Discrete-time Feedback Research Articles

P th moment exponential stabilisation of hybrid stochastic differential equations by feedback controls based on discrete‐time state observations with a time delay

The authors are concerned with the stability of hybrid stochastic differential equations by feedback controls based on discrete-time state observations. Under some reasonable conditions, they establish an upper bound on the duration τ between two consecutive state observations. Moreover, we can design the discrete-time state feedback control to stabilise the given hybrid stochastic differential equations in the sense of p th moment exponential stability by developing a new theory. In comparison to the results given in the previous literature, this study has two new characteristics: (i) the stability criterion concerns p th moment exponential stability, which is different from the existing works; (ii) discrete-time state observations depend on time delays.

On pth moment stabilization of hybrid systems by discrete-time feedback control

ABSTRACTSince Mao initiated the study of stabilization of continuous-time hybrid stochastic differential equations (SDEs) by feedback controls based on discrete-time state observations in 2013, many authors have further studied and developed it. However, so far no work on the pth moment stabilization has been reported. This paper is to investigate how to stabilize a given unstable hybrid SDE by feedback controls based on discrete-time state observations, in the sense of H∞, asymptotic and exponential stability in pth moment for all p > 1. The main techniques used are constructions of the Lyapunov functionals and generalizations of inequalities.

Discrete-time feedback stabilization

Abstract This paper presents an algorithm for designing dynamic compensator for infinitedimensional systems with bounded input and bounded output operators using finite dimensional approximation. The proposed method was then implemented in order to find the control function for thin rod heating process. The optimal sampling time was found depending on discrete output measurements.

Synchronization of stochastic coupled systems via feedback control based on discrete-time state observations

In this paper, we formulate and investigate the synchronization of stochastic coupled systems via feedback control based on discrete-time state observations (SCSFD). The discrete-time state feedback control is used in the drift parts of response system. Combining Lyapunov method with graph theory, the upper bound of duration between two consecutive state observations is provided. And a global Lyapunov function of SCSFD is presented, which derives some sufficient criteria to guarantee the synchronization of drive–response systems in the sense of mean-square asymptotical synchronization. In addition, the theoretical results are applied to stochastic coupled oscillators and second-order Kuramoto oscillators. Finally, two numerical examples are given to verify the effectiveness of the theoretical results.

Potential Benefits of Discrete-Time Controller-based Treatments over Protocol-based Cancer Therapies

In medical practice, the effectiveness of fighting cancer is not only determined by the composition of the used drug, but determ ined by the administration method as well. As a result, having drugs with a suitable action profile is just a promising beginning, but without appropriate delivery method s , the therapy still can be ineffective. Finding the optimal biologic dose is an empir ical process in medical practice; however, using controllers, an automated optimal administration can be determined . In this paper , we evaluate the effectiveness of different drug delivery protocols; using in silico simulations (like bolus dose s, low - dose metron omic regimen and continuous infusion therapy ). In addition, we compare these results with discrete - time controller - based treatments containing state feedback, setpoint control, actual state observer and load estimation.

Design of Robust Controller for a Class of Uncertain Discrete-Time Systems Subject to Actuator Saturation

This technical note studies the robust output tracking controller design for a class of uncertain discrete-time systems subject to actuator saturation. To achieve this capability, a new controller is proposed by robustifying the discrete-time composite nonlinear feedback (DCNF) control law. Since, the proposed controller may be saturated; a precise analysis is done to show its robust performance in spite of presence of actuator saturation and time-varying external disturbances. Additionally, a theorem is given and proved which guarantees the disturbance attenuation via the proposed control law for three different cases of the saturation function and it is shown that even if the control signal is saturated, the proposed controller achieves steady-state error of order $O(T)$ for state regulation. Finally, computer simulations are performed for a practical system and the applicability of the proposed controller is shown.

Stabilization of Regime-Switching Processes by Feedback Control Based on Discrete Time Observations

This work aims to extend X.R. Mao's work [Automatica J. IFAC, 49 (2013), pp. 3677--3681] on stabilization of hybrid stochastic differential equations by discrete-time feedback control. In X.R. Mao's work, the feedback control depends on discrete-time observation of the state process but on continuous-time observation of the switching process, while, in this work, we study the feedback control depending on discrete-time observations of the state process and the switching process. Our criteria depend explicitly on the regular conditions of the coefficients of the stochastic differential equation and on the stationary distribution of the switching process. The sharpness of our criteria is shown through studying the stability of linear systems, which also shows explicitly that the stability of hybrid stochastic differential equations depends essentially on the long time behavior of the switching process.

<i>p</i>th moment exponential stability of hybrid stochastic functional differential equations by feedback control based on discrete-time state observations

In this paper, we discuss the \begin{document} $p$ \end{document} th moment exponential stabilization of continuous-time hybrid stochastic functional differential equations by feedback control based on discrete-time state observations. The hybrid stochastic functional differential equations are also known as stochastic functional differential equations with the Markovian switching. We follow Mao's paper to consider the auxiliary system whose control is based on continuous-time state observation. The lemma is provided that if the \begin{document} $p$ \end{document} th moment of the solution \begin{document} $y(t)$ \end{document} of the auxiliary system decays exponentially then the same with the \begin{document} $p$ \end{document} th moment of the functional \begin{document} $y_t$ \end{document} . With the help of this lemma, the criterion for \begin{document} $p$ \end{document} th moment exponential stability of the primary system is given, and the margin of the duration of the discrete-time state observation is presented. Then the special case like the linear system is considered and the discrete-time feedback control is designed.

The Control of Non-Linear Chaotic System Including Noise Using Genetic Based Algorithm

In this study, the Lorenz chaotic system including the nonlinear equations has been analyzed against the noise changes. The discrete-time state feedback control method and discrete-time PI controller method have been used for these noisy system controls. Optimization of the controller parameters was performed using a genetic algorithm method. The study was implemented in MATLAB-Simulink simulation program. In terms of noise, the Gaussian white noise was used as a system and measurement noise. Noise has emerged as a significant impact on the Lorenz chaotic system. Changes associated with this condition are given in detail on the graphics. The discrete-time PI controller method was shown to better performance when compared to discrete-time state feedback control method for the system control. Furthermore, the error performance change was given in the literature as an important parameter.

On Chaotic Neural Network Design: A New Framework

The theory of chaos and chaotic neural networks (CNNs) has been widely investigated in the past two decades. However, most researchers in this area have merely focused on how to make full use of CNNs to solve various problems in areas such as pattern recognition, classification, associate memory and cryptography. The philosophy of how to design a CNN is seldom discussed. In this paper, we present a general methodology for designing CNNs. By appropriately choosing a self-feedback mechanism, and also including coupling functions and an external stimulus, we have succeeded in proving that a dynamical system, defined by discrete time feedback equations, does, indeed, possess interesting chaotic properties. To the best of our knowledge, the results presented here are novel and pioneering.

Neural Approximation-Based Adaptive Control for a Class of Nonlinear Nonstrict Feedback Discrete-Time Systems.

In this paper, an adaptive control approach-based neural approximation is developed for a class of uncertain nonlinear discrete-time (DT) systems. The main characteristic of the considered systems is that they can be viewed as a class of multi-input multioutput systems in the nonstrict feedback structure. The similar control problem of this class of systems has been addressed in the past, but it focused on the continuous-time systems. Due to the complicacies of the system structure, it will become more difficult for the controller design and the stability analysis. To stabilize this class of systems, a new recursive procedure is developed, and the effect caused by the noncausal problem in the nonstrict feedback DT structure can be solved using a semirecurrent neural approximation. Based on the Lyapunov difference approach, it is proved that all the signals of the closed-loop system are semiglobal, ultimately uniformly bounded, and a good tracking performance can be guaranteed. The feasibility of the proposed controllers can be validated by setting a simulation example.

Almost Sure Exponential Stabilization by Discrete-Time Stochastic Feedback Control

Given an unstable linear scalar differential equation $\dot{x}(t)=\alpha x(t)$ $(\alpha>0)$ , we will show that the discrete-time stochastic feedback control $\sigma x([t/\tau]\tau)dB(t)$ can stabilize it. That is, we will show that the stochastically controlled system $dx(t)=\alpha x(t)dt+\sigma x([t/\tau]\tau)dB(t)$ is almost surely exponentially stable when $\sigma^{2}>2\alpha$ and $\tau>0$ is sufficiently small, where $B(t)$ is a Brownian motion and $[t/\tau]$ is the integer part of $t/\tau$ . We will also discuss the nonlinear stabilization problem by a discrete-time stochastic feedback control. The reason why we consider the discrete-time stochastic feedback control is because that the state of the given system is in fact observed only at discrete times, say $0,\tau,2\tau,\ldots$ , for example, where $\tau>0$ is the duration between two consecutive observations. Accordingly, the stochastic feedback control should be designed based on these discrete-time observations, namely the stochastic feedback control should be of the form $\sigma x([t/\tau]\tau)dB(t)$ . From the point of control cost, it is cheaper if one only needs to observe the state less frequently. It is therefore useful to give a bound on $\tau$ from below as larger as better.

Two-Step System Identification and Trajectory Tracking Control of a Small Fixed-Wing UAV

An approach for obtaining dynamically feasible reference trajectories and feedback controllers for a small unmanned aerial vehicle (UAV) based on an aerodynamic model derived from flight tests is presented. The modeling method utilizes stepwise multiple regression to determine relevant explanatory terms for the aerodynamic coefficients. A dynamically feasible trajectory is then obtained through the solution of an optimal control problem using pseudospectral optimal control software. Discrete-time feedback controllers are further designed to regulate the vehicle along the desired reference trajectory. Simulations in a realistic operational environment as well as flight testing of the feedback controllers on the aircraft platform demonstrate the capabilities of the approach.

Unified Control of a Buck Converter for Wide-Load-Range Applications

A new discrete-time state feedback controller is presented, which allows high-bandwidth voltage control of a buck converter for any load condition, whether it operates in discontinuous conduction mode (DCM), continuous conduction mode (CCM), or at the boundary of these regions. This makes the buck converter applicable for a wide range of applications. For the control design process, two large-signal models, which represent the buck converter's discrete time dynamics in CCM and DCM, are developed. A simple proportional-integral regulator is used for the voltage control of the converter. The operation mode is detected and the voltage controller is connected in cascade to a current controller in CCM or to a nonlinear state feedback decoupling structure in DCM. In this paper, the modeling and design of the proposed control topology are introduced and its performance is demonstrated in simulation and experiment.

A robust ℋ∞ observer-based stabilization method for systems with uncertain parameters and Lipschitz nonlinearities

Summary This paper deals with the robust observer-based control design for a class of Lipschitz nonlinear discrete-time systems with parameter uncertainties. Based on the use of a reformulated Lipschitz property combined with the slack variable techniques and some mathematical artifacts, it is shown that the solution of the discrete-time output feedback stabilization problem is conditioned by a set of bilinear matrix inequalities, which become linear matrix inequalities by freezing some scalars. Furthermore, we show that some existing and elegant results reported in the literature can be regarded as particular cases of the stability conditions presented here. Numerical examples are provided to show the validity and superiority of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.

RF Input Matching Design for Closed-Loop Direct Delta–Sigma Receivers

Emerging digital-intensive receiver architectures require new methods for input matching design. In particular, closed-loop $\Delta \Sigma$ -based receivers inject discrete-time global feedback to the RF low-noise amplifier (LNA) output. When using feedback LNA topologies with local internal feedback, receiver input matching thus no longer depends only on analog LNA characteristics, but also on the transfer function of the full receiver chain. This paper proposes a systematic input matching design method for such receivers. We demonstrate how this method is applied to the recently introduced active direct delta–sigma receiver (DDSR). We also show that global $\Delta \Sigma$ feedback in the DDSR counteracts the effects of the local feedback of the LNA on receiver input impedance, and how this can be used to improve receiver performance. A generic DDSR input impedance model is thus developed to facilitate input matching design. The related design method does not require transistor-level description of the post-LNA blocks, but relies instead only on easily obtainable system-level properties. A design example and measurements of a 0.7–2.7-GHz DDSR in 40-nm CMOS verify a good match between the theoretical and experimental results.

A Simplified Two-Stage Design of Linear Discrete-Time Feedback Controllers

In this paper, we have shown how to simplify an algorithm for the two-stage design of linear feedback controllers by reducing computational requirements. The algorithm is further simplified for linear discrete-time systems with slow and fast modes (multitime scale systems or singularly perturbed systems), providing independent and accurate designs in slow and fast time scales. The simplified design procedure and its very high accuracy are demonstrated on the eigenvalue assignment problem of a steam power system.

Discrete-time output feedback quasi-sliding mode control for robust tracking and model following of uncertain systems

A discrete-time output feedback quasi-sliding mode control scheme is proposed to realize the problem of robust tracking and model following for a class of uncertain linear systems in which states are unavailable and estimated states are not required. The proposed scheme guarantees the stability of the closed-loop system and achieves a very small ultimate boundedness of the tracking error in the presence of matched uncertain parameters and external slow disturbances. This scheme ensures the robustness to matched parametric uncertainties and disturbances. Since the proposed controller is designed without any switching element, the chattering phenomenon is eliminated. Furthermore, the knowledge of upper bound of uncertainties is not required. Simulation results demonstrate the effectiveness of the proposed scheme.

On the Solution of a Nonlinear Semidefinite Program Arising in Discrete-Time Feedback Control Design

A sequential quadratic programming method with line search is analyzed and studied for finding the local solution of a nonlinear semidefinite programming problem resulting from the discrete-time output feedback problem. The method requires an initial feasible point with respect to two positive definite constraints. By parameterizing the optimization problem we ease that requirement. The method is tested numerically on several test problems chosen from the benchmark collection (Leibfritz, 2004).

Disturbance-adaptive stochastic optimal control of energy harvesters, with application to ocean wave energy conversion

This paper proposes a theory for optimizing the power generated from stationary stochastic vibratory disturbances, using a resonant energy harvester. Although the theory is general, the target application of the paper concerns ocean wave energy harvesting. The control technique involves the use of a causal discrete-time feedback algorithm to dynamically optimize the power extracted from the waves. The theory assumes that the input impedance of the converter is known precisely, but that a priori models are unavailable for the characterization of the stochastic behavior of the waves, as well as their hydrodynamic excitation of the system. For these assumptions, we develop an adaptive control technique, which iteratively re-optimizes the feedback law for the controller based on recursive subspace identification of the stochastic disturbance dynamics. The technique is demonstrated on a simulation example pertaining to a cylindrical surface-floating wave energy converter in heave.