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1.
Let φ(s ,a )=φ0(s ,a )+ a 1φ1(s )+a 2 φ2(s )+ . . .+a kφ k(s )=φ0(s )-q(s , a ) be a family of real polynomials in s , with coefficients that depend linearly on parameters a i which are confined in a k -dimensional hypercube Ωa . Let φ0(s ) be stable of degree n and the φi(s ) polynomials (i ⩾1) of degree less than n . A Nyquist argument shows that the family φ(s ) is stable if and only if the complex number φ0(j ω) lies outside the set of complex points -q (j ω,Ωa) for every real ω. In a previous paper (Automat. Contr. Conf., Atlanta, GA, 1988) the authors have shown that -q (j ω,Ωa ), the so-called `-q locus', is a 2k convex parpolygon. The regularity of this figure simplifies the stability test. In the present paper they again exploit this shape and show that to test for stability only a finite number of frequency checks need to be done; this number is polynomial in k , 0(k 3), and these critical frequencies correspond to the real nonnegative roots of some polynomials 相似文献
2.
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
3.
A network-theoretic approach to the design of a dynamic precompensator C (s ) for a multiinput, multioutput plant T (s ) is considered. The design is based on the relative degree of each element of T (s ). Specifically, an efficient algorithm is presented for determining whether a given plant T (s ) has a diagonal precompensator C ( s ) such that, for almost all cases, T (s )C (s ) has a diagonal interactor. The algorithm also finds any optimal precompensator, in the sense that the total relative degree is minimal. The algorithm can be easily modified to work even when a T (s ) represented by a nonsquare matrix is given 相似文献
4.
Cheetham R.P. Oommen B.J. Ng D.T.H. 《Knowledge and Data Engineering, IEEE Transactions on》1993,5(4):695-704
Consider a set A ={A 1,A 2 ,. . ., A n} of records, where each record is identified by a unique key. The records are accessed based on a set of access probabilities S =[s 1,s 2 ,. . ., s N] and are to be arranged lexicographically using a binary search tree (BST). If S is known a priori, it is well known that an optimal BST may be constructed using A and S . The case when S is not known a priori is considered. A new restructuring heuristic is introduced that requires three extra integer memory locations per record. In this scheme, the restructuring is performed only if it decreases the weighted path length (WPL) of the overall resultant tree. An optimized version of the latter method, which requires only one extra integer field per record has, is presented. Initial simulation results comparing this algorithm with various other static and dynamic schemes indicates that this scheme asymptotically produces trees which are an order of magnitude closer to the optimal one than those produced by many of the other BST schemes reported in the literature 相似文献
5.
The commenter argues that the result of the above-titled work (see ibid., vol.37, no.10, p.1558-1561, Oct. 1992) is incorrect. It is pointed out that when sampling a continuous-time system G (s ) using zero-order hold, the zeros of the resulting discrete-time system H (z ) become complicated functions of the sampling interval T . The system G (s ) has unstable continuous-time zeros, s =0.1±i . The zeros of the corresponding sampled system start for small T from a double zero at z =1 as exp(T (0.1±i )), i.e., on the unstable side. For T >1.067 . . . the zeros become stable. The criterion function of the above-titled work, F (T )=G *(j ωs/2)= H (-1)T /2, is, however, positive for all T , indicating only stable zeros. The zero-locus crosses the unit circle at complex values 相似文献
6.
The eigenvalue assignment problem of a T -periodic linear system using discrete periodic state feedback gains is discussed. For controllable systems, an explicit formula for the feedback law is given that can be used for the arbitrary assignment of the eigenvalues of Φc1(T ,0), the closed-loop state transition matrix from 0 to T . For the special case of periodic systems controllable over one period, this control law can be used to obtain any desired Φc1(T ,0) 相似文献
7.
Let a family of polynomials be P (s )=t 0s n+t 1s n±1 + . . . + t n where 0<a j⩽t j⩽b j. V.L. Kharitonov (1978) derived a necessary and sufficient condition for the above equation to have only zeros in the open left-half plane. The present authors derive some similar results for the equation to be strictly aperiodic (distinct real roots) 相似文献
8.
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
9.
Simultaneous controller design for linear time-invariant systems 总被引:1,自引:0,他引:1
The use of generalized sampled-data hold functions (GSHF) in the problem of simultaneous controller design for linear time-invariant plants is discussed. This problem can be stated as follows: given plants P 1, P 2, . . ., P N , find a controller C which achieves not only simultaneous stability, but also simultaneous optimal performance in the N given systems. By this, it is meant that C must optimize an overall cost function reflecting the closed-loop performance of each plant when it is regulated by C . The problem is solved in three aspects: simultaneous stabilization, simultaneous optimal quadratic performance, and simultaneous pole assignment in combination with simultaneous intersampling performance 相似文献
10.
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
11.
Let a family of polynomials be P (s )=t 0S n+t 1s n-1 . . .+t n where O <α j⩽t j⩽β. Recently, C.B. Soh and C.S. Berger have shown that a necessary and sufficient condition for this equation to have a damping ratio of φ is that the 2n+1 polynomials in it which have t k=αk or t k=βk have a damping ratio of φ. The authors derive a more powerful result requiring only eight polynomials to be Hurwitz for the equation to have a damping ratio of φ using Kharitonov's theorem for complex polynomials 相似文献
12.
Considers the polynomial P (s )=t 0 S n+t 1 S n-1 +···+t n where 0<a j⩽t j⩽b j. Recently, V.L. Kharitonov (1978) derived a necessary and sufficient condition for this polynomial to have only zeros in the open left-half plane. Two lemmas are derived to investigate the existence of theorems similar to the theorem of Kharitonov. Using these lemmas, the theorem of Kharitonov is generalized for P(s) to have only zeros within a sector in the complex plane. The aperiodic case is also considered 相似文献
13.
Explicit expressions for two different cascade factorizations of any detectable left invertible nonminimum phase systems are given. The first one is a well known minimum phase/all-pass factorization by which all nonminimum phase zeros of a transfer function G (s ) are collected into an all-pass factor V (s ), and G (s ) is written G m(s)V$ where G ms is considered as a minimum phase image of G (s ). The second one is a new cascade factorization by which G (s ) is rewritten as G M( s )U (s ) where U (s ) collects all `awkward' zeros including all nonminimum phase zeros of G ( s ). Both G m(s ) and G M(s ) retain the given infinite zero structure of G (s ). Further properties of G m(s ), G M(s ), and U (s ) are discussed. These factorizations are useful in several applications including loop transfer recovery 相似文献
14.
A general state-space representation is used to allow a complete formulation of the H ∞ optimization problem without any invertibility condition on the system matrix, unlike existing solutions. A straightforward approach is used to solve the one-block H ∞ optimization problem. The parameterization of all solutions to the discrete-time H ∞ suboptimal one-block problem is first given in transfer function form in terms of a set of functions in H ∞ that satisfy a norm bound. The parameterization of all solutions is also given as a linear fractional representation 相似文献
15.
The L 1 optimal control problem with rational controllers for continuous-time systems is considered in which it is shown that the optimal L 1 performance index with rational controllers is equal to that of irrational controllers. A sequence of rational controllers that approximates the optimal index is constructed. Convergence properties of such a sequence are studied. That the corresponding sequence of objective transfer functions is shown to converge in weak-* topology in BV (R +) in the time domain and uniformly in a wider sense in the frequency domain 相似文献
16.
The theorem states that every block square matrix satisfies its own m -D (m -dimensional, m ⩾1) matrix characteristic polynomial. The exact statement and a simple proof of this theorem are given. The theorem refers to a matrix A subdivided into m blocks, and hence having dimension at least m . The conclusion is that every square matrix A with dimension M satisfies several m -D characteristic matrix polynomials with degrees N 1 . . ., N m, such that N 1+ . . . +N m ⩽M 相似文献
17.
The problem of distributed detection with consulting sensors in the presence of communication cost associated with any exchange of information (consultation) between sensors is considered. The system considered has two sensors, S 1 and S 2; S 1 is the primary sensor responsible for the final decision u 0 , and S 2 is a consulting sensor capable of relaying its decision u 2 to S 1 when requested by S 1. The final decision u 0 is either based on the raw data available to S 1 only, or, under certain request conditions, also takes into account the decision u 2 of sensor S 2. Random and nonrandom request schemes are analyzed and numerical results are presented and compared for Gaussian and slow-fading Rayleigh channels. For each decision-making scheme, an associated optimization problem is formulated whose solution is shown to satisfy certain set design criteria that the authors consider essential for sensor fusion 相似文献
18.
It is proved that placing the poles of a linear time-invariant system arbitrarily far to the left of the imaginary axis is not possible if small perturbations in the model coefficients are taken into account. Given a nominal controllable system (A 0, B 0) with one input and at least two states and an open ball around B 0 (no matter how small), there exists a real number γ and a perturbation B within that ball such that for any feedback matrix K placing the eigenvalues of A 0+B 0K to the left of Res=γ, there is an eigenvalue of A 0+BK with real part not less than γ 相似文献
19.
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
20.
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