摘要:

In the paper we consider time-varying systems with coefficients depending mero-morphically on time. In differential operator representations these systems are described by matrices over a skew polynomial ring with coefficients in the field of real meromorphic functions. Different kinds of indices (controllability, minimal, geometric and dynamical) are introduced and it is proved that they essentially coincide. The input module and the formal transfer matrix are defined and used for an algebraic description of time-varying systems. A characterization of system equivalence is given in these terms and also a complete list of invariants of similarity for time-varying state-space systems.

ISSN:0020-7179    

DOI:10.1080/00207178508933396

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

This paper investigates the problem of controlling a discrete-time linear system with jump parameters. A review of the literature is presented as well as a development of the application of dynamic programming to this class of control problems. Dynamic programming has been applied by many researchers and it was observed that no closed-form analytical solution could be constructed because of the ‘dual’ aspects of the controller. The main contribution of the present work is an algorithm, suitable for computer implementation, for the optimal dual control. The construction of the algorithm is based on transforming the dynamic programming relations into a space of sufficient statistics and using a finite-dimensional optimization procedure to obtain the optimal control as a function of the statistics. This is achieved by first developing a suitable recursive realization of a ‘filter’ which generates the sufficient statistics for the problem and then embedding this filter into the dynamic programming equations. Several examples are presented to illustrate the use of the algorithm for constructing optimal and suboptimal controllers.

ISSN:0020-7179    

DOI:10.1080/00207178508933397

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

The problem of discrete-time stochastic model reduction (approximation) is considered. Using the canonical correlation analysis approach of Akaike (1975), a new order-reduction algorithm is developed. Furthermore, it is shown that the inverse of the reduced-order realization is asymptotically stable. Next, an explicit relationship between canonical variables and the linear least-squares estimate of the state vector is established. Using this, a more direct approach for order reduction is presented, and also a new design for reduced-order Kalman filters is developed. Finally, the uniqueness and symmetry properties for the new realization—the balanced stochastic realization—along with a simulation result, are presented.

ISSN:0020-7179    

DOI:10.1080/00207178508933398

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

We deal with Stackelberg games in which a leader has access not only to the state information but also to information on the follower's strategy. We derive sufficient conditions for incentive schemes using information on the follower's strategies in both linear and non-linear differential games, and show that the incentive schemes using information on the follower's strategies depend on an initial state value. We also derive a sufficient condition for the incentive scheme using the follower's strategy in the linear quadratic differential game with infinite time interval.

ISSN:0020-7179    

DOI:10.1080/00207178508933399

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

Several digital control algorithms for linear single-input single-output systems are examined and the effect of the sampling period on their performance is analysed in terms of rippling, overshoot and settling time. The problem is addressed in the frequency domain (z-transform) and it is shown that each controller works for some classes of systems but that none works for all. The similarities and differences of these controllers are established and an explanation of their deficiencies is given based on the location of the zeros of the discrete system. The insight gained leads to a simple new rule for the design of a controller which combines the advantages of the different algorithms but at the same time is free of their problems. A single tuning parameter is included which directly affects the closed-loop speed of response and bandwidth. The parameter can be used to detune the controller in the event that the real system differs from the model on which the controller design is based. No tuning is necessary when the available model is exact, unless smaller values for the manipulated variable, at the cost of a slower response, are preferred.

ISSN:0020-7179    

DOI:10.1080/00207178508933400

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

A method is proposed for the design of constant-gain feedback-control laws for linear multivariable discrete-time systems which reduce trajectory sensitivity to small system parameter variations and ensure the closed-loop eigenvalues at the origin. The given quadratic index of performance including a sensitivity term is minimized in an average sense. An efficient computational procedure based on direct cost optimization using gradient type algorithm is also reported. An example is worked out to illustrate the proposed technique.

ISSN:0020-7179    

DOI:10.1080/00207178508933401

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

This paper is concerned with the synthesis of a state feedback control system which possesses both integrity and good responses. System integrity in multivariable control systems is defined as the property that the overall closed-loop system remains asymptotically stable in the presence of a failure in the feedback loop. A state feedback control law which retains asymptotic stability against arbitrary actuator failure is derived using a positive semidefinite solution of a type of matrix quadratic equation, and some properties of the closed-loop system are considered. Moreover, a design procedure by which the closed-loop system has the desired dynamical characteristics while maintaining integrity is proposed, and the effectiveness of the procedure is demonstrated with a numerical example.

ISSN:0020-7179    

DOI:10.1080/00207178508933402

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

We present here a new method for realization ofminimal-order proper rational transfer functions from z-domain samples. A criterion for determining the minimal order of the transfer function is given. The theory is developed first for strictly proper rational transfer functions and then extended to the case of transfer functions with a direct-coupling term. The theory is valid for arbitrary z-domain samples. The special case of uniform frequency response samples is shown to allow a computationally efficient derivation of the realization. Examples are given to illustrate the theory. The theory developed here has many applications, such as modelling of communication channels, identification of systems from frequency measurements and infinite impulse response filter design.

ISSN:0020-7179    

DOI:10.1080/00207178508933403

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

In this work the disturbance decoupling problem in decentralized linear systems (DDPD) is formulated and solved without making any assumption on the kind of decentralized pattern of information in the system. Necessary and sufficient conditions are given under which disturbance decoupling is possible by applying local control laws formed by a combination of measured disturbance feedforward and non-dynamic feedback of state or measurement. For the solution of DDPD, the new geometric concepts ofk—(A, Bi, 𝓈i)- andk-(CiA, Bi)-invariant subspaces are developed. They extend the(A, B)- and(C, A, B)-invariance respectively to decentralize systems. A geometric description of the maximal elements of the class of these subspaces that are candidates for generating a solution to various DDPDs considered are also developed. Numerical examples are given.

ISSN:0020-7179    

DOI:10.1080/00207178508933404

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor

摘要:

This work extends disturbance decoupling to decentralized linear systems with direct control and disturbance feedthrough. Necessary and sufficient conditions are given under which disturbance decoupling is possible by applying local state of measurement feedback laws combined with measured disturbance feedforwards. Numerical examples are given.

ISSN:0020-7179    

DOI:10.1080/00207178508933405

出版商:Taylor & Francis Group    

年代:1985

数据来源: Taylor