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1.
This article presents a new approach for solving the Optimal Control Problem (OCP) of linear time-delay systems with a quadratic cost functional. The proposed method can also be used for designing optimal control time-delay systems with disturbance. In this study, the Variational Iteration Method (VIM) is employed to convert the original Time-Delay Optimal Control Problem (TDOCP) into a sequence of nonhomogeneous linear two-point boundary value problems (TPBVPs). The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence. The feedback term is determined by solving Riccati matrix differential equation. By using the finite-step iteration of a nonlinear compensation sequence, we can obtain a suboptimal control law. Finally, Illustrative examples are included to demonstrate the validity and applicability of the technique. 相似文献
2.
We establish a numerically feasible algorithm to find a simplicial approximation A to a certain part
of the boundary of the set
of stable (or Hurwitz) polynomials of degree 4. Moreover, we have that
. Using this, we build an algorithm to find a piecewise-linear approximation to the intersection curve of a given surface contained in
4 with
. We have also devised an efficient computer program to perform all these operations. The main motivation is to find the curve of nondegenerate bifurcation points in parameter space for a given 2-parametric Hopf bifurcation problem of dimension 4. 相似文献
3.
In this note the stability of a second-order quasi-polynomial with a single delay is studied. Although there is a vast literature on this problem, most available solutions are limited to some particular cases. Moreover, some published results on this subject appear to contain imprecise, or even wrong, conditions. The purpose of this note is to show that by accurate application of known theories, a complete explicit characterization of stability regions can be derived in a most general case. As a byproduct of the proposed analysis, we show that in the high-order case the quasi-polynomial is delay-independent unstable whenever its delay-free version has an odd number of unstable roots (or, equivalently, a negative static gain). 相似文献
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5.
《Journal of Process Control》2014,24(5):550-567
For many practical industrial spatially distributed processes (SDPs), their dynamics are usually described by highly dissipative nonlinear partial differential equations (PDEs). In this paper, we address the L2 disturbance attenuation problem of nonlinear SDPs using the Hamilton–Jacobi–Isaacs (HJI) approach. Firstly, by collecting an ensemble of PDE states, Karhunen–Loève decomposition (KLD) is employed to compute empirical eigenfunctions (EEFs) of the SDP based on the method of snapshots. Subsequently, these EEFs together with singular perturbation (SP) technique are used to obtain a finite-dimensional slow subsystem of ordinary differential equation (ODE) that accurately describes the dominant dynamics of the PDE system. Secondly, based on the slow subsystem, the L2 disturbance attenuation problem is reformulated and a finite-dimensional H∞ controller is synthesized in terms of the HJI equation. Moreover, the stability and L2-gain performance of the closed-loop PDE system are analyzed. Thirdly, since the HJI equation is a nonlinear PDE that has proven to be impossible to solve analytically, we combine the method of weighted residuals (MWR) and simultaneous policy update algorithm (SPUA) to obtain its approximate solution. Finally, the simulation studies are conducted on a nonlinear diffusion-reaction process and a temperature cooling fin of high-speed aerospace vehicle, and the achieved results demonstrate the effectiveness of the developed control method. 相似文献
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8.
ON GENERALIZED FRACTIONAL PROCESSES 总被引:3,自引:0,他引:3
Abstract. A class of stationary long-memory processes is proposed which is an extension of the fractional autoregressive moving-average (FARMA) model. The FARMA model is limited by the fact that it does not allow data with persistent cyclic (or seasonal) behavior to be considered. Our extension, which includes the FARMA model as a special case, makes use of the properties of the generating function of the Gegenbauer polynomials, and we refer to these models as Gegenbauer autoregressive moving-average (GARMA) models. While the FARMA model has a peak in the spectrum at f = 0, the GARMA process can model long-term periodic behavior for any frequency 0 f 0.5. Properties of the GARMA process are examined and techniques for generation of realizations, model identification and parameter estimation are proposed. The use of the GARMA model is illustrated through simulated examples as well as with classical sunspot data. 相似文献
9.
Farid Ablayev Alexander Vasiliev 《International Journal of Software and Informatics》2013,7(4):485-500
In the paper, we develop a method for constructing quantum algorithms for computing Boolean functions by quantum ordered read-once branching programs (quantum OBDDs). Our method is based on ˉngerprinting technique and representation of Boolean functions by their characteristic polynomials. We use circuit notation for branching programs for desired algorithms presentation. For several known functions our approach provides optimal QOBDDs. Namely we consider such functions as MODm, EQn, Palindromen, and PERMn (testing whether given Boolean matrix is the Permutation Matrix). We also propose a generalization of our method and apply it to the Boolean variant of the Hidden
Subgroup Problem. 相似文献
10.