共查询到10条相似文献,搜索用时 156 毫秒
1.
Y. Yavin 《Computers & Mathematics with Applications》2005,50(10-12):1659-1668
This work deals with the stabilization and control of a system which is composed of a disk rolling on a plane, and a circular rotor plate fixed in the disk's plane. The disk's motion is controlled by the above-mentioned rotor, a “tillting moment” and a pedalling moment. It is shown here that by applying a kind of inverse dynamics control, the motion of the disk is stabilized about a given angle, while simultaneously controlling its speed and direction in such a manner that the point of contact between the disk and the horizontal plane will be able, during a given time interval [0, tf], to move from a given point. rA to a another given point rB, both of them fixed in the plane. 相似文献
2.
We consider a class of two-sided stochastic control problems. For each continuous process πt = πt+ − πt− with bounded variation, the state process (xt) is defined by xt = Bt + f0t I(xs - a)dπs+ − f0t I(xs a)dπs−, where a is a positive constant and (Bt) is a standard Brownian motion. We show the existence of an optimal policy so as to minimize the cost function J(π) = E [f0∞ e−αsXs2 ds], with discount rate α > 0, associated with π. 相似文献
3.
The optimal least-squares filtering of a diffusion x(t) from its noisy measurements {y(τ); 0 τ t} is given by the conditional mean E[x(t)|y(τ); 0 τ t]. When x(t) satisfies the stochastic diffusion equation dx(t) = f(x(t)) dt + dw(t) and y(t) = ∫0tx(s) ds + b(t), where f(·) is a global solution of the Riccati equation /xf(x) + f(x)2 = f(x)2 = αx2 + βx + γ, for some
, and w(·), b(·) are independent Brownian motions, Benes gave an explicit formula for computing the conditional mean. This paper extends Benes results to measurements y(t) = ∫0tx(s) ds + ∫0t dx(s) + b(t) (and its multidimensional version) without imposing additional conditions on f(·). Analogous results are also derived for the optimal least-squares smoothed estimate E[x(s)|y(τ); 0 τ t], s < t. The methodology relies on Girsanov's measure transformations, gauge transformations, function space integrations, Lie algebras, and the Duncan-Mortensen-Zakai equation. 相似文献
4.
Stochastic stabilisation of functional differential equations 总被引:3,自引:2,他引:1
In this paper we investigate the problem of stochastic stabilisation for a general nonlinear functional differential equation. Given an unstable functional differential equation dx(t)/dt=f(t,xt), we stochastically perturb it into a stochastic functional differential equation , where Σ is a matrix and B(t) a Brownian motion while Xt={X(t+θ):-τθ0}. Under the condition that f satisfies the local Lipschitz condition and obeys the one-side linear bound, we show that if the time lag τ is sufficiently small, there are many matrices Σ for which the stochastic functional differential equation is almost surely exponentially stable while the corresponding functional differential equation dx(t)/dt=f(t,xt) may be unstable. 相似文献
5.
Plant template generation is the key step in applying quantitative feedback theory (QFT) to design robust control for uncertain systems. In this paper we propose a technique for generating plant templates for a class of linear systems with an uncertain time delay and affine parameter perturbations in coefficients. The main contribution lies in presenting a necessary and sufficient condition for the zero inclusion of the value set f(T,Q)={f(τ,q): τT[τ−,τ+], qQ∏k=0m−1[qk−,qk+]}, where f(τ,q)=g(q)+h(q)e−jτω*, g(q) and h(q) are both complex-valued affine functions of the m-dimensional real vector q, and ω* is a fixed frequency. Based on this condition, an efficient algorithm which involves, in the worst case, evaluation of m algebraic inequalities and solution of m2m−1 one-variable quadratic equations, is developed for testing the zero inclusion of the value set f(T,Q). This zero-inclusion test algorithm allows one to utilize a pivoting procedure to generate the outer boundary of a plant template with a prescribed accuracy or resolution. The proposed template generation technique has a linear computational complexity in resolution and is, therefore, more efficient than the parameter gridding and interval methods. A numerical example illustrating the proposed technique and its computational superiority over the interval method is included. 相似文献
6.
The authors introduce and investigate various properties of a general class;,which unifies and extends several (known or new) subclasses of meromorphically multivalent functions. The properties and characteristics of this general class, which are presented here, include growth and distortion theorems; they also involve Hadamard products (or convolution) of functions belonging to the class Uk[p,α,β,A,B]. 相似文献
Uk[p,a,β,A,B]
p, k ε N {1, 2, 3,…,}; 0 α < p; β 0
−1 A < B 1; 0 < B 1)
7.
A moving line L(x,y;t)=0 is a family of lines with one parameter t in a plane. A moving line L(x,y;t)=0 is said to follow a rational curve P(t) if the point P(t0) is on the line L(x,y;t0)=0 for any parameter value t0. A μ-basis of a rational curve P(t) is a pair of lowest degree moving lines that constitute a basis of the module formed by all the moving lines following P(t), which is the syzygy module of P(t). The study of moving lines, especially the μ-basis, has recently led to an efficient method, called the moving line method, for computing the implicit equation of a rational curve [3 and 6]. In this paper, we present properties and equivalent definitions of a μ-basis of a planar rational curve. Several of these properties and definitions are new, and they help to clarify an earlier definition of the μ-basis [3]. Furthermore, based on some of these newly established properties, an efficient algorithm is presented to compute a μ-basis of a planar rational curve. This algorithm applies vector elimination to the moving line module of P(t), and has O(n2) time complexity, where n is the degree of P(t). We show that the new algorithm is more efficient than the fastest previous algorithm [7]. 相似文献
8.
O. Zeitouni 《Systems & Control Letters》1983,3(6):329-330
The one-dimensional diffusion xt satisfying dxt = f(xt)dt + dwt, where wt is a standard Brownian motion and f(x) satisfies the Bene
condition f′(x) + f2(x) = ax2 + bx + c for all real x, is considered. It is shown that this diffusion does not admit a stationary probability measure except for the linear case f(x) = αx + β, α < 0. 相似文献
9.
Xuerong Mao 《Systems & Control Letters》1995,26(4)
The aim of this paper is to investigate the exponential stability in mean square for a neutral stochastic differential functional equation of the form d[x(t) − G(xt)] = [f(t,x(t)) + g(t, xt)]dt + σ(t, xt)dw(t), where xt = {x(t + s): − τ s 0}, with τ > 0, is the past history of the solution. Several interesting examples are a given for illustration. 相似文献
10.
Nonlinear eigenvalue problems for quasilinear systems 总被引:1,自引:0,他引:1
The paper deals with the existence of positive solutions for the quasilinear system (Φ(u'))' + λh(t)f(u) = 0,0 < t < 1 with the boundary condition u(0) = u(1) = 0. The vector-valued function Φ is defined by Φ(u) = (q(t)(p(t)u1), …, q(t)(p(t)un)), where u = (u1, …, un), andcovers the two important cases (u) = u and (u) = up > 1, h(t) = diag[h1(t), …, hn(t)] and f(u) = (f1(u), …, fn (u)). Assume that fi and hi are nonnegative continuous. For u = (u1, …, un), let , f0 = maxf10, …, fn0 and f∞ = maxf1∞, …, fn∞. We prove that the boundary value problem has a positive solution, for certain finite intervals of λ, if one of f0 and f∞ is large enough and the other one is small enough. Our methods employ fixed-point theorem in a cone. 相似文献