On the stability of time-varying systems using an observer for feedback control†

The effects upon stability are considered when an observer is incorporated in a time-varying system to estimate the immeasurable state variables in order to implement the feedback control law.     

On the controllability of systems with a time-varying delay†

This paper is concerned with the controllability of a system with a time-varying delay. The system to be considered here is described by a linear differential-difference equation of a retarded type, where a time-varying delay is a certain class of a time-varying function. First, the concepts of controllability for linear differential-difference systems with a constant delay, introduced by Weiss (1987), are developed to the system with a time-varying delay. Second, necessary and sufficient conditions for controllability are obtained. Finally, the controllability of a stationary system with a constant delay is treated, including the results of Chyung and Lee (1966).     

On the stability of interconnected systems†

This paper investigates the stability of systems which can be regarded as composed of interconnected subsystems. A sufficient condition for inputs-output L ^p stability, in terms of the L ^p gains of the subsystems and their interconnections is derived. For the case of L ² stability, it is compared with other criteria for asymptotic stability, obtained by Lyapunov techniques, and shown to give better results for a certain class of systems.     

Controllability of linear time-varying systems with delay in control†

This paper is concerned with the study of controllability of linear systems with delay in the control function. It has been illustrated that many of the techniques which proved to be useful in the study of linear systems with no delay (alman et al. 19G2, Kroindlcr and Sarachik 1964) can be generalized when dealing with systems having delay in the control.

An explicit expression is given for transferring a given state to any desired state using minimum control energy.

The corresponding conditions for linear time-invariant systems (ebakhy and Bayoumi 1971) are obtained as a special case. Extensions to multiple- delays systems are also included.

A new degree of controllability is introduced and the corresponding criteria are obtained.     

On the decoupling of multivariable control systems with time delays†

The decoupling problem is solved for an m-input m-output linear time-invariant system with multiple delays in the state and/or the control. The conditions under which such a system can be decoupled are found and the class of the feedback decoupling operators is given. These operators are realized by means of digital filters. Then, the more general linear model in which the input effects directly the output is considered which, upon the introduction of both feedback and feedforward, is shown to be decoupled, Two illustrative examples are included to support the theoretical results.     

On the asymptotic stability of a particular class of distributed parameter feedback control systems†

In this paper the stability problem for a particular class of non-linear feedback control systems governed by a parabolic partial differential equation is considered. A sufficient condition for global asymptotic stability of the null equilibrium state is derived by the method of comparison functions.     

On various types of decoupling for time-varying systems†

This paper deals with the problem of decoupling a class of linear time-varying multi-variable systems, based on the defining property that the impulse response matrix of a decoupled system is diagonal. Depending on the properties of the coefficient matrices of the vector differential equation of the open-loop system, the system may be uniformly or totally decoupled. The necessary and sufficient conditions that permit a system to be uniformly or totally decoupled by state variable feedback are given. The main contribution of this paper is the precise definition of these two classes of decoupling and a rigorous derivation of the necessary and sufficient conditions which show the necessity of requiring that the system be of constant ordered rank with respect to observability. A simple example illustrates the importance of having several definitions of decoupling. Finally, the results are specialized to the case of time invariant systems.     

On the stability of a class of non-linear continuous systems†

A procedure to find the existence and domain of asymptotic stability for a class of systems described by a set of non-linear partial differential equations is presented in the context of semigroup theory.

No a priori bound is imposed on the non-linearity which is assumed to be a quad ratic (bilinear) or multilinear form.

The linearized system can be non-self-adjoint and need not be asymptotically stable equation by equation.

The solution of the stability problem is carried out. in two steps :

(a) the development of an L₂-like norm that bounds above the sup norm, a requirement to obtain a useful estimate of the non-linear term, and

(a)the computation of an estimate of the L₂-likc norm of the semigroup generated by the linearized system in terms of its usual L₂ norm.     

On the design of optimal output feedback control systems†

For a linear control system with quadratic performance index the optimal control takes a feedback form of all state variables. However, if there are some states which are not fed in the control system, it is impossible to obtain the optimal feedback control by using the usual mathematical optimization technique such as dynamic programming or the maximum principle.

This paper presents the optimal control of output feedback systems for a quadratic performance index by using a new parameter optimization technique.

Since the optimal feedback gains depend on the initial states in the output feedback control system, two cases where (1) the initial states are known, and (2) the statistical properties of initial states such as mean and covariance matrices are known, are considered here. Furthermore, the proposed method for optimal output feedback control is also applied to sampled-data systems.     

On the design of optimal and sub-optimal control systems†

Though dynamic programming is an excellent and versatile algorithm, there are many cases in which we cannot apply this algorithm favourably to control system design because of the limited capacity of a digital computer and other difficulties.

Considering these facts, the successively optimizing method and the combined algorithm of dynamic programming and successively optimizing method are presented in this paper.

One of the objects of this paper is to present a practical method for obtaining the optimal solution of control systems with an integral form performance index by the use of dynamic programming.

The other is to present sub-optiinal solutions by the successively optimizing method and the combined algorithm.

These methods are very easy when compared with dynamic programming. Furthermore, these sub-optimal solutions can be made to converge to the optimum by using the recurrent equations repeatedly.     

Delay-dependent criteria for the robust stability of systems with time-varying delay

The problem of delay-dependent robust stability for systems with time-varying delay has been considered. By using the S-procedure and the Park's inequality in the recent issue, a delay-dependent robust stability criterion which is less conservative than the previous results has been derived for time-delay systems with time-varying structured uncertainties. The same idea has also been easily extended to the systems with nonlinear perturbations. Numerical examples illustrated the effectiveness and the improvement of the proposed approach.     

On performance sensitivity of optimal control systems†

Formulae for the differential, with respect to plant parameters of an optimized performance index (performance sensitivity), are extended to include hard (instantaneous) as well as soft (isoperimetric) constraints on the control. In particular, this extends to discontinuous and bang-bang controls the Pagurek-Witscnhausen result on the equality of such differentials for open and closed-loop optimal systems     

Sensitivity of optimal control systems with bang-bang control†

The effects of small parameter variations on the performance index of optimal control systems with initial and final target manifolds, free end time, and bang-bang control are analysed in this paper. A new approach to the sensitivity equation is presented. This approach takes into account the pulse-shaped variation produced by the parameter change on the bang-bang control. An expression, that relates the variations of the performance index, the trajoctory, the final time, and the parameter, is derived. This expression extends to the class of optimal systems with bang-bang control, a result previously obtained by Courtin and Rootenberg (1971).     

On the optimal control of two classes of non-linear distributed parameter systems†

An optimal control problem, for two classes of non-linear distributed parameter systems, is formulated. Sufficient conditions on the optimal control are derived. These conditions form a two-point boundary value problem of partial differential equations.     

On the stability problem for distributed parameter energy systems†

In this paper asymptotic stability of the non-trivial or operating equilibrium state of a distributed parameter energy system is considered. Sufficient conditions are obtained by the method of comparison functions. This enables one to obtain bounds on the maximum value of the state variables. The criteria derived depend on the eigenvalues of the linearized system as well as on a bound for the feedback control law.     

Design of control systems with random parameters†

In this paper a method for designing control systems with random parameters and random initial state is presented. The observed signal available for feedback is a function of the state and system parameters corrupted by additive white Gaussian noise with zero mean. The proposed control consists of an open-loop term, which is the optimal control for the parameters and initial state equal to their mean values, plus a feedback correction term. The feedback correction term is a linear function of the estimated values of the deviation in initial state and system parameters from their mean values. The control tends to the optimally sensitive control when the measurement noise tends to zero, and the feedback correction tends to zero when the measurement noise tends to infinity. A numerical experiment with a simplified model for nuclear reactor control shows that in spite of fairly large measurement noise, significant improvement in performance can be achieved using the proposed control compared to open-loop control.     

On the optimal control for a class of distributed parameter systems†

An optimal control problem for a class of distributed parameter systems is discussed. A non-linear integral equation of a signum type is derived as a necessary and sufficient condition for the optimal control. Under very weak conditions, existence and unique ness of the solution to this non-linear integral equation are proved.     

On the conjunction practical stability and controllability of large-scale impulsive control systems

1Introduction Asystem may be defined as a series of programs whichare designed to run sequentially.With the development ofscience,the scale of the systems with complicated structureis increasing.This causes the generationand development ofthe theory oflarge_scale system.Now,thelarge_scale systemhas become one of the important theoretic foundations ofthe systems engineering.There has been a significantdevelopment in the theory of impulsive differentialequations inthe past10years[1~3].If we wan…     

On the boundedness of the solutions of some systems with retarded arguments†

The boundedness of the solutions of delay-differential systems with large retardation is proved. The result is obtained by comparing with a system whose exact solutions are obtained.     

Effects of controller dynamics on the stability of a class of optimal control systems†

In this paper, the effects of controller dynamics on the stability characteristics of a class of multivariate optimal control systems are investigated. The results of this investigation indicate that the asymptotic stability of systems of this class may well be lost because of the practical impossibility of implementing control laws derived on the basis of the classical optimal control theory of Kalman (1960),