共查询到20条相似文献,搜索用时 15 毫秒
1.
Robust disturbance rejection bounds obtained recently by Zhu et al. are tight with respect to the disturbance set that has a specified L 2 norm bound. It is shown that the bounds are also tight with respect to a weighted L 2 disturbance set that has a specified bound on its outer product by choosing a special weight matrix in the L 2 norm. The matrix can computed by numerical iteration 相似文献
2.
It is shown that H ∞ optimization is equivalent to weighted H 2 optimization in the sense that the solution of the latter problem also solves the former. The weighting rational matrix that achieves this equivalence is explicitly computed in terms of a state-space realization. The authors do not suggest transforming H ∞ optimization problems to H 2 optimization problems as a computational approach. Rather, their results reveal an interesting connection between H ∞ and H 2 optimization problems which is expected to offer additional insight. For example, H 2 optimal controllers are known to have an optimal observer-full state feedback structure. The result obtained shows that the minimum entropy solution of H ∞ optimal control problems can be obtained as an H 2 optimal solution. Therefore, it can be expected that the corresponding H ∞ optimal controller has an optimal observer-full state feedback structure 相似文献
3.
The focus of this work is L 1-optimal control of sampled-data systems. A converging approximation procedure is derived to compute the L ∞-induced norm of closed-loop finite-dimensional linear time-invariant (LTI) sampled-data systems. An approximation method is developed to synthesize L 1-optimal sampled-data regulators. Finally, an example is provided that illustrates the L 1 analysis and design techniques presented 相似文献
4.
The worst-case effect of a disturbance system on the H 2 norm of the system is analyzed. An explicit expression is given for the worst-case H 2 norm when the disturbance system is allowed to vary over all nonlinear, time-varying and possibly noncausal systems with bounded L 2-induced operator norm. An upper bound for this measure, which is equal to the worst-case H 2 norm if the exogeneous input is scalar, is defined. Some further analysis of this upper bound is done, and a method to design controllers which minimize this upper bound over all robustly stabilizing controllers is given. The latter is done by relating this upper bound to a parameterized version of the auxiliary cost function studied in the literature 相似文献
5.
The H 2-optimal control of continuous-time linear time-invariant systems by sampled-data controllers is discussed. Two different solutions, state space and operator theoretic, are given. In both cases, the H 2 sampled-data problem is shown to be equivalent to a certain discrete-time H 2 problem. Other topics discussed include input-output stability of sampled-data systems, performance recovery in digital implementation of analog controllers, and sampled-data control of systems with the possibility of multiple-time delays 相似文献
6.
The problem of finding an internally stabilizing controller that minimizes a mixed H 2/H ∞ performance measure subject to an inequality constraint on the H ∞ norm of another closed-loop transfer function is considered. This problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint. Both the state-feedback and output-feedback problems are considered. It is shown that in the state-feedback case one can come arbitrarily close to the optimal (even over full information controllers) mixed H 2/H ∞ performance measure using constant gain state feedback. Moreover, the state-feedback problem can be converted into a convex optimization problem over a bounded subset of (n ×n and n ×q , where n and q are, respectively, the state and input dimensions) real matrices. Using the central H ∞ estimator, it is shown that the output feedback problem can be reduced to a state-feedback problem. In this case, the dimension of the resulting controller does not exceed the dimension of the generalized plant 相似文献
7.
Unser M. Aldroubi A. Eden M. 《IEEE transactions on pattern analysis and machine intelligence》1993,15(4):364-379
The authors are concerned with the derivation of general methods for the L 2 approximation of signals by polynomial splines. The main result is that the expansion coefficients of the approximation are obtained by linear filtering and sampling. The authors apply those results to construct a L 2 polynomial spline pyramid that is a parametric multiresolution representation of a signal. This hierarchical data structure is generated by repeated application of a REDUCE function (prefilter and down-sampler). A complementary EXPAND function (up-sampler and post-filter) allows a finer resolution mapping of any coarser level of the pyramid. Four equivalent representations of this pyramid are considered, and the corresponding REDUCE and EXPAND filters are determined explicitly for polynomial splines of any order n (odd). Some image processing examples are presented. It is demonstrated that the performance of the Laplacian pyramid can be improved significantly by using a modified EXPAND function associated with the dual representation of a cubic spline pyramid 相似文献
8.
A solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system. It is shown that the concept of disturbance attenuation, in the sense of truncated L 2 norms, can be given an interpretation in terms of the response to periodic inputs in the sense of RMS amplitude, even in the nonlinear setup. In the case of state feedback, a family of controllers is also provided. The proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem 相似文献
9.
A method is presented for the decomposition of the frequency domain of 2-D linear systems into two equivalent 1-D systems having dynamics in different directions and connected by a feedback system. It is shown that under some assumptions the decomposition problem can be reduced to finding a realizable solution to the matrix polynomial equation X (z 1)P (z 2 )+Q (z 1)Y (z 2 )=D (z 1, z 2). A procedure for finding a realizable solution X (z 1 ), Y (z 2) to the equation is given 相似文献
10.
The problems of filtering and smoothing are considered for linear systems in an H ∞ setting, i.e. the plant and measurement noises have bounded energies (are in L 2), but are otherwise arbitrary. Two distinct situations for the initial condition of the system are considered; the initial condition is assumed known in one case, while in the other the initial condition is not known but the initial condition, the plant, and measurement noise are in some weighted ball of R nXL 2. Finite-horizon and infinite-horizon cases are considered. Necessary and sufficient conditions are presented for the existence of estimators (both filters and smoothers) that achieve a prescribed performance bound, and algorithms that result in performance within the bounds are developed. In case of smoothers, the optimal smoother is also presented. The approach uses basic quadratic optimization theory in a time-domain setting, as a consequence of which both linear time-varying and time-invariant systems can be considered with equal ease. (In the smoothing problem, for linear time-varying systems, one considers only the finite-horizon case) 相似文献
11.
It is shown that D.S. Bernstein and W.M. Hadad's (ibid., vol.34, no.3, p.293, 1989) necessary condition for full-order mixed H 2 and H ∞ optimal control is also sufficient, and that J.C. Doyle et al.'s (Proc. Amer. Control Conf., p.2065, 1989) sufficient condition for full-order mixed H 2 and H ∞ optimal control is also necessary. They are duals of one another 相似文献
12.
Some transient and asymptotic performance properties are established for the model reference adaptive controller proposed by A.S. Morse (Proc. US-Italy Joint Seminar Syst., Models Feedback 1992). It is proved that the L 2 norm of the tracking error is uniformly bounded by the initial parameter estimation error. Further, if the initial conditions are sufficiently small, it is shown that the L ∞ norm of the tracking error is uniformly bounded by the L m2 norm of the reference signal. These transient bounds are independent of the signals richness and the adaptation gain, making them arguably the strongest transient results available in the literature. Second, excitation conditions for exponential stability, a property which is well known to insure some local performance measures, are given. To this end, it is shown that, modulo a signal dependent time scale change, Morse's estimator is equivalent to a normalized gradient plus filtering identifier 相似文献
13.
The solution of the l 1 sensitivity minimization problem is shown to have two properties which contrast markedly with properties of the solutions to the better-known H ∞ sensitivity minimization problem or the LQG (linear quadratic Gaussian) problem is given of a one-parameter family of first-order plants where the order of the l 1-optimal compensator can be arbitrarily large, and thus it is impossible to bound the order of an l 1-optimal compensator in terms of the order of the plant. A plant is considered which has a continuous one-parameter family of l 1-optimal compensators, and thus l 1-optimal compensators need not be unique. The author's two examples are considered to answer two questions left open by M.A. Daleh and J.B. Pearson (ibid., vol.32, p.314-23, 1987) 相似文献
14.
An LQG (linear quadratic Gaussian) control-design problem involving a constraint on H ∞ disturbance attenuation is considered. The H ∞ performance constraint is embedded within the optimization process by replacing the covariance Lyapunov equation by a Riccati equation whose solution leads to an upper bound on L 2 performance. In contrast to the pair of separated Riccati equations of standard LQG theory, the H ∞-constrained gains are given by a coupled system of three modified Riccati equations. The coupling illustrates the breakdown of the separation principle for the H ∞ -constrained problem. Both full- and reduced-order design problems are considered with an H ∞ attenuation constraint involving both state and control variables. An algorithm is developed for the full-order design problem and illustrative numerical results are given 相似文献
15.
The robust optimal control of linear uncertain systems with L 2-bounded uncertainties is addressed. The optimal state feedback control law in the so-called worst disturbance case is derived. The LQL method, minimax state estimation-maximin state feedback closed loop control scheme (LQL means linear quadratic L 2-bounded uncertainties), is proposed. In a sense, the LQL method uses the idea of the linear-quadratic-Gaussian (LQG) method to treat H ∞-optimizing design problems 相似文献
16.
Frankl P.G. Weyuker E.J. 《IEEE transactions on pattern analysis and machine intelligence》1993,19(3):202-213
Several relationships between software testing criteria, each induced by a relation between the corresponding multisets of subdomains, are examined. The authors discuss whether for each relation R and each pair of criteria, C 1 and C 2 , R (C 1, C 2) guarantees that C 1 is better at detecting faults than C 2 according to various probabilistic measures of fault-detecting ability. It is shown that the fact that C 1 subsumes C 2 does not guarantee that C 1 is better at detecting faults. Relations that strengthen the subsumption relation and that have more bearing on fault-detecting ability are introduced 相似文献
17.
Previously obtained results on L 2-gain analysis of smooth nonlinear systems are unified and extended using an approach based on Hamilton-Jacobi equations and inequalities, and their relation to invariant manifolds of an associated Hamiltonian vector field. On the basis of these results a nonlinear analog is obtained of the simplest part of a state-space approach to linear H ∞ control, namely the state feedback H ∞ optimal control problem. Furthermore, the relation with H ∞ control of the linearized system is dealt with 相似文献
18.
A new type of controller is proposed which detects the i th plant output N i times during a period of T 0 and changes the plant inputs once during T 0. It is shown that an arbitrary state feedback can be realized by such controllers if the plant is observable. This implies, for instance, that arbitrary symmetric pole assignment is possible if the plant is controllable. It is also shown that, if the plant has no zeros at the origin, the state transition matrix of the controller itself can be set arbitrarily without changing the state feedback to be realized. That is to say, inversely expressed, any state feedback can be equivalently realized by a controller with any prescribed degree of stability 相似文献
19.
The problem of tightly bounding and shaping the frequency responses of two objective functions T i(s )( i =1,2) associated with a closed-loop system is considered. It is proposed that an effective way of doing this is to minimize (or bound) the function max {∥T 1(s )∥ ∞, ∥T 2(s)∥∞} subject to internal stability of the closed-loop system. The problem is formulated as an H ∞ control problem, and an iterative solution is given 相似文献
20.
It is shown that the constant gain state-feedback solution to the infinite-time linear quadratic regulator problem is optimal not only for arbitrarily initial conditions or white noise disturbances, but also for worst-case L 1 disturbances. Using a similar technique, it is shown that in the stationary Kalman filter, the white disturbance and measurement noise can be replaced by unknown bounded energy signals, and that optimality still holds if the performance criterion is a time domain L ∞ normal of the state estimation errors in the presence of worst-case energy signals 相似文献