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1.
Wassim M. Haddad 《Systems & Control Letters》1990,14(2)
Recent papers have considered the problem of minimizing an entropy functional subject to an H∞ performance constraint. Since the entropy is an upper bound for the H2 cost, there remains a gap between entropy minimization and H2 minimization. In this paper we consider a generalized cost functional involving both H2 and entropy aspects. This approach thus provides a means for optimizing H2 performance within H∞ control design. 相似文献
2.
William M. McEneaney 《Systems & Control Letters》1998,33(5):66
A robust (or H∞) approach to filtering for nonlinear systems is considered. A bound on the estimate error as a function of the disturbance energy is obtained. The corresponding dynamic programming equation is a first-order PDE. This has computational ramifications. The case where the measurements are discrete time is considered also. A numerical method is discussed. 相似文献
3.
A robust (or H∞) approach to filtering for nonlinear systems is considered. A bound on the estimate error as a function of the disturbance energy is obtained. The corresponding dynamic programming equation is a first-order PDE. This has computational ramifications. The case where the measurements are discrete time is considered also. A numerical method is discussed. 相似文献
4.
For a linear time invariant system, the infinity-norm of the transfer function can be used as a measure of the gain of the system. This notion of system gain is ideally suited to the frequency domain design techniques such as H∞ optimal control. Another measure of the gain of a system is the H2 norm, which is often associated with the LQG optimal control problem. The only known connection between these two norms is that, for discrete time transfer functions, the H2 norm is bounded by the H∞ norm. It is shown in this paper that, given precise or certain partial knowledge of the poles of the transfer function, it is possible to obtain an upper bound of the H∞ norm as a function of the H2 norm, both in the continuous and discrete time cases. It is also shown that, in continuous time, the H2 norm can be bounded by a function of the H∞ norm and the bandwidth of the system. 相似文献
5.
The problem of unbiased filtering for a discrete-time linear periodic system is faced by means of linear matrix inequality techniques. As leading case, we derive the synthesis conditions to obtain an unbiased filter and an unbiased fixed-lag smoother enforcing a bound on the H∞ performance on the error dynamics. 相似文献
6.
The paper investigates the problem of identifying uncertainty models of causal, SISO, LTI, discrete-time, BIBO stable, unknown systems, using frequency domain measurements corrupted by Gaussian noise of known covariance. Additive uncertainty models are looked for, consisting of a nominal model and an additive dynamic perturbation accounting for the modeling error. The nominal model is chosen within a class of affinely parametrized models with transfer function of given (possibly low) order. An estimate of the parameters minimizing the H∞ modeling error is obtained by minimizing an upper bound of the worst-case (with respect to the modeling error) second moment of the estimation error. Then, a bound in the frequency domain guaranteeing to include, with probability α, the frequency response error between the estimated nominal model and the unknown system is derived. 相似文献
7.
We derive an output feedback controller which stabilizes a system and satisfies a prescribed H∞ norm bound of the closed loop transfer function. The proposed design method is available for any system, i.e. there are no restrictions on D12 and D21. This approach utilizes only algebraic operations, thus proofs are simple and clear. 相似文献
8.
This paper deals with the problem of H∞ observer design for a class of uncertain linear systems with delayed state and parameter uncertainties. This problem aims at designing the linear state observers such that, for all admissible parameter uncertainties, the observation process remains robustly stable and the transfer function from exogenous disturbances to error state outputs meets the prespecified H∞ norm upper bound constraint, independently of the time delay. The time delay is assumed to be unknown, and the parameter uncertainties are allowed to be norm-bounded and appear in all the matrices of the state-space model. An effective matrix inequality methodology is developed to solve the proposed problem. We derive the conditions for the existence of the desired robust H∞ observers, and then characterize the analytical expression of these observers in terms of some free parameters. A numerical example demonstrates the validity and applicability of the present approach. 相似文献
9.
This paper investigates the problem of H∞ filtering for a class of uncertain continuous-time nonlinear systems with real time-varying parameter uncertainty and unknown initial state. We develop an infinite horizon H∞ filtering methodology which provides both robust stability and a guaranteed H∞ performance for the filtering error irrespective of the parameter uncertainty. 相似文献
10.
James A. Cadzow 《Digital Signal Processing》2002,12(4):293
Cadzow, J. A., Minimum ℓ1, ℓ2, and ℓ∞ Norm Approximate Solutions to an Overdetermined System of Linear Equations, Digital Signal Processing12 (2002) 524–560Many practical problems encountered in digital signal processing and other quantitative oriented disciplines entail finding a best approximate solution to an overdetermined system of linear equations. Invariably, the least squares error approximate solution (i.e., minimum ℓ2 norm) is chosen for this task due primarily to the existence of a convenient closed expression for its determination. It should be noted, however, that in many applications a minimum ℓ1 or ℓ∞ norm approximate solution is preferable. For example, in cases where the data being analyzed contain a few data outliers a minimum ℓ1 approximate solution is preferable since it tends to ignore bad data points. In other applications one may wish to determine an approximate solution whose largest error magnitude is the smallest possible (i.e., a minimum ℓ∞ norm approximate solution). Unfortunately, there do not exist convenient closed form expressions for either the minimum ℓ1 or the minimum ℓ∞ norm approximate solution and one must resort to nonlinear programming methods for their determination. Effective algorithms for determining these two solutions are herein presented (see Cadzow, J. A., Data Analysis and Signal Processing: Theory and Applications). 相似文献
11.
The problem of H∞-optimal state estimation of linear continuous-time systems that are measured with an additive white noise is addressed. The relevant cost function is the expected value of the standard H∞ performance index, with respect to the measurement noise statistics. The solution is obtained by applying the matrix version of the maximum principle to the solution of the min–max problem in which the estimator tries to minimize the mean square estimation error and the exogenous disturbance tries to maximize it while being penalized for its energy. The solution is given in terms of two coupled Riccati difference equations from which the filter gains are derived. In the case where an infinite penalty is imposed on the energy of the exogenous disturbance, the celebrated Kalman filter is recovered. In the stationary case, where all the signals are stationary, an upper-bound on the solutions of the coupled Riccati equations is obtained via a solution of coupled linear matrix inequalities. The resulting filter then guarantees a bound on the estimation error covariance matrix. An illustrative example is given where the velocity of a maneuvering target has to be estimated utilizing noisy measurements of the position. 相似文献
12.
Let H(z) be a given function in H2 A classical problem in engineering analysis is to find a rational function G (z) ε H2 degree M say, which is closest to H(z) in 2-norm. This problem is typically approached using the cost function |H(z) − G(z)|2, in which G(z) is allowed to vary over the set of Mth-order rational functions in H2 and for which stationary points are sought. We show that each stationary point of degree M of this functional coincides with a weighted Hankel-norm approximant to H(z). The weighting function derives from the outer factor of the error function H(z) − G(z) stationary point of the rational H2 approximation problem. 相似文献
13.
α-Fe2O3 ultra-fine powder with an average particle size of 6–26nm has been prepared by a sol-gel process. Thermal analysis, X-ray diffraction and transmission electron microscope were used to study its formation process and micro-structure. The temperature dependence of the electric conductance of the elements made of nanocrystalline α-Fe2O3 shows that the gas-sensing properties are strongly related to its surface. The elements exhibited good sensitivity and selectivity to ethyl alcohol, indicating it is a promising alcohol-sensing material. 相似文献
14.
The problem of mixed H2/H∞ filtering for polytopic Delta operator systems is investigated. The aim is to design a linear asymptotically stable filter which guarantees that the filtering error system has different performances in different filtering channels. Based on a parameter-dependent Lyapunov function, a new mixed H2/H∞ performance criterion is presented. Upon this performance criterion, a sufficient condition for the full-order mixed H2/H∞ filter is derived in terms of linear matrix inequalities. The filter can be obtained from the solution of a convex optimization problem. The proposed filter design procedure is less conservative than the strategy based on the quadratic stability notion. A numerical example is given to illustrate the feasibility of the proposed approach. 相似文献
15.
16.
The paper addresses the problem of quadratic stabilisability with H∞-norm bound of uncertain discrete-time control-affine systems by norm-bounded controls. Both structured parameter uncertainties and unstructured exogenous disturbances are taken into account. The given definition of quadratic stabilisability is a generalisation of that used for linear systems so far. A necessary condition of the stabilisability is formulated. A state feedback control satisfying an a priori constraint is proposed for the solution of the formulated H∞ problem. The proposed method may be applicable even in such cases when the linearisation technique cannot be used. 相似文献
17.
The problem of H∞ filtering of stationary discrete-time linear systems with stochastic uncertainties in the state space matrices is addressed, where the uncertainties are modeled as white noise. The relevant cost function is the expected value, with respect to the uncertain parameters, of the standard H∞ performance. A previously developed stochastic bounded real lemma is applied that results in a modified Riccati inequality. This inequality is expressed in a linear matrix inequality form whose solution provides the filter parameters. The method proposed is applied also to the case where, in addition to the stochastic uncertainty, other deterministic parameters of the system are not perfectly known and are assumed to lie in a given polytope. The problem of mixed H2/H∞ filtering for the above system is also treated. The theory developed is demonstrated by a simple tracking example. 相似文献
18.
This paper develops a new method for the synthesis of linear parameter-varying (LPV) controllers in discrete time. LPV plants under consideration have a linear fractional transformation (LFT) representation. In contrast to earlier results which are restricted to single-objective LPV problems, the proposed method can handle a set of H2/H∞ specifications that can be defined channel-wise. This practically attractive extension is derived by using specific transformations of both the Lyapunov and scaling/multiplier variables in tandem with appropriate linearizing transformations of the controller data and of the controller scheduling function. It is shown that the controller gain-scheduling function can be constructed as an affine matrix-valued function in the polytopic coordinates of the scheduled parameter, hence is easily implemented on line. Finally, these manipulations give rise to a tractable and practical LMI formulation of the multi-objective LPV control problem. 相似文献
19.
The problem of finding bounds on the H∞-norm of systems with a finite number of point delays and distributed delay is considered. Sufficient conditions for the system to possess an H∞-norm which is less or equal to a prescribed bound are obtained in terms of Riccati partial differential equations (RPDE’s). We show that the existence of a solution to the RPDE’s is equivalent to the existence of a stable manifold of the associated Hamiltonian system. For small delays the existence of the stable manifold is equivalent to the existence of a stable manifold of the ordinary differential equations that govern the flow on the slow manifold of the Hamiltonian system. This leads to an algebraic, finite-dimensional, criterion for systems with small delays. 相似文献
20.
LetL
p
be the plane with the distanced
p
(A
1
,A
2
) = (¦x
1 –x
2¦
p
+ ¦y1 –y
2¦p)/1p
wherex
i
andy
i
are the cartesian coordinates of the pointA
i
. LetP be a finite set of points inL
p
. We consider Steiner minimal trees onP. It is proved that, for 1 <p < , each Steiner point is of degree exactly three. Define the Steiner ratio
p
to be inf{L
s
(P)/L
m
(P)¦PL
p
} whereL
s
(P) andL
m
(P) are lengths of the Steiner minimal tree and the minimal spanning tree onP, respectively. Hwang showed 1 = 2/3. Chung and Graham proved 2 > 0.842. We prove in this paper that {} = 2/3 and (2/2)12 p 3/2 for anyp.This work was supported in part by the National Science Foundation of China and the President Foundation of Academia Sinica. 相似文献