Disturbances In Linear Systems Research Articles

Distributed Economic MPC for Dynamically Coupled Linear Systems With Uncertainties.

In this article, we propose a novel economic model-predictive control (MPC) algorithm for a group of disturbed linear systems and implement it in a distributed manner. The system consists of multiple subsystems interacting with each other via dynamics and aims to optimize an economic objective. Each subsystem is subject to constraints both on states and inputs as well as unknown but bounded disturbances. First, we divide the computation of control inputs into several local optimization problems based on each subsystem's local information. This is done by introducing compatibility constraints to confine the difference between the actual information and the previously published reference information of each subsystem, which is the key feature of the proposed distributed algorithm. Then, to ensure the satisfaction of both state and input constraints under disturbances, constraints are tightened on the state and the input of nominal systems by considering explicitly the effect of uncertainties. Moreover, based on an overall optimal steady state, a dissipativity constraint and a terminal constraint are designed and incorporated in the local optimization problems to establish recursive feasibility and guarantee stability for the resulting closed-loop system. Finally, the efficiency of the distributed economic MPC algorithm is demonstrated in a building temperature control case study.

A Robust Nonlinear Model Reference Adaptive Control for Disturbed Linear Systems: An LMI Approach

In this article, a robust nonlinear model reference adaptive control (MRAC) is proposed for disturbed linear systems, i.e., linear systems with parameter uncertainties, and external time-dependent perturbations or nonlinear unmodeled dynamics matched with the control input. The proposed nonlinear control law is composed of two nonlinear adaptive gains. Such adaptive gains allow the control to counteract the effects of some perturbations and nonlinear unmodeled dynamics ensuring asymptotic convergence of the tracking error to zero, and the boundedness of the adaptive gains. The nonlinear controller synthesis is given by a constructive method based on the solution of linear matrix inequalities. Besides, the simulation results show that, due to the nonlinearities, the rate of convergence of the proposed algorithm is faster than that provided by a classic MRAC.

Event‐triggered model predictive control for disturbed linear systems under two‐channel transmissions

SummaryThis article studies an event‐triggered model predictive control problem for constrained continuous‐time linear systems subject to bounded disturbances. Two different event‐triggered strategies are constructed in the sensor and the controller nodes for reducing the communication and computational loads, respectively. The continuous predicted control trajectory generated by the controller is applied to the plant under a sample‐and‐hold implementation. By constructing a feasible control sequence, the sufficient conditions are derived to guarantee the feasibility and stability of the closed‐loop system. Furthermore, the case of multiple samples within an event‐triggered control update interval is considered. It is shown that a larger number of samples will improve the triggering performance while increasing the amount of transmission information. Finally, a simulation example is provided to show the feasibility and the effectiveness of the proposed strategy.

Event-Triggered Output-Feedback Control for Disturbed Linear Systems

In the last few decades, event-triggered control received considerable attention, because of advantages in reducing the resource utilization, such as communication load and processor. In this paper, we propose an event-triggered output-feedback controller for disturbed linear systems, in order to achieve both better resource utilization and disturbance attenuation properties at the same time. Based on our prior work on state-feedback H∞ control for disturbed systems, we propose an approach to design an output-feedback H∞ controller for the system whose states are not completely observable, and a sufficient condition guaranteeing the asymptotic stability and robustness of the system is given in the form of LMIs (Linear Matrix Inequalities).

Disturbance attenuation in linear systems revisited

A variety of methods have been proposed for attenuating or rejecting disturbances in linear systems. Most of the approaches, however, are targeting the performance either near resonance or across the whole frequency range. Weighting functions can be utilized to shape the frequency response function over target frequency band but they are usually of rule-of-thumb nature. A methodology is necessitated for designing controllers with performance specified at any discrete frequency or over any desired frequency band. The paper aims to develop such a methodology. Besides this, the proposed method can tell performance limitations and determine the problem of existence of optimal controllers, as well as providing a useful framework to improve the performance of an existing controller. A number of important results are obtained and these results are subsequently validated through a practical application to a rotor blade example.

Algorithms of Fast Adaptive Compensation of Disturbance in Linear Systems with Arbitrary Input Delay

The problem of fast compensation of multisinusoidal disturbance affecting on linear time-invariant (LTI) plants with known parameters and arbitrary input delay is considered. The disturbance is modeled as unmeasurable bounded output of linear exosystem of known order but with unknown parameters. Disturbance compensation is provided by means of direct adaptive control with two schemes of adaptation algorithm. The first scheme is based on the standard gradient adaptation algorithm, while the second one uses modified adaptation algorithm with integral cost function and improved parametric convergence. The stability of the closed-loop system in presence of delay and integral action (due to direct adaptation) in the feedforward loop is ensured by appropriate modifications of the adaptation schemes. These modifications allow to remove the limitations on upper bounds on adaptation gains (gain margins) corresponding to certain upper bounds of time delays (delay margins). The performance of proposed schemes of disturbance compensation is demonstrated via simulation.

H∞ output tracking control of uncertain and disturbed nonlinear systems based on neural network model

ABSTRACTThe work presented in this paper seeks to address the tracking problem for uncertain continuous nonlinear systems with external disturbances. The objective is to obtain a model that uses a reference-based output feedback tracking control law. The control scheme is based on neural networks and a linear difference inclusion (LDI) model, and a PDC structure and H∞ performance criterion are used to attenuate external disturbances. The stability of the whole closed-loop model is investigated using the well-known quadratic Lyapunov function. The key principles of the proposed approach are as follows: neural networks are first used to approximate nonlinearities, to enable a nonlinear system to then be represented as a linearised LDI model. An LMI (linear matrix inequality) formula is obtained for uncertain and disturbed linear systems. This formula enables a solution to be obtained through an interior point optimisation method for some nonlinear output tracking control problems. Finally, simulations and comparisons are provided on two practical examples to illustrate the validity and effectiveness of the proposed method.

Robust fault diagnosis of disturbed linear systems via a sliding mode high order differentiator

A fault estimator for linear systems affected by disturbances is proposed. Faults appearing explicitly in the state equation and in the system output (actuator faults and sensor faults) are considered. With this design neither the estimation of the state vector nor the estimation of the disturbances is required, implying that the structural conditions are less restrictive than the ones required to design an unknown input observer. Furthermore, the number of unknown inputs (faults plus disturbances) may be greater than the number of outputs. The faults are written as an algebraic expression of a high-order derivative of a function depending on the output. Thus, the reconstruction of the fault signals is carried out by means of a sliding mode high-order differentiator, which requires the derivative of the faults to have a bounded norm.

Partial unknown input reconstruction for linear systems

The problem of partial unknown input (UI) reconstruction is addressed. It is considered that a linear functional of the UI vector has to be reconstructed using output information only. Necessary and sufficient conditions are given allowing for the reconstruction in finite time of the required UI’s; analogous conditions are obtained for the asymptotic reconstruction of the required UI’s. The solution of the problem under consideration provides a means to solve the problem of fault detection and isolation for disturbed linear systems.

Time maximum disturbance design for stable linear systems: a model predictive scheme

It is known that the most stressful bounded (time maximum) disturbance for stabilized linear systems is of bang-bang type. This bang-bang disturbance can often be implemented with a switch set of current states for second-order systems. The isochrones, as the level sets, determine the value of the disturbance index in a state space setting. We suggest an efficient way to construct the time maximum disturbance from the information of the isochronal wave front using it in a model predictive scheme. This overcomes the shortcomings of the original switch set which are constructed through time backward computation and only available for first and second-order systems. Simulation results show how the isochrones evolve and can be utilized in synthesizing the time maximum disturbance for linear systems of second and then higher order. For third-order systems, the associated L/sub /spl infin//-gain of the time maximizing disturbance is found.

Order of Residual Generators - Bounds and Algorithms

This contribution analyses residual generators that perfectly decouples disturbances in linear systems. The analysis focuses on the orders of the residual generators and it is shown how low order, local relationships in the model can be utilized to increase robustness properties. Easily computed bounds on minimum and maximum order residual generators are derived and presented. An upper bound on the minimal row-degree is derived and is given directly by the number of measurements, the number of linearly independent disturbances, and the number of states in the model. A lower bound is given by the minimum observability index of the model. An upper bound for the maximum order is the number of states in the model.

Optimall∞ disturbance attenuation and global stabilization of linear systems with bounded control

This papers addresses the problem of globally minimizing the worst-case response to persistent l∞ bounded disturbances in linear systems with bounded control action. The main result of the paper shows that in the state-feedback case the best performance among all stabilizing controllers (possibly discontinuous, nonlinear time varying) is achieved by a memoryless, continuous, feedback control law. In the case of open-loop stable plants the proposed control law renders the system globally stable and provides the best possible l∞ attenuation in every neighbourhood of the origin. In the case of open-loop unstable plants this law optimizes performance in the region where a finite l∞ gain can be achieved. Copyright © 1999 John Wiley & Sons, Ltd.

Optimal l disturbance attenuation and global stabilization of linear systems with bounded control

This papers addresses the problem of globally minimizing the worst-case response to persistent l∞ bounded disturbances in linear systems with bounded control action. The main result of the paper shows that in the state-feedback case the best performance among all stabilizing controllers (possibly discontinuous, nonlinear time varying) is achieved by a memoryless, continuous, feedback control law. In the case of open-loop stable plants the proposed control law renders the system globally stable and provides the best possible l∞ attenuation in every neighbourhood of the origin. In the case of open-loop unstable plants this law optimizes performance in the region where a finite l∞ gain can be achieved. Copyright © 1999 John Wiley & Sons, Ltd.

Optimal l∞ Disturbance Rejection and Global Stabilization of Linear Systems with Saturating Control

This papers addresses the problem of globally minimizing the worst case response to persistent l∞ bounded disturbances in linear systems with bounded control action. We propose a linear-like feedback control law with state-dependent gains such that the resulting dosed-loop system is globally stable and provides the best possible l∞ attenuation in every neighborhood of the origin.

A set-based approach for white noise modeling

This paper provides a new framework for analyzing white noise disturbances in linear systems; rather than the usual stochastic approach, noise signals are described as elements in sets, and their effect is analyzed from a worst-case perspective. The paper studies how these sets must be chosen to have adequate properties for system response in the worst-case, statistics consistent with the stochastic point of view, and simple descriptions that allow for tractable worst-case analysis. The method is demonstrated by considering its implications in two problems: rejection of white noise signals in the presence of system uncertainty and worst-case system identification.

On the accumulation of disturbances in linear systems

On the accumulation of disturbances in linear systems