摘要:

In this paper we define and solve the multiple linear quadratic gaussian (LQG) problem for discrete-time systems using Salukvadze's ideal point method which treats dynamic, but deterministic, multicriteria optimization problems. The solution consists in designing a scalar regulator where the weighting matrices are replaced by the sums of their counterparts in the individual criteria. The resulting control is optimal, in the sense that it minimizes the difference between the cost of the implemented policy from the cost that would occur if we optimized each criterion separately and added the outcomes. All the nice properties of the scalar LQG regulator are enjoyed by the multicriteria regulator as well. Extension to the continuous-time case is straightforward, yielding identical results.

ISSN:0020-7179    

DOI:10.1080/00207178608933470

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

A solution to the Hx optimal-control problem is obtained by employing a standard LQG polynomial-based solution procedure. The derivation is straightforward and avoids many of the more abstract mathematical results usually employed. The relationship between the LQG and Hm design methods becomes transparent and the similarities and differences can be identified.

ISSN:0020-7179    

DOI:10.1080/00207178608933471

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The fixed-point method is developed for obtaining an efficient numerical solution of the linear quadratic gaussian problem for singularly perturbed systems. It is shown that each iteration step improves the accuracy by an order of magnitude, that is, the accuracy 0(ek) can be obtained by performing only k — 1 iterations. In addition, only low-order systems are involved in algebraic manipulations and no analyticity requirements are imposed on the system coefficients.

ISSN:0020-7179    

DOI:10.1080/00207178608933472

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The problem of minimizing the sensitivity of the output or input of a plant under a feedback control with respect to external additive disturbances is considered. The mathematical model assumed for the plant is a rectangular matrix of transfer functions which can arise from both lumped-parameter and distributed-parameter systems (including time delays). The feedback controller is assumed to guarantee the closed-loop stability. It is shown that an arbitrarily small sensitivity function on a compact set of complex frequencies can be obtained by a suitable choice of feedback transfer function, provided no zero of the plant transfer function is in this set. Additionally, the sensitivity function can be designed to be bounded on an unbounded region containing the imaginary axis, if there are no zeros of the plant in the right half-plane and a certain hypothesis holds. Multiplicative delays are not excluded. If there are zeros in the right half-plane the latter design is not realizable, since minimizing the sensitivity on a bounded interval implies its increasing without bounds on the remaining part of the imaginary axis (an appropriate inequality is derived) The paper extends recent results of Zames and coworkers.

ISSN:0020-7179    

DOI:10.1080/00207178608933473

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

An improvement of the quantitative feedback theory (QFT) (Horowitz 1982) for MIMO systems is presented. The advantages of this approach are as follows, (a) In the ‘improved method’ the fundamental design relation (for theith free functionli,) has the form |1 +li| > φ(buv,quv) wherebuvare related to the performance tolerances of the closed loop, andquvto the plant parameters. We show that the right side can be replaced by a constant. This makes the design much easier and even more economical in terms of cost of feedback, (b) The SISO systems that replace the original MIMO problem are now defined by induction. This gives a better insight into the tradeoffs between the loop transmissions and make computer implementation easier.

ISSN:0020-7179    

DOI:10.1080/00207178608933474

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

We present some bounds for the eigenvalues and certain sums and products of the eigenvalues of the solution of the discrete Riccati and Lyapunov matrix equations and the continuous Lyapunov matrix equation. Nearly all of our bounds for the discrete Riccati equation are new. The bounds for the discrete and continuous Lyapunov equations give a completion of some known bounds for the extremal eigenvalues and the determinant and the trace of the solution of the respective equation.

ISSN:0020-7179    

DOI:10.1080/00207178608933475

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

We present a numerical method of solving the time-varying Lyapunov and Sylvester matrix differential equations. The method is easy to program, fast, and accurate. It is shown that the error of computation is O(Δt3) where Δtis the interval of computation. Two examples are given.

ISSN:0020-7179    

DOI:10.1080/00207178608933476

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

We present a technique for overestimating the reachable set from the origin for a class ofn-dimensional linear control systems. The proposed ‘box’ method is based upon decomposing the system into one and two-dimensional subsystems for which bounds on the new variables can readily be found. Using these bounds enables the construction of an-dimensional parallelepiped containing the reachable set of the original system. Examples of this procedure are given as well as a comparison to an overapproximation afforded by a Lyapunov approach.

ISSN:0020-7179    

DOI:10.1080/00207178608933477

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Sufficient conditions of asymptotic stability independent of delay of both the retarded and neutral types of delay-differential systems are obtained. The main results are based on the sufficient conditions under which the roots of the determinant of a given (l,l) complex matrix polynomial lie either in the open left half-plane or inside the unit circle. Therefore the explicit computation of the determinant polynomial is not required.

ISSN:0020-7179    

DOI:10.1080/00207178608933478

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

This note proposes a new model for neutral delay-differential systems, in which the state space is M2, commonly used for the study of retarded systems, rather than W12which is more conventional for the study of neutral systems. This M2model is derived using the realization procedure proposed previously by Yamamoto (1982). The M2model derived is also seen to be advantageous in obtaining a ‘diagram configuration’ of the model.

ISSN:0020-7179    

DOI:10.1080/00207178608933479

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor