Artstein Reduction Research Articles

A novel distributed finite-time economic dispatch for DC microgrids with time delays

This paper delineates an advanced distributed control paradigm for finite-time generation cost optimization in DC Microgrids (MGs), taking into account time delays. Firstly, to enhance system stability with time delays, Artstein's reduction approch is utilized to convert the time-delayed system into an equivalent delay-free model. Subsequently, a finite-time consensus-based distributed algorithm for cost optimization is formulated to equilibrate the incremental costs (ICs) of all distributed generators (DGs) in a predefined convergence time, while adhering to the DGs' capacity limits. Moreover, a distributed control mechanism for finite-time voltage stabilization is developed for sustaining the balance between the generated powers and consumptions across the MG. Rigorous convergence analysis proves that the proposed controller maintains finite-time stability. The efficacy of this innovative control strategy is substantiated through a series of comprehensive case studies.Top of Form

An Integro-differential-delay Operator Approach to Transformations of Linear Differential Time-delay Systems

In this paper, we further develop the study of rings of integro-differential-delay operators considered as noncommutative polynomial algebras satisfying standard calculus identities. Within the algebraic analysis approach, we show that transformations and reductions of linear differential time-delay systems can be interpreted as homomorphisms and isomorphisms of finitely presented left modules over an algebra of integro-differential-delay operators. In particular, we show how Fiagbedzi-Pearson's transformation can be found again and generalized. This transformation maps the solutions of a first-order differential linear system with state and input delays to the solutions of a purely state-space linear system. Fiagbedzi-Pearson's transformation reduces to the well-known Artstein's reduction when the system has no state delay and yields an isomorphism of the solution spaces.

Inventory control of a class of logistic networks

This paper focuses on a prediction-based control for a class of convolution systems subject to constant input delays, also known as the reduction approach. We propose here a characterization of the D -invariance property of polytope sets for continuous-time systems. Our motivations come from production management, where a general model for a production network is considered. The system is subject to product losses and multiple delays, with bounded demand. This model is transformed into an equivalent free-delay system using Artstein reduction. The question of regulating the inventory levels of the nodes of this production network is then reduced to a pair of sub-problems, that are the regulation of the equivalent system without delay, and the relationship between the output of the system and that of the reduced system. A pair of conditions is therefore obtained, for the verification that a large class of control solutions allow to satisfy the external demand, while meeting the constraints that are imposed to the system. At the end, explicit conditions are found for an example of a supply chain with two nodes.

Robust predictive scheme for input delay systems subject to nonlinear disturbances

The predictor-based control is known as an effective method to compensate input delays. Yet the traditional predictors, like Smith predictor, have poor robustness with respect to system disturbances. In this paper, with the consideration of future disturbances, a novel robust predictive scheme is developed for input delay systems subject to nonlinear disturbances. The Artstein reduction method is used to provide performance analysis of different predictor-based controllers, which shows that the proposed predictor-based controller can provide better disturbance attenuation than previous approaches in the literature for a wide range of disturbances.

New formulation of predictors for finite-dimensional linear control systems with input delay

This paper focuses on a prediction-based control for linear time invariant systems subject to a constant input delay, also known as the Artstein reduction approach. Standardly, this method consists in considering a predicted delay-free system, on which one can design straightforwardly a stabilizing controller. The resulting controller is then defined through an implicit integral equation, involving both the original system state and past values of the input. We propose here an alternative formulation which allows to write explicitly the Artstein transformation, and thus the corresponding controller, in terms of past values of the state only. This formal explicit formulation is the main contribution of the paper.

A constructive algebraic analysis approach to Artstein's reduction of linear time-delay systems

Artstein's results show that a first-order linear differential system with delayed inputs is equivalent to a first-order linear differential system without delay under an invertible transformation which includes integral and time-delay operators. Within a constructive algebraic approach, we show how this reduction can be found again, generalized and interpreted as a particular isomorphism between modules defining the two above linear systems. Moreover, we prove that Artstein's reduction can be obtained in an automatic way by means of symbolic computation techniques, and thus can be implemented in dedicated computer algebra systems.

Robust output feedback stabilization for discrete-time systems with time-varying input delay

In this paper, a robust output feedback stabilization method is proposed for discrete-time systems subject to time-varying input delay. By introducing an augmented state, the robust stabilization problem is converted into that of a delay-free system. Using Artstein's reduction method and the scaled-bounded real lemma, sufficient conditions for robust stability are established via matrix inequalities, by which the output feedback controller can be derived. A tuning parameter is introduced to efficiently solve these matrix inequalities, therefore facilitating the improvement of control performance. An illustrative example is used to show the effectiveness and merit of the proposed method.

Predictive control of disturbed systems with input delay: experimental validation on a DC motor

This paper deals with the speed control of a DC motor with known input delay and unknown disturbances. A recent predictive technique is used in order to design two controllers that will be able to satisfactorily reject disturbances in spite of the time delay. A comparison between the Artstein reduction method and this new one is performed throughout the article. The control laws are validated first by simulation and then by a practical implementation. The paper presents the very first application of this new predictive method.

New predictive scheme for the control of LTI systems with input delay and unknown disturbances

A new predictive scheme is proposed for the control of Linear Time Invariant (LTI) systems with a constant and known delay in the input and unknown disturbances. It has been achieved to include disturbances effect in the prediction even though there are completely unknown. The Artstein reduction is then revisited thanks to the computation of this new prediction. An extensive comparison with the standard scheme is presented throughout the article. It is proved that the new scheme leads to feedback controllers that are able to reject perfectly constant disturbances. For time-varying ones, a better attenuation is achieved for a wide range of perturbations and for both linear and nonlinear controllers. A criterion is given to characterize this class of perturbations. Finally, some simulations illustrate the results.

Lyapunov Stability of Linear Predictor Feedback for Distributed Input Delays

Compensation of distributed delays in MIMO, LTI systems is achieved using Artstein's reduction method. In this technical note, we construct a Lyapunov functional for the resulting closed-loop system and establish exponential stability. The key element in our work is the introduction of an infinite-dimensional forwarding-backstepping transformation of the infinite-dimensional actuator states. We illustrate the construction of the Lyapunov functional with a detailed example of a single-input system, in which the input is entering through two individual channels with different delays. Finally, we develop an observer equivalent to the predictor feedback design, for the case of distributed sensor delays and prove exponential convergence of the estimation error.