Control Method For Linear Systems Research Articles

Control for Time‐Varying Delay Systems by Integrating Semi‐Discretization and Hysteresis‐Based Switching

AbstractIn this paper, we develop an innovative control method for linear systems with time‐varying delay by integrating the semi‐discretization method and the hysteresis‐based switching algorithm. The semi‐discretization method is adopted to design an optimal controller for each fixed time‐delay and form a candidate controller family. The switching algorithm acts as the principal law for switching among various controllers according to the instantaneous value of the time‐delay. A theoretical proof is presented regarding the stability of the switching time‐delay system. It is shown that the most significant factors that affect the system stability are the size of the candidate controller family, the value of the switching coefficient, and the changing rate of the time‐delay. Two case studies are presented to show the effectiveness of the proposed method.

Adaptive control for input-constrained linear systems

This paper proposes a direct model reference adaptive control method for linear systems with unknown parameters in the presence of input constraints. First, we used the well-known linear quadratic regulator (LQR) technique to develop a modified reference model, which is the optimal model under input constraints. Second, a model reference adaptive controller, which tracked the modified reference model instead of the reference model, was designed to compensate for parametric uncertainties. Using Lyapunov stability theory, we proved that the modified reference model tracking error converges to zero. Simulation results demonstrate the effectiveness of the proposed controller.

A fast nonlinear control method for linear systems with input saturation

We present a novel, fast saturating nonlinear feedback law for single input systems with linear dynamics and input saturation. It is fast in the sense that it yields a better performance than a saturating linear control law. The control law is based on implicit soft variable-structure control. A convex optimization procedure for the controller synthesis based on linear matrix inequalities (LMIs) is derived at the price of some conservatism. As an example, we consider the control of a submarine.

An optimal control method for linear systems with time delay via recurrent neural networks

An optimal control method for linear systems with time delay via recurrent neural networks

An optimal control method for linear systems with time delay

An optimal control method for linear systems with time delay is developed in this paper. In the proposed control method, the differential equation with time delay of the system dynamics is first rewritten into a form without any time delay through a particular transformation. Then, the optimal controller is designed by using the classical optimal control theory. A numerical algorithm for control implementation is presented, since the obtained expression of the optimal controller contains an integral term that is not convenient for online calculation. The time delay is considered at the very beginning of the control design, and no approximation and estimation are made in the control system. Thus the system performance and stability are prone to be guaranteed. Instability in responses might occur only if a system with time delay is controlled by the optimal controller that was designed with no consideration of time delay. The effectiveness of the proposed optimal controller is demonstrated by simulation studies.

RELATIONS BETWEEN STABLE PREDICTIVE CONTROL AND POLE PLACEMENT

In this paper, several relations between pole placement (PP) controller and unconstrained predictive controller are investigated. The placement of poles at certain positions leads to various types of time optimal control and has a direct relation to the choice of minimum control and output horizons for stabilising MPC. On the other hand, a predictive control method for linear systems is derived that can be turned into some well known stabilising MPC methods. This MPC method is closely related to the PP design.

Application of true linearization in stochastic quasi‐optimal control problems

AbstractThe problem of quasi‐optimal linear feedback control laws for nonlinear systems with quadratic performance criteria under Gaussian white noise excitations is considered. To determine the quasi‐optimal control a modified version of standard iterative procedure is used, where three versions of statistical linearization methods and true linearization method were combined with the optimal control method for linear systems with the mean‐square criterion. The validity of this method is shown by analytical and numerical calculations for examples.

A closed-loop, approximately time-optimal control method for linear systems

In this paper, a method is developed for the closed-loop, approximately time-optimal control of a class of linear systems with a total effort constraint. This method is based on a special class of solutions of the Hamilton-Jacobi equation, called eigenvector scalar products. The procedure to be followed is systematically presented, and the method is shown to represent an effective compromise between system complexity and speed of response. In designing a closed-loop system using this method, the controller-computer must only solve algebraic equations, and hence the control can be computed continuously.This is to be contrasted with many of the present methods which require on-line solution of two-point boundary value problems, and hence discrete control. The method is illustrated by an example.