in terms of linear matrix inequalities (LMIs), which can be reduced to some previous results, are presented to cope with this FD problem. Further, fault detection filters (FDFs) can be constructed by solving the derived LMIs. Finally, such an FD scheme is utilized to an aircraft model, and the effectiveness of proposed method is demonstrated by the simulation results.     

Magnetic Field Diffusion Through Infinite Conducting Media

The diffusion of the magnetic field due to a step current in an infinitely long ideal conductor, through infinite media is discussed. An analytical solution of the field diffusion through two concentric cylinders of different conductivity is derived using a generalized Ohm's law which considers both solid and fluid conductors. A rigorous mathematical treatment which can be generalized to any number of conducting cylinders is presented.The limiting case of an external superconducting medium is discussed and it is shown that with all the other parameters fixed it represents a lower limit in diffusion time.     

A Graph Theoretic Approach to Switching Function Minimization

In this paper we pursue the graph theoretic approach to the switching function minimization problem which is still important in view of today's technological innovations such as programmable logic arrays. We use switching functions graphs (SFG) for studying the structure of switching functions and the minimization problem. The graph theoretic interpretation of the classical minimization problem leads to an alternative and powerful approach to logic design that is suitable for computer implementations. The approach is particularly useful in the analysis and design of suboptimum algorithms for minimization of arbitrarily complex switching functions arising in practice for which exact algorithms are known to be computationally intractable. A few graph theoretic algorithms leading to minimization of switching functions are presented and examples indicating the power of our approach, and algorithms are worked out. Further work needed in the area is indicated.     

An initial value method for solving Fredholm integral equation of the first kind

The difficulties in solving Fredholm integral equations of the first kind are well known. A classical method has been to convert the equation into a set of m linear algebraic equations in n unknowns (m?n). For computational convenience, it is customary to force m = n and solve the resulting ill-conditioned system using one technique or other. In the general case, a feasible solution, if it exists, can be found by determining the generalized inverse of the coefficient matrix. One method of finding the generalized inverse is to reformulate the problem and observe the steady state response of a system of ordinary differential equations with prescribed initial conditions. Results obtained from this reformulation are found to be comparable in quality to those obtained earlier by other methods. Analog and digital computer implementations are discussed.     

Disturbance-observer-based control design for a class of uncertain systems with intermittent measurement

The robust control problem of a class of uncertain systems subject to intermittent measurement as well as external disturbances is considered. The disturbances are supposed to be generated by an exogenous system, while the state information is assumed to be available only on some nonoverlapping time intervals. A composite design consisting of an intermittent state feedback controller augmented by a disturbance compensation term derived from a disturbance observer is formulated. Unlike the conventional disturbance observers, the proposed disturbance observer is modelled by a switched impulsive system, which makes use of the intermittent state data to estimate the disturbances. Stability analysis of the resulting closed-loop system is performed by applying a piecewise time-dependent Lyapunov function. Then a sufficient condition for the existence of the proposed composite controllers is derived in terms of linear matrix inequalities (LMIs). The controller and observer gains can be achieved by solving a set of LMIs. Further, a procedure to limit the norms of the controller and observer gains is given. Finally, an illustrative example is presented to demonstrate the validity of the results.