摘要:

The action of the Riccati group on the Riccati differential equation is associated with the action of a subgroup of the symplectic group on a set of hamiltonian matrices. Within this framework various sets of canonical forms are developed for the matrix coefficients of the Riccati differential equation. The canonical forms presented are valid for arbitrary Kronecker indices, and it is shown that the Kronecker indices are invariants for this group action. These canonical forms are useful for studying problems arising in the areas of optimal decentralized control and the spectral theory of optimal control problems.

ISSN:0020-7179    

DOI:10.1080/00207178308933118

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

This paper is concerned with the finite spectrum assignment problem for systems with multiple commensurate delays in state variables. The necessary and sufficient condition for finite spectrum assignability is clarified. A systematic design procedure which can straightforwardly yield a control law is presented.

ISSN:0020-7179    

DOI:10.1080/00207178308933119

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The structure of the Smith-MacMillan form of a rational matrixT(s) inside a regionP=ω∪{∞} (where ω is asymmetric with respect to the real axis subset of the finite complex plane C) is determined. Algorithmic procedures based on elementary row and column operations over the euclidean ringRP(s) consisting of all rational functions with no poles inPare given. Coprimeness inPof a pair of rational matrices is studied in detail. These results lead to constructive procedures for determining the coprime inPmatrix fraction descriptions ofT(a).

ISSN:0020-7179    

DOI:10.1080/00207178308933120

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

A difference approximation to a singularly perturbed linear, time-varying, continuous-time control system is presented, and is called a singularly perturbed linear discrete-time control system. Under several assumptions, it is shown that the Riccati equation for the reduced system, in the sense of singular perturbation, agrees with that for the associated subsystem of the full (non-reduced) system when a small parameter in the equation is set zero. On the basis of this result, it is also shown that the optimal controls and the corresponding trajectories for the two systems are consistent with each other when a small parameter for the full system is set zero.

ISSN:0020-7179    

DOI:10.1080/00207178308933121

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

This paper studies the feedback and filter properties of the Smith regulator and concludes that it does not in any way alleviate the sensitivity and disturbance attenuation limitations in feedback systems with non-minimum phase plants. Also, its single advantage is shown to be in the realization of one-degree-of-freedom feedback structures, wherein the non-minimum phase constraints preclude the achievement, in the typical conventional design, of a bandwidth (rise time) which may be within the plant's capabilities. Even then, this is secured only for command input tracking, but its sensitivity and disturbance regulation properties in the extra achieved band width are worse than in an open-loop design. They may also easily be much poorer in the low frequency range than in a conventional design. A modification exists for a sub-class of plants where the output of the nmp plant element- may be measured and used for feedback purposes. It has whatever advantage of the original and better sensitivity to the nmp elements and disturbance regulation.

ISSN:0020-7179    

DOI:10.1080/00207178308933122

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

This paper considers the identification of a class of stochastic bilinear systems in which the transfer matrix in state equation is the sum of a constant matrixAand a random matrixS(i), and observation equation is linear. Estimations of covariance matrices of the random disturbances, including the state noise, observation noise and random part in transfer matrix, associated with this system are also presented. Strong consistency of the estimations is also established.

ISSN:0020-7179    

DOI:10.1080/00207178308933123

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The operational properties of the forward and backward integration and the product of Chebyshev polynomials are derived. These properties are applied to the analysis and optimal control of time-varying linear systems by the approximation of time functions by truncated Chebyshev series. Due to the unique property of the Chebyshev polynomials excellent results are obtained as demonstrated by examples.

ISSN:0020-7179    

DOI:10.1080/00207178308933124

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The paper unifies proofs of several results on the stability of linear control systems. The proofs are based on a criterion of controllability derived in the paper. This criterion suggests an efficient test of controllability.

ISSN:0020-7179    

DOI:10.1080/00207178308933125

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

In this paper, sufficient conditions for chaos in non-linear sampled-data control systems are investigated by applying Marotto's (1978) Theorem and Shiraiwa and Kurata's (1980) Theorem. It is shown that a state-feedback sampled-data control system with sampling periodTis chaotic ifT >T*for sufficiently largoT*. It is also shown that if a sampled-data control system has an output-feedback and can be split into two subsystems, the existence of chaos in the system can be checked only by the lower-dimensional subsystem behaviour.

ISSN:0020-7179    

DOI:10.1080/00207178308933126

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The paper introduces the concept of mean square detectability and relates this to the recently introduced concept of mean square observability. It is shown that under appropriate mean square detectability and stabilizability conditions the infinite-horizon optimal control problem for the general case of linear discrete time systems and quadratic criteria, both with stochastic parameters which are statistically independent of time, has a unique solution when the control system is mean square stable. A simple necessary and sufficient condition, explicit in the system matrices, is given to determine if a system is mean square detectable. This condition also holds for deterministic systems to be detectable in the usual sense. The mean square detectability property coincides with the usual one if the parameters are deterministic.

ISSN:0020-7179    

DOI:10.1080/00207178308933127

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor