A multirate controller design of linear periodic time delay systems

This paper presents a multirate controller design for a linear periodic system with multiple delays at input and output. The approach first converts the periodic time-delay system into a periodic delay-free system, and then stabilizes and optimizes it by a multirate controller with pulse compensation. A significant advantage of this approach is that by using multirate sampling, the controller can provide more substantial design freedoms, so that although the system does not provide complete state information, it remains possible to convert the controller design into the dual of a regular complete state feedback problem. This enables one to derive a simple algorithm for choosing the optimal parameters of the controller and, by use of the optimal pulse compensation, to improve the transient response.     

On a general optimal algorithm for multirate output feedbackcontrollers for linear stochastic periodic systems

A modified optimal algorithm for multirate output feedback controllers of linear stochastic periodic systems is developed. By combining the discrete-time linear quadratic regulation (LQR) control problem and the discrete-time stochastic linear quadratic regulation (SLQR) control problem to obtain an extended linear quadratic regulation (ELQR) control problem, one derives a general optimal algorithm to balance the advantages of the optimal transient response of the LQR control problem and the optimal steady-state regulation of the SLQR control problem. In general, the solution of this algorithm is obtained by solving a set of coupled matrix equations. Special cases for which the coupled matrix equations can be reduced to a discrete-time algebraic Riccati equation are discussed. A reducable case is the optimal algorithm derived by H.M. Al-Rahmani and G.F. Franklin (1990), where the system has complete state information and the discrete-time quadratic performance index is transformed from a continuous-time one     

Feedback control of linear systems by multirate pulse-widthmodulation

In this note, sampled-data methods for modeling and control design of pulse-width modulated systems are examined. Both single-rate and multirate approaches are considered. Local controllability and observability analyses of the sampled-data models are performed, and feedback linearizability conditions for the sampled-data models are derived. Multirate nonlinear state and output feedback designs are presented that permit asymptotic regulation or tracking     

A periodic fixed-structure approach to multirate control

We develop an approach to designing reduced-order multirate controllers. A discrete-time model that accounts for the multirate timing sequence of measurements is presented and is shown to have periodically time-varying dynamics. Using discrete-time stability theory, the optimal projection approach to fixed-order (i.e. full- and reduced-order) dynamic compensation is generalized to obtain reduced-order periodic controllers that account for the multirate architecture. It is shown that the optimal reduced-order controller is characterized by means of a periodically time-varying system of equations consisting of coupled Riccati and Lyapunov equations. In addition, the multirate static output-feedback control problem is considered. For both problems, the design equations are presented in a concise, unified manner to facilitate their accessibility for developing numerical algorithms for practical applications     

A stability criterion for asynchronous multirate linear systems

A stability criterion is developed for linear, asynchronous multirate sampled-data systems. Such systems typically include a linear, time variant, continuous-time plant and several unsynchronized digital controllers. The analysis method uses a time-domain approach based on the closed-loop state transition matrix. The result is sufficient stability criterion which gives an objective measure of long-term and short-term stability. A simple example illustrates the method     

Design of multirate observers and multirate control systems

In this paper, the design problem of the observer-based multirate control system is considered. First, a reduced-order observer of the current type is proposed on the basis of the mode-decoupling transformation. It is shown that, under the multirate measurement, the state estimates can be achieved by two low-order multirate observers which possess the hierarchical structure. Second, the multirate control system incorporating such reduced-order observers is studied. Furthermore, a design problem of the multirate observer which runs in its natural time scale is investigated. Finally, in order to verify the validity of these results, an application to the longitudinal control problem of an aircraft is given.     

Satisfactory control of discrete-time linear periodic systems

In this paper satisfactory control for discrete-time linear periodic systems is studied. Based on a suitable time-invariant state sampled reformulation, periodic state feedback controller has been designed such that desired requirements of steady state covariance, H-infinity rejection bound and regional pole assignment for the periodic system are met simultaneously. By using satisfactory control theory, the problem of satisfactory periodic controller can be transformed into a linear programming problem subject to a set of linear matrix inequalities （LMIs）, and a feasible designing approach is presented via LMI technique. Numeric example validates the obtained conclusion.     

Uniformly optimal control of linear feedback systems

The problem of uniformly optimal control is posed in the context of linear time-varying discrete-time systems; the controller is optimal uniformly over a pre-specified set of exogenous signals. Existence of an optimal controller is proved and a formula for the minimum cost is derived. The time-invariant case is treated in the frequency domain. It is shown that for time-invariant systems an optimal time-varying controller is no better than an optimal time-invariant controller.     

Uniformly optimal control of linear time-varying systems

An optimal control problem is formulated in the context of linear, discrete-time, time-varying systems. The cost is the supremum, over all exogenous inputs in a weighted ball, of the sum of the weighted energies of the plant's input and output. The controller is required to be causal and to achieve internal stability. Existence of an optical controller is proved and a formula for the minimum cost is derived.     

Robust properties of periodic discrete and multirate systems

For discrete periodic and multirate systems new bounds are derived for three different robustness problems: disturbance attenuation, and stability with time-varying structured and unstructured parameter variations. These results generalize the single rate results to allow multirate capability     

分段线性系统最优控制设计的一种混合算法

将分段线性系统的最优控制设计问题转化成以反馈增益为寻优参数，以最优控制性能上界为目标的一组双线性矩阵不等式(BMI)问题．将遗传算法与内点法相结合设计出一种混合算法，对BMI问题进行求解．算例仿真表明该算法是简便而有效的．     

On linear quadratic optimal control of linear time-varying singular systems

Linear time-varying singular systems are treated in this paper. We focus on systems with constant-rank E matrices. It is shown that the existence of state feedback for impulse elimination is both sufficient and necessary for the existence of linear-quadratic optimal control. Also optimal control exists if and only if the corresponding fast subsystem is impulse-controllable. The results obtained are extensions of the existing time-invariant theory.     

Closed-loop sensitivity reduction of linear optimal control systems

Inequalities are derived which demonstrate the reduction of sensitivity to plant-parameter variations of closed-loop linear optimal systems (as compared to nominally equivalent open-loop systems) according to a particular measure of sensitivity. The shortcomings of some other measures of sensitivity are discussed and illustrated in numerical examples. Numerical results for the sensitivity comparison of a first-order system and a third-order pitch-axis control system are given.     

Stable and optimal fuzzy control of linear systems

A number of stable and optimal fuzzy controllers are developed for linear systems. Based on some classical results in control theory, we design the structure and parameters of fuzzy controllers such that the closed-loop fuzzy control systems are stable, provided that the process under control is linear and satisfies certain conditions. It turns out that if stability is the only requirement, there is much freedom in choosing the fuzzy controller parameters. Therefore, a performance criterion is set to optimalize the parameters. Using the Pontryagin minimum principle, we design an optimal fuzzy controller for linear systems with quadratic cost function. Finally, the optimal fuzzy controller is applied to a ball-and-beam system     

Hermite polynomial analysis of linear optimal control systems

The analysis of optimal control systems incorporating observers has been approached using Hermite polynomials. The method simplifies the system of equations into the successive solution of a set of linear algebraic equations. An illustrative example is given and accurate results obtained.     

Data-driven optimal control of switched linear autonomous systems

In this paper, a novel data-driven optimal control approach of switching times is proposed for unknown continuous-time switched linear autonomous systems with a finite-horizon cost function and a prescribed switching sequence. No a priori knowledge on the system dynamics is required in this approach. First, some formulas based on the Taylor expansion are deduced to estimate the derivatives of a cost function with respect to the switching times using system state data. Then, a data-driven optimal control approach based on the gradient decent algorithm is designed, taking advantage of the derivatives to approximate the optimal switching times. Moreover, the estimation errors are analysed and proven to be bounded. Finally, simulation examples are illustrated to validate the effectiveness of the approach.     

Deadbeat control of linear discrete-time systems by periodic output-feedback

Two deadbeat control problems for open-loop, time-invariant linear, discrete-time multivariable systems by periodic output-feedbacks are formulated and solved. Sufficient conditions for the existence of solutions to the problems are established. Procedures for finding solutions to the problems are presented and illustrated by numerical examples.     

Design of linear time-invariant controllers for multirate systems

In this paper we discuss a frequency domain approach to model multirate single-input single-output (SISO) systems which facilitates design of linear time-invariant (LTI) controllers operating at the fast rate. To illustrate the approach we consider a dual-rate system with slow output measurements and fast control actions. We obtain necessary and sufficient conditions for the existence of stabilizing linear time-invariant (LTI) controllers for which model matching is also achieved at the fast rate with a desired single-rate system. Moreover, a solution to the problem of parameterizing the set of such LTI controllers is also given.     

线性多变量系统有限时间最优解耦控制

针对线性多变量系统, 将前馈解耦控制与有限时间最优跟踪控制相结合, 提出一种新的最优解耦控制方法. 首先, 将关于状态的微分方程转化成关于输出的微分方程, 将系统内部矩阵和控制输入矩阵分别分解成对角矩阵和对角元为零的矩阵; 然后, 通过引入中间虚拟变量, 采用前馈和输出反馈的方法对系统进行解耦; 最后, 采用有限时间最优跟踪控制方法实现系统对任意参考输入的跟踪. 仿真结果表明了所提出方法的有效性和优越性.     

Low-sensitivity optimal feedback control for linear discrete-time systems

The problem of reducing sensitivity of discrete-time systems to parameter variations is considered. State and output feedback gains are obtained to minimize a quadratic criterion which includes sensitivity functions. Necessary conditions for optimality are derived and numerical examples are discussed.