Problem Of Discrete-time Systems Research Articles

Overlapping Decentralized Guaranteed Cost Control Method for Discrete-Time Systems of Building Structures with Uncertain Parameters under Earthquake Action

This paper proposes a discrete-time overlapping decentralized guaranteed cost control algorithm via state feedback. Based on the inclusion principle, a structure system is decoupled into multiple subsystems, and the discretized subsystems’ controllers are designed by using the guaranteed cost control algorithm. Finally, the subsystems’ controllers are contracted into overlapping controllers of the original system, and the design of the control system is completed. This control method is introduced to the civil engineering field to solve the seismic control problem for discrete-time systems of building structures with uncertain parameters. The numerical analysis of the nine-story building structure model with uncertain parameters is carried out. The results show that the proposed control method can still effectively reduce the seismic response of discrete-time system when the structural parameters are uncertain, and the control effect is similar to the centralized control strategy; at the same time, the sampling rate and data transmission speed of the system are improved to ensure the reliability of the system. It illustrates the feasibility and effectiveness of the presented approach.

Tobit Kalman filter with channel fading and dead-zone-like censoring

In complex control systems, the channel fading and the measurement censoring are often unavoidable due to sudden environmental changes, intermittent transmission congestions, random failures and repairs of components. To this end, the Tobit Kalman filtering problem for discrete-time systems with the dead-zone-like censoring and channel fading is studied where the censoring and fading phenomena are, respectively, described by the Tobit measurement model and the -order Rice fading channel model. The design of the filter is carried out in two stages: (1) the state augmentation technique is firstly adopted to remove the time-delay effect caused by the fading channel; and (2) the statistical information of censored measurements is used to determine the optimal filter structure in the minimum mean-square error sense, where the orthogonal projection principle is utilised to avoid the deep correlations among the multiple random variables induced by measurement censoring and channel fading. Besides, the desired filter is also devised based on the approach of the conditional expectation. For the convenience of calculation, the filter with the dead-zone-like censoring is converted into an equivalent one with one-side censoring. Finally, a numerical example of estimating the ballistic ball rates is given to verify the effectiveness of the proposed filters.

Fault estimation and active fault-tolerant control for discrete-time systems in finite-frequency domain

The active fault-tolerant control (FTC) problem for discrete-time systems in finite-frequency domain is addressed based on faults’ estimation. By the descriptor system approach, the observers are designed such that the stability and H∞ performance index of dynamic error systems are analyzed in finite frequency domain. The estimation of faults is obtained by the designed observers. By using the estimation of faults, a H∞ FTC method is presented to show the stability analyses of closed-loop systems in term of GYP lemma. Numerical simulations are given to demonstrate proposed FTC methods’ effectiveness.

Stabilisation of discrete-time systems via Schur stability region

ABSTRACTIn this paper, we consider the stabilisation problem of discrete-time systems by affine compensator. Using the known properties of the Schur stability region of monic polynomials, we give conditions under which stabilising controllers exist. A necessary and sufficient condition is obtained when the difference of the order of the system and the number of stabilising parameters is one. In the general case, two solution algorithms: division-elimination and least-square minimisation algorithms are suggested.

Reachable Set Estimation for Discrete-Time Systems with Interval Time-Varying Delays and Bounded Disturbances

The reachable set estimation problem for discrete-time systems with delay-range-dependent and bounded disturbances is investigated. A triple-summation term, the upper bound, and the lower bound of time-varying delay are introduced into the Lyapunov function. In this case, an improved delay-range-dependent criterion is established for the addressed problem by constructing the appropriate Lyapunov functional, which guarantees that the reachable set of discrete-time systems with time-varying delay and bounded peak inputs is contained in the ellipsoid. It is worth mentioning that the initial value of the system does not need to be zero. Then, the reachable set estimation problem for time-delay systems with polytopic uncertainties is investigated. The effectiveness and the reduced conservatism of the derived results are demonstrated by an illustrative example.

Optimal discrete-time H∞/γ0 filtering and control under unknown covariances

ABSTRACTNew stochastic γ0 and mixed H∞/γ0 filtering and control problems for discrete-time systems under completely unknown covariances are introduced and solved. The performance measure γ0 is the worst-case steady-state averaged variance of the error signal in response to the stationary Gaussian white zero-mean disturbance with unknown covariance and identity variance. The performance measure H∞/γ0 is the worst-case power norm of the error signal in response to two input disturbances in different channels, one of which is the deterministic signal with a bounded energy and the other is the stationary Gaussian white zero-mean signal with a bounded variance provided the weighting sum of disturbance powers equals one. In this framework, it is possible to consider at the same time both deterministic and stochastic disturbances highlighting their mutual effects. Our main results provide the complete characterisations of the above performance measures in terms of linear matrix inequalities and therefore both the γ0 and H∞/γ0 optimal filters and controllers can be computed by convex programming. H∞/γ0 optimal solution is shown to be actually a trade-off between optimal solutions to the H∞ and γ0 problems for the corresponding channels.

Optimal tracking control for discrete-time systems with multiple input delays under sinusoidal disturbances

This study researches the tracking control problem for discrete-time systems with multiple input delays affected by sinusoidal disturbances. This study is organized around the expression of sinusoidal and disturbances and the delay-free transformation. First, based on the periodic characteristic of the sinusoidal disturbance, the sinusoidal disturbances are considered as the output of an exosystem. By proposing a discrete variable transformation, the discrete-time system with multiple input delays and the quadratic performance index are transformed into equivalent delay-free ones. Then, by constructing an augmented system that comprises the states of the exosystems of sinusoidal disturbances, the reference input, and the delay-free transformation systems, the original tracking problem is transformed into the optimal tracking problem for a delay-free system with respect to the simplified performance index. The optimal tracking control (OTC) law is obtained from Riccati and Stein equations. The existent and uniqueness of the optimal control law is proved. A reduced-order observer is constructed to solve the problem of physically realizable for the items of the reference input and sinusoidal disturbances. Finally, the feasibility and effectiveness of the proposed approaches are validated by numerical examples.

White noise estimation for discrete-time systems with random delay and packet dropout

This paper is concerned with the optimal and suboptimal deconvolution problems for discrete-time systems with random delayed observations. When the random delay is known online, i.e., time stamped, the random delayed system is reconstructed as an equivalent delay-free one by using measurement reorganization technique, and then an optimal input white noise estimator is presented based on the stochastic Kalman filtering theory. However, the optimal white-noise estimator is time- varying, stochastic, and doesn't converge to a steady state in general. Then an alternative suboptimal input white-noise estimator with deterministic gains is developed under a new criteria. The estimator gain and its respective error covariance-matrix information are derived based on a new suboptimal state estimator. It can be shown that the suboptimal input white-noise estimator converges to a steady-state one under appropriate assumptions.

Discrete-TimeH∞Preview Control Problem in Finite Horizon

This paper considers theH∞preview control problem for discrete-time systems. It investigates the problem via game theory and dynamic programming. Different from the existing results, on one hand, the proposed approach is suitable for dealing with the corresponding multiple preview channels problem; on the other hand, the approach provides a possibility in explaining how the preview controller improves theH∞performance and why the performance will be saturated.

Robust Quantized Guaranteed Cost Control

In this paper, the robust state feedback guaranteed cost control problem for discrete-time systems with signal quantization is studied. A dynamic quantization control strategy is proposed with updating the quantizer’s parameter such that the system is asymptotically stable and the performance index is with a upper bound.

On the Computation of Optimal Static Output Feedback Controllers for Discrete-Time Systems

In this article, we consider the static output feedback problem for discrete-time systems when complete set of state variables is not available. It has been reported that quasi-Newton methods have substandard performance on this problem. A structured quasi-Newton method with trust region globalization is analyzed and studied for solving this problem. Moreover, the classical Anderson-Moore method is enhanced by using the trust region mechanism to ensure global convergence instead of the line search technique. The algorithms are tested numerically on test problems of engineering applications.

H∞ Control for Networked Control Systems with Limited Communication

By the insertion of a limited communication network in the feedback control loop, this paper investigates the quantized H ∞ control problem for discrete-time systems with random packet losses. A new quantized random packet-loss model is proposed and exploited to study the relationship among the packet-loss rate, the upper bound of consecutive packet losses, the quantizer range and the system performance. A convex optimization method is proposed to optimize static quantzier ranges, and further an observer-based H ∞ control strategy with minimized static quantizer range is proposed to guarantee the closed-loop system exponentially mean-square stable and with a prescribed H ∞ disturbance attenuation level. A numerical example is given to illustrate the effectiveness and the significance of the proposed control method.

Stability of first and high order iterative learning control with data dropouts

This paper presents a stability analysis of the iterative learning control (ILC) problem for discrete-time systems when the plants are subject to output measurement data dropouts. It is assumed that data dropout occurs during the data transfers from the plant to the ILC controller, resulting in what is called intermittent ILC. Using the super-vector approach for ILC, the expectation of output error is used to develop conditions for stability of the first order ILC and high order ILC processes. Through the theoretical analysis, it is shown that the convergence of the intermittent ILC is guaranteed although some measurements are missing. The analysis is also supported by numerical examples.

Near-optimal tracking control for discrete-time systems with delayed input

This paper considers the near-optimal tracking control problem for discrete-time systems with delayed input. Using a variable transformation, the system with delayed input is transformed into a non-delayed system, and the quadratic performance index of the optimal tracking control is transformed into a relevant format. The optimal tracking control law is constructed by the solution of a Riccati matrix equation and a Stein matrix equation. A reduced-order observer is constructed to solve the physically realizable problem of the feedforward compensator and a near-optimal tracking control is obtained. Simulation results demonstrate the effectiveness of the optimal tracking control law.

Linear quadratic tracking problem for discrete‐time systems with multiple delays in single input channel

AbstractThe linear quadratic tracking problem for discrete‐time systems with multiple delays in single input channel is considered. In this paper, we provide an approach without resorting to system state augmentation. The optimal tracking control is given in terms of the current state, the previous inputs, and the output of an auxiliary backward deterministic delay system which is formulated for the first time in this paper. The solution relies on a Riccati difference equation of the same dimension as the plant (ignoring the delays). The key to our development is the establishment of a duality between the optimal tracking control and the optimal smoothing estimation of an associated stochastic backward system as well as the introduction of the auxiliary backward deterministic delay system. An analysis of the computational complexity of the proposed approach and its comparison with that of the augmentation method, which is to incorporate the delayed inputs into the augmented state, are provided. An example is given to demonstrate the effectiveness of the results. Copyright © 2009 John Wiley & Sons, Ltd.

Filtering for discrete-time linear noise delay systems

Optimal state estimation problem for discrete-time systems with delays in noise sequence is investigated. Predictor similar to the traditional Kalman ones is derived based on projection formula in Hilbert space. Filter and fixed-lag smoother are obtained at the same time. The estimators are presented by solving two coupled Riccati-type difference equations. One example shows the effectiveness of the proposed approach.

2-Regularity and 2-Normality Conditions in Discrete Optimal Control Problems

The paper is devoted to general optimal control problems for discrete-time systems with equality type of constraints on end points and control. We derive first-order necessary optimality conditions that are meaningful under the new nontriviality condition.

Stability analysis of discrete-time iterative learning control systems with interval uncertainty

This paper presents a stability analysis of the iterative learning control (ILC) problem for discrete-time systems when the plant Markov parameters are subject to interval uncertainty. Using the so-called super-vector approach to ILC, vertex impulse response matrices are employed to develop sufficient conditions for both asymptotic stability and monotonic convergence of the ILC process. It is shown that the stability of such interval ILC systems can be determined by checking the stability of the system using only the vertex points of the interval Markov parameters.

Discrete-time Systems—A Unified Approach

In this paper, the concept of delta operator formulation of Discrete-time systems is presented in a unified manner. The philosophy of the discrete-time modeling using delta operator and the investigation of the problem of discrete-time systems in modelling, identification and control without ignoring the underlying the continuous-time systems is discussed. Use of delta operator against the conventional shift operator is presented to heilight the improved numerical robustness of the computational algorithms at high sampling frequency

Singular $$\mathcal{H}$$ 2-optimization problems for discrete-time systems

Singular $$\mathcal{H}$$ 2-optimization problems are considered for the standard discrete-time control system. Two types of singularity (type I and type II) are distinguished. A detailed treatment of problems with singularity of type II, which leads to nonuniqueness of solution, is presented. New algorithms for design of optimal controllers are presented both in frequency domain and state space, which generalize standard procedures onto the case of singular $$\mathcal{H}$$ 2-problems. A parameterization of the set of optimal controllers is given.