Locally distributed control of wave equations with variable coefficients

For wave equations with variable coefficients on regions which are not necessarily smooth, we obtain a sufficient condition for the subregion on which the application of control will yield the exact controllability property by using piecewise multiplier method and Riemannian geometry method. Some examples are presented.     

A probabilistic solution of robust H∞ control problem with scaled matrices

This paper addresses the robust H_∞ control problem with scaled matrices. It is difficult to find a global optimal solution for this non-convex optimisation problem. A probabilistic solution, which can achieve globally optimal robust performance within any pre-specified tolerance, is obtained by using the proposed method based on randomised algorithm. In the proposed method, the scaled H_∞ control problem is divided into two parts: (1) assume the scaled matrices be random variables, the scaled H_∞ control problem is converted to a convex optimisation problem for the fixed sample of the scaled matrix and a optimal solution corresponding to the fixed sample is obtained; (2) a probabilistic optimal solution is obtained by using the randomised algorithm based on a finite number N optimal solutions, which are obtained in part (1). The analysis shows that the worst case complexity of proposed method is a polynomial.     

Stabilization of the Euler–Bernoulli plate with variable coefficients by nonlinear internal feedback

We consider the energy decay for solutions of the Euler–Bernoulli plate equation with variable coefficients where a nonlinear internal feedback acts in a suitable subregion of the domain. The Riemannian geometric method is used to deal with variable coefficient problems. When the feedback region has a structure similar to that for the wave equation with constant coefficients, we establish the stabilization of the system in the case of fixed boundary conditions. Several energy decay rates are established according to various growth restrictions on the nonlinear feedback near the origin and at infinity. We further show that, unlike for the case of constant coefficients, choices of such feedback regions depend not only on the type of boundary conditions but also on the curvature of a Riemannian metric, based on the coefficients of the system.     

Robust variable admittance control for human–robot co-manipulation of objects with unknown load

Over the last years, physical Human–Robot Interaction (pHRI) has become a particularly interesting topic for industrial tasks. An important issue is allowing people and robots to collaborate in an useful, simple and safe manner. In this work, we propose a new framework that allows the person to collaborate with a robot manipulator, while the robot has its own predefined task. To allow the robot to smoothly switch from its own task to be a compliant collaborator for the person, a variable admittance control is developed. Furthermore, in general the task to accomplish requires the robot to carry variable, unknown, loads at the end-effector. To include this feature in our framework, a robust control is also included to preserve the performance of the robot despite uncertainties coming from the unknown load. To validate our approach, experiments were carried out with a Kuka LBR iiwa 14 R820, first to validate both parts of the controller, and finally, to study a use-case scenario similar to an industrial production line. Results show the efficiency of this approach to allow the person to collaborate at any moment while the robot is capable of performing another task. This flexible framework for object co-manipulation also allows unknown loads up to 2 kg to be handled without making the task more difficult for the person.     

Wiener?Hopf design of optimal decoupling one-degree-of-freedom controllers for plants with rectangular transfer matrices

This paper is a sequel to an earlier one which treated the design of optimal decoupling one-degree-of-freedom stabilizing multivariable controllers for plants with square transfer matrices. Here designs for plants with rectangular transfer matrices are given which allow for feedforward compensation and more generality in the specification of the desired closed-loop transfer matrix. As in the earlier work, all controllers are placed in the forward path of the feedback loop and non-unity feedback is permitted. The criterion for optimality is a quadratic-cost functional that penalizes both tracking error and saturation. Explicit formulas are derived which give the set of all those controllers that yield finite cost, as well as the ones that are optimal. It is shown that these controllers are strictly-proper under conditions usually prevailing in practice. The solution for plants with rectangular transfer matrices is expressed in terms of both Schur and Kronecker matrix products. When the plant transfer matrix is square, the solution reduces to the one obtained in the earlier work and involves only Schur matrix products.     

On the orders of transformation matrices (mod n) and two types of generalized Arnold transformation matrices

With the rapid development of information technology, more and more private and public information is distributed through the Internet. The problem of how to distribute information securely through the Internet has arisen. Recently, a lot of technologies have been developed to ensure the security of information. Information hiding[1] is one of these, ranging from digital watermarking, digital fingerprint to steganography. The scrambling transformation is one of the technologies of image infor…     

group added another band (R f=0.36). The activites of peroxidase is

es were changed greatly at rest concentrations of Cd 2 、Hg 2 and 10 -4 -10 -8 mol/L Ni 2 treatment groups. It suggested that Hg 2 and Cd 2 have stro     

Design of fractional-order PIλDμ controllers with an improved differential evolution

Differential evolution (DE) has recently emerged as a simple yet very powerful technique for real parameter optimization. This article describes an application of DE to the design of fractional-order proportional–integral–derivative (FOPID) controllers involving fractional-order integrator and fractional-order differentiator. FOPID controllers’ parameters are composed of the proportionality constant, integral constant, derivative constant, derivative order and integral order, and its design is more complex than that of conventional integer-order proportional–integral–derivative (PID) controller. Here the controller synthesis is based on user-specified peak overshoot and rise time and has been formulated as a single objective optimization problem. In order to digitally realize the fractional-order closed-loop transfer function of the designed plant, Tustin operator-based continuous fraction expansion (CFE) scheme was used in this work. Several simulation examples as well as comparisons of DE with two other state-of-the-art optimization techniques (Particle Swarm Optimization and binary Genetic Algorithm) over the same problems demonstrate the superiority of the proposed approach especially for actuating fractional-order plants. The proposed technique may serve as an efficient alternative for the design of next-generation fractional-order controllers.     

A Syntactic Proof of the Conservativity ofλ_ω overλ_2

In this paper,the relationship between the second order typed λ－calculus λ2 and its higher order version λω is discussed.A purely syntactic proof of the conservativity of λωover λ2 is given.     

Comment on ‘Stability of interval matrices’

Liao Xiao Xin (1987) gave necessary and sufficient conditions for the stability of a class of interval matrices. It can easily be shown that these results follow directly from a theorem relating stable Metzler matrices and quasidominant negative diagonal matrices by McKenzie (1966) which states (see also Siljak 1978)

A Metzler matrix A is stable if and only if it is quasidominant negative diagonal.

As the author considers Metzler matrices, Theorems 1,2 and 3 are obvious. Also, a theorem by Fiedler and Ptak (1962) concerning a pair of Minkowski matrices (see also Siljak 1978) leads to the same results.     

Dynamic properties of the Fisher–Kolmogorov–Petrovskii–Piscounov equation with the deviation of the spatial variable

We consider the problem of the density wave propagation of a logistic equation with the deviation of the spatial variable and diffusion (the Fisher–Kolmogorov equation with the deviation of the spatial variable). The Ginzburg–Landau equation was constructed in order to study the qualitative behavior of the solution near the equilibrium state. We analyzed the profile of the wave equation and found conditions for the appearance of oscillatory regimes. The numerical analysis of the wave propagation shows that, for a fairly small spatial deviation, this equation has a solution similar to that the classical Fisher–Kolmogorov equation. An increase in this spatial deviation leads to the existence of the oscillatory component in the spatial distribution of solutions. A further increase in the spatial deviation leads to the destruction of the traveling wave. This is expressed in the fact that undamped spatiotemporal fluctuations exist in a neighborhood of the initial perturbation. These fluctuations are close to the solution of the corresponding boundary value problem with periodic boundary conditions. Finally, when the spatial deviation is large enough we observe intensive spatiotemporal fluctuations in the whole area of wave propagation.     

A note on “A multiple-vendor single-buyer integrated inventory model with a variable number of vendors”

In this technical note, an alternative solution procedure to the model that Glock (2011) developed is presented. In particular, we take into account the same assumptions, but the total cost function is reformulated, i.e., the step-type discontinuity is replaced by a logistic approximation and the total costs of the system are computed on the whole set of preselected suppliers. Subsequently, we show that the total cost function possesses some properties in terms of convexity and continuity that allow the exploitation of standard constrained nonlinear minimization algorithms. Finally, tests conducted on the same set of problems that Glock (2011) originally considered illustrate the good performances of the solution procedure developed in this note.     

Comments on “Design of two-layered fractional order fuzzy logic controllers applied to robotic manipulator with variable payload”

Sharma et al. have investigated the performance of two-layered fractional order fuzzy logic controller (TL-FOFLC) for a 2-link rigid planer robotic manipulator with payload. In this work, the performance of TL-FOFLC has been compared with two-layered FLC (TL-FLC), single-layered FLC (SL-FLC) and the conventional proportional-integral-derivative (PID) controllers, for trajectory tracking, model uncertainties and disturbance rejection. In this comment, it is pointed out that this work has several missing essential parameters, and therefore, it is not possible for the reader to validate all the claimed results of Sharma et al. (2016). Six numerical values, three gains for each of the used two PID controllers are found to be unreported in addition to the six gains for each of the used two SL-FLCs. Since the performances of the PIDs and the SL-FLCs are highly dependent on their tuned gains it is concluded that the reported performances of these controllers cannot be validated.     

The “up-and-down” method with a variable step in digital sampling conversion

The author proposes a method for reducing the errors of conversion and/or the number of strobings with using a variable step in the “up-and-down” method.