This paper develops the double generating function method for the discrete-time linear quadratic optimal control problem. This method can give generators for optimal solutions only in terms of pre-computed coefficients and boundary conditions, which is useful for the on-line repetitive computation for different boundary conditions. Moreover, since each generator contains inverse terms, the invertibility analysis is also performed to conclude that the terms in the generators constructed by double generating functions with opposite time directions are invertible under some mild conditions, while the terms with the same time directions will become singular when the time goes infinity which may cause instability in numerical computations. Examples demonstrate the effectiveness of the developed method.

Discrete-Time fractional Brownian motion (DFBM) and its increment process, called discrete-time fractional Gaussian noise (DFGN), are usually used to describe natural and biomedical phenomena. These two processes are dominated by one parameter, called the Hurst exponent, which needs to be estimated in order to capture the characteristics of physical signals. In the previous work, a variance estimator for estimating the Hurst exponent directly via DFBM was provided, and it didn't consider point selection for linear regression. Since physical signals often appear to be DFGN-type, not DFBM-type, it is imperative to first transform DFGN into DFBM in real applications. In this paper, we show that the variance estimator possesses another form, which can be estimated directly via the autocorrelation functions of DFGN. The above extra procedure of transforming DFGN into DFBM can thus be avoided. On the other hand, the point selection for linear regression is also considered. Experimental results show that 4-point linear regression is almost optimal in most cases. Therefore, our proposed variance estimator is more efficient and accurate than the original one mentioned above. Besides, it is also superior to AR and MA methods in speed and accuracy.

This paper considers the discrete model of the cart-pendulum system modeled by discrete mechanics, which is known as a good discretizing method for mechanical systems and has not been really applied to control theory. We first sum up basic concepts on discrete mechanics and discuss the explicitness of the linear approximation of the discrete Euler-Lagrange Equations. Next, the discrete cart-pendulum system is derived and analyzed from the viewpoint of solvability of implicit nonlinear control systems. We then show a control algorithm to stabilize the discrete cart-pendulum based on the discrete-time optimal regulator theory. Finally, some simulations are shown to demonstrate the effectiveness of the proposed algorithm.

In optical packet switches, the overhead of reconfiguring a switch fabric is not negligible with respect to the packet transmission time and can adversely affect switch performance. The overhead increases the average waiting time of packets and worsens throughput performance. Therefore, scheduling packets requires additional considerations on the reconfiguration frequency. This work intends to analytically find the optimal reconfiguration frequency that minimizes the average waiting time of packets. It proposes an analytical model to facilitate our analysis on reconfiguration optimization for input-buffered optical packet switches with the reconfiguration overhead. The analytical model is based on a Markovian analysis and is used to study the effects of various network parameters on the average waiting time of packets. Of particular interest is the derivation of closed-form equations that quantify the effects of the reconfiguration frequency on the average waiting time of packets. Quantitative examples are given to show that properly balancing the reconfiguration frequency can significantly reduce the average waiting time of packets. In the case of heavy traffic, the basic round-robin scheduling scheme with the optimal reconfiguration frequency can achieve as much as 30% reduction in the average waiting time of packets, when compared with the basic round-robin scheduling scheme with a fixed reconfiguration frequency.

This letter is devoted to derivation of a transformation law which converts a class of nonlinear affine control systems with n-states and 2-iputs into simpler systems with chained structure. First, we give a problem formulation that we consider throughout this letter. We next introduce a transformation law and gives its mathematical certification. Then, we apply the transformation method to an example and consider control design based on chained structure for the example in order to confirm the effectiveness of our approach.

This paper presents an ultra-wideband amplifier embedded with band-pass filter design. The scattering parameters of a frequency-domain GaAs field effect transistor are converted into z-domain representations by employing the weighted linear least squares method. A least squares scheme is employed to obtain characteristic impedances of transmission line elements that form the amplifier having a flat gain in the passband and good fall-off selectivity in the stopband. Experimental results illustrate the validity of the proposed design method.

The robust reduced order observer for a class of discrete-time Lipschitz nonlinear systems with external disturbance is proposed. It is shown that the proposed observer design can suppress the effect on the estimation error of external disturbance up to the prescribed level. Also, linear matrix inequalities are used to represent sufficient conditions on the existence of the proposed observer. Moreover, the maximum admissible Lipschitz constant of the proposed design is obtained for a given disturbance attenuation level. Finally, an illustrative example is given to verify the effectiveness of the proposed design.

This paper proposes the Gramian-preserving frequency transformation for linear discrete-time state-space systems. In this frequency transformation, we replace each delay element of a discrete-time system with an allpass system that has a balanced realization. This approach can generate transformed systems that have the same controllability/observability Gramians as those of the original system. From this result, we show that the Gramian-preserving frequency transformation gives us transformed systems with different magnitude characteristics, but with the same structural property with respect to the Gramians as that of the original system. This paper also presents a simple method for realization of the Gramian-preserving frequency transformation. This method makes use of the cascaded normalized lattice structure of allpass systems.

Software rejuvenation is a preventive and proactive solution that is particularly useful for counteracting the phenomenon of software aging. In this article, we consider periodic software rejuvenation models based on the expected cost per unit time in the steady state under discrete-time operation circumstance. By applying the discrete renewal reward processes, we describe the stochastic behavior of a telecommunication billing application with a degradation mode, and determine the optimal periodic software rejuvenation schedule minimizing the expected cost. Similar to the earlier work by the same authors, we develop a statistically non-parametric algorithm to estimate the optimal software rejuvenation schedule, by applying the discrete total time on test concept. Numerical examples are presented to estimate the optimal software rejuvenation schedules from the simulation data. We discuss the asymptotic behavior of estimators developed in this paper.

This paper discusses the behavior of the second-order modes (Hankel singular values) of linear discrete-time systems under bounded-real transformations, where the transformations are given by arbitrary transfer functions with magnitude bounded by unity. Our main result reveals that the values of the second-order modes are decreased under any of the above-mentioned transformations. This result is the generalization of the theory of Mullis and Roberts, who proved that the second-order modes are invariant under any allpass transformation, i.e. any lossless bounded-real transformation. We derive our main result by describing the controllability/observability Gramians of transformed systems with the help of the discrete-time bounded-real lemma.

A multiple-places reservation discipline is studied in a discrete-time priority queueing system. We obtain the joint distribution of system state, from which the delays of high and low priority packets are derived. Comparison is made with the cases of FIFO, single-place reservation discipline and HOL priority.

This paper studies the problem of the relations between existence conditions of common quadratic and those of common infinity-norm Lyapunov functions for sets of discrete-time linear time-invariant (LTI) systems. Based on the equivalence between the robust stability of a class of time-varying systems and the existence of a common infinity-norm Lyapunov function for the corresponding set of LTI systems, the relations are determined. It turns out that although the relation is an equivalent one for single stable systems, the existence condition of common infinity-norm type is strictly implied by that of common quadratic type for the set of systems. Several existence conditions of a common infinity-norm Lyapunov functions are also presented for the purpose of easy checking.

A new control scheme is proposed to improve the system performance for discrete-time fuzzy systems by tuning control grade functions using neural networks. According to a systematic method of constructing the exact Takagi-Sugeno (T-S) fuzzy model, the system uncertainty is considered to affect the membership functions. Then, the grade functions, resulting from the membership functions of the control rules, are tuned by a back-propagation network. On the other hand, the feedback gains of the control rules are determined by solving a set of LMIs which satisfy sufficient conditions of the closed-loop stability. As a result, both stability guarantee and better performance are concluded. The scheme applied to a truck-trailer system is verified by satisfactory simulation results.

The lifting scheme is an efficient and flexible method for the construction of linear and nonlinear wavelet transforms. In this paper, a novel lossless image coding technique based on the lifting scheme using discrete-time cellular neural networks (DT-CNNs) is proposed. In our proposed method, the image is interpolated by using the nonlinear interpolative dynamics of DT-CNN, and since the output function of DT-CNN works as a multi-level quantization function, our method composes the integer lifting scheme for lossless image coding. Moreover, the nonlinear interpolative dynamics by A-template is used effectively compared with conventional CNN image coding methods using only B-template. The experimental results show a better coding performance compared with the conventional lifting methods using linear filters.

This paper proposes an analysis and design methodology for the robust control of affine-in-control nonlinear systems subject to actuator saturation in discrete-time formulation. The robust stability condition is derived for the closed-loop system by the introduction of the fuzzy Kronecker delta. Based on the newly acquired stability condition, a design method is proposed to guarantee the robust H∞ performance. In the design, LMI-based pole placement is employed to use the freedom allowed in the selection of the controller. The validity of the proposed method is asserted by the computer simulation.

Evaluation of cyclic transitions in the discrete-time neural networks with antisymmetric and circular interconnection weights has been derived in an asymptotic mathematical form. The type and the number of limit cycles generated by circular networks, in which each neuron is connected only to its nearest neurons, have been investigated through analytical method. The results show that the estimated numbers of state vectors generating n- or 2n-periodic limit cycles are an exponential function of (1.6)n for a large number of neuron, n. The sufficient conditions for state vectors to generate limit cycles of period n or 2n are also given.

A new robust extended Kalman filter is proposed for the discrete-time nonlinear systems with norm-bounded parameter uncertainties. After linearization of the nonlinear systems, the uncertainties described by the energy bounded constraint can be converted into an indefinite quadratic cost function to be minimized. The solution to the minimization problem is given by the extended Kalman filter derived in a Krein space, which leads to a robust version of the extended Kalman filter. Since the resulting robust filter has the same structure as a standard extended Kalman filter, the proposed filter can be readily designed by simply including the uncertainty terms in its formulas. The results of simulations are presented to demonstrate that the proposed filter achieves the robustness against parameter variation and performs better than the standard extended Kalman filter.

Software rejuvenation is a proactive fault management technique that has been extensively studied in the recent literature. In this paper, we focus on an example for a telecommunication billing application considered in Huang et al. (1995) and develop the discrete-time stochastic models to estimate the optimal software rejuvenation schedule. More precisely, two software availability models with rejuvenation are formulated via the discrete semi-Markov processes, and the optimal software rejuvenation schedules which maximize the steady-state availabilities are derived analytically. Further, we develop statistically non-parametric algorithms to estimate the optimal software rejuvenation schedules, provided that the complete sample data of failure times are given. Then, a new statistical device, called the discrete total time on test statistics, is introduced. Finally, we examine asymptotic properties for the statistical estimation algorithms proposed in this paper through a simulation experiment.

In this paper, we propose a novel higher order time-frequency distribution (GDH) for a discrete time signal. This distribution is defined over the original discrete time-frequency grids through a delicate discretization of an equivalent expression of a higher order distribution, for a continuous time signal, in [4]. We also present a constructive design method, for the kernel of the GDH, by which the distribution satisfies (i) the alias free condition as well as (ii) the marginal conditions. Numerical examples show that the proposed distributions reasonably suppress the artifacts which are observed severely in the Wigner distribution and its simple higher order generalization.

This paper proposes new recursive fixed-point smoother and filter using covariance information in linear discrete-time stochastic systems. In this paper, to be able to treat the estimation of the stochastic signal, a performance criterion, extended from the criterion in the H estimation problem, is newly proposed. The criterion is transformed equivalently into a min-max principle in game theory, and an observation equation in a Krein space is obtained as a result. The estimation accuracy of the proposed estimators are compared with the recursive least-squares (RLS) Wiener estimators, the Kalman filter and the fixed-point smoother based on the state-space model.