Decentralized Guaranteed Cost Control for Uncertain Large-Scale Systems Using Delayed Feedback: LMI Optimization Approach

In this paper, we propose a design method of guaranteed cost controllers for uncertain large-scale systems with time delays in subsystem interconnections using delayed feedback. Using the Lyapunov method, a linear matrix inequality (LMI) optimization problem is formulated to design a delayed feedback controller which minimizes the upper bound of a given quadratic cost function. A numerical example is included to illustrate the design procedures.Communicated by Q. C. ZhaoThe authors thank the Associate Editor and three anonymous referees for careful reading and useful suggestions.     

On the optimality equation for average cost Markov control processes with Feller transition probabilities

We consider Markov control processes with Borel state space and Feller transition probabilities, satisfying some generalized geometric ergodicity conditions. We provide a new theorem on the existence of a solution to the average cost optimality equation.     

Magnetization relaxation of uniaxial anisotropic ferromagnetic particles with linear reaction dynamics driven by DC/AC magnetic field

The response of uniaxial anisotropic ferromagnetic particles with linear reaction dynamics subjected to alternating current(AC) or direct current(DC) bias magnetic field is evaluated by the reaction–diffusion equation for the probability distribution function of the molecular concentration in the spherical coordinate system. The magnetization function and the probability distribution function of the magnetic particles in the reaction system are derived by using the Legendre polynomials and Laplace transform. We discuss the characteristics of magnetization and probability distribution of the magnetic particles with different anisotropic parameters driven by a DC and AC magnetic fields, respectively. It is shown that both the magnetization and the probability distribution decrease with time increasing due to the reaction process. The uniformity of the probability distribution and the amplitude of the magnetization are both affected by the anisotropic parameters.Meanwhile, the difference between the case with linear reaction dynamics and the non-reaction case is discussed.     

On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems

This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the problem dimension, i.e., if the initial point belongs to the sufficiently small neighbourhood of the solution set. Proposed method could be applied for solving large systems of linear inequalities.     

Adaptive synchronization of chaotic systems with less measurement and actuation

We investigate the synchronization problem between identical chaotic systems only when necessary measurement(output) and actuation(input) are needed to be implemented by the adaptive controllers. A sufficient condition is derived based on the Lyapunov stability theory and Schur complementary lemma. Moreover, the theoretic result is applied to the Rikitake system and the hyperchaotic Liu system to show its effectiveness and correctness. Numerical simulations are presented to verify the results.     

Study of Coulomb collisional effects on the propagation of electromagnetic waves in a turbulent plasma

The presence of Weibel instability in laser-irradiated fuel could be detrimental to the process of ablative implosion, which is necessary for achieving thermonuclear fusion reactions. In this paper, the effect of the Coulomb collisional within the turbulent plasma on the Weibel instability growth rate has been investigated for linear and circular polarization. The results indicate that the Weibel instability growth rate at circular polarization near the ignition centre of the fuel fusion (collisional plasma) is about 10⁵ times higher than the collisional Weibel instability growth rate at linear polarization. The Weibel instability growth rate is observed near the critical density of the fuel fusion (collisionless plasma) at linear polarization and enhancement near the foot of the heat in front of the fuel fusion. By increasing the steps of the density gradient plasma in the low-density corona, electromagnetic instability occurs at a higher stress flow. Therefore, the deposition condition of electron beam energy in circular polarization of turbulent plasma can be shifted to the fuel core for suitable ignition.     

Viewing the noise propagation mechanism in a unidirectional transition cascade from the perspective of stability

Noise and noise propagation are inevitable and play a constructive role in various biological processes. The stability of cell homeostasis is also a critical issue. In the unidirectional transition cascade of colon cells, stem cells (SCs) are the source. They differentiate into transit-amplifying cells (TACs), and TACs differentiate into fully differentiated cells (FDCs). Two differentiation processes are irreversible. The stability factor is introduced so that the noise propagation mechanism from the perspective of stability is studied according to the noise propagation formulas. It is found that the value of the stability factor corresponding to the minimum noise in FDCs may be the best choice to enable colon cells to maintain high stability and low noise of the cascade. Moreover, for the source cell, the total noise only includes intrinsic noise; for the downstream cell with self-proliferation capability, the total noise mainly depends on its intrinsic noise and transmitted noise from upstream cells, and its intrinsic noise is dominant. For the downstream cell without self-proliferation capability, the total noise is mainly determined by transmitted noises from upstream cells, and there is a minimum value. This work provides a new approach for studying the mechanism of noise propagation while considering the stability of cell homeostasis in biological systems.     

Random forests for functional covariates

We propose a form of random forests that is especially suited for functional covariates. The method is based on partitioning the functions' domain in intervals and using the functions' mean values across those intervals as predictors in regression or classification trees. This approach appears to be more intuitive to applied researchers than usual methods for functional data, while also performing very well in terms of prediction accuracy. The intervals are obtained from randomly drawn, exponentially distributed waiting times. We apply our method to data from Raman spectra on boar meat as well as near‐infrared absorption spectra. The predictive performance of the proposed functional random forests is compared with commonly used parametric and nonparametric functional methods and with a nonfunctional random forest using the single measurements of the curve as covariates. Further, we present a functional variable importance measure, yielding information about the relevance of the different parts of the predictor curves. Our variable importance curve is much smoother and hence easier to interpret than the one obtained from nonfunctional random forests.     

Hierarchy of equations to calculate the linear spectra of molecular aggregates: Time‐dependent and frequency domain formulation

In a recent publication (Ritschel et al., J. Chem. Phys. 2015, 142, 034115) we have derived a hierarchy of coupled differential equations in time domain to calculate the linear optical properties of molecular aggregates. Here, we provide details about issues concerning the numerical implementation. In addition we present the corresponding hierarchy in frequency domain.