Digital stochastic control of distributed-parameter systems

This paper presents a method for discrete-time control and estimation of flexible structures in the presence of actuator and sensor noise. The approach consists of complete decoupling of the modal equations and estimator dynamics based on the independent modal-space control technique and modal spatial filtering of the system output. The solution for the Kalman filter gains reduces to that of independent second-order modal estimators, thus permitting real-time digital control of distributed-parameter systems in a noisy environment. The method can be used to control and estimate any number of modes without computational restraints and is theoretically free of observation spillover. Two examples, the first using nonlinear, quantized control and the second using linear, state feedback control are presented.This work was supported by the National Science Foundation, Grant No. PFR-80-20623.     

A linear differential flatness approach to controlling the Furuta pendulum

^** Email: caguilar{at}cic.ipn^*** Email: hsira{at}mail.cinvestav.mx The aim of this work is to motivate the use of linear flatness,or controllability, to design a feedback control law for therather challenging mechanism known as the ‘Furuta pendulum’.This is achieved by introducing three feedback controller designoptions for the stabilization and rest-to-rest trajectory trackingtasks: a direct pole placement approach, a hierarchical high-gainapproach and a generalized proportional integral approach synthesizedon the basis of measured inputs and outputs.     

Minimum-fuel control of high-order systems

The minimum-fuel control problem is of special interest in various space systems. To date, solutions of minimum-fuel control problems have been carried out for relatively low-order systems. Space structures, however, are generally characterized by a large number of degrees of freedom, so that minimum-fuel control of such systems requires a new approach. In the independent modal-space control (IMSC) method, the control laws are designed in the modal space for each mode independently. The minimum-fuel problem reduces to that of a set of independent second-order systems, so that minimum-fuel control is possible. This paper shows how the IMSC method can be used to control a space structure with a minimum amount of fuel. A numerical example is presented.This research was supported by NASA Research Grant No. NAG-1-225, sponsored by the Spacecraft Control Branch, Langley Research Center.     

On the problem of observation spillover in self-adjoint distributed-parameter systems

The problem of observation spillover in self-adjoint distributed-parameter systems is investigated. Observation spillover occurs when the output of a limited number of sensors, located at various points on the distributed domain, cannot synthesize the modal coordinates exactly. To this end, two techniques of state estimation (namely, observers and modal filters) are described. Both techniques can be used to extract modal coordinates from the system output and to implement feedback controls. It is shown that, if the residual modes are included in the observer dynamics, observation spillover cannot lead to instability in the residual modes. The problem of the unmodeled modes does remain, however. It is also shown that the modal filters have some very attractive features. In particular, modal filters can be designed to estimate the modal coordinates with such accuracy that observation spillover can be virtually eliminated. In addition, when modal filters are used, in conjunction with a sufficiently large number of sensors, the entire infinity of the system modes can be regarded as modeled, which implies that actual distributed control of the system is possible. It is also demonstrated that modal filters are quite easy to design and are not plagued by instability problems.     

Intelligent control of chaos using linear feedback controller and neural network identifier

A method for controlling chaos when the mathematical model of the system is unknown is presented in this paper. The controller is designed by the pole placement algorithm which provides a linear feedback control method. For calculating the feedback gain, a neural network is used for identification of the system from which the Jacobian of the system in its fixed point can be approximated. The weights of the neural network are adjusted online by the gradient descent algorithm in which the difference between the system output and the network output is considered as the error to be decreased. The method is applied on both discrete-time and continuous-time systems. For continuous-time systems, equivalent discrete-time systems are constructed by using the Poincare map concept. Two discrete-time systems and one continuous-time system are tested as examples for simulation and the results show good functionality of the proposed method. It can be concluded that the chaos in systems with unknown dynamics may be eliminated by the presented intelligent control system based on pole placement and neural network.     

Control of time-periodic systems via symbolic computation with application to chaos control

A general method for the control of linear time-periodic systems employing symbolic computation of Floquet transition matrix is considered in this work. It is shown that this method is applicable to chaos control. Nonlinear chaotic systems can be driven to a desired periodic motion by designing a combination of a feedforward controller and a feedback controller. The design of the feedback controller is achieved through the symbolic computation of fundamental solution matrix of linear time-periodic systems in terms of unknown control gains. Then, the Floquet transition matrix (state transition matrix evaluated at the end of the principal period) can determine the stability of the system owing to classical techniques such as pole placement, Routh–Hurwitz criteria, etc. Thus it is possible to place the Floquet multipliers in the desired locations to determine the control gains. This method can be applied to systems without small parameters. The Duffing’s oscillator, the Rössler system and the nonautonomous parametrically forced Lorenz equations are chosen as illustrative examples to demonstrate the application.     

奇异系统的微分和比例输出反馈正则化

奇异系统的微分和比例输出反馈正则化储德林（清华大学应用数学系）ＲＥＧＵＬＡＲＩＺＡＴＩＯＮＯＦＳＩＮＧＵＬＡＲＳＹＳＴＥＭＳＢＹＤＥＲＩＶＡＴＩＶＥＡＮＤＰＲＯＰＯＲＴＩＯＮＡＬＯＵＴＰＵＴＦＥＥＤＢＡＣＫ￥ＣｈｕＤｅ－ｌｉｎ（ＴｓｉｎｇｈｕａＵｎｉ...     

Robust pole placement controller design in LMI region for uncertain and disturbed switched systems

This paper concerns the state feedback control for continuous-time, disturbed and uncertain linear switched systems with arbitrary switching rules. The main result of this work consists in getting a LMI (Linear Matrix Inequalities) condition guaranteeing a robust pole placement according to some desired specifications. Then, external disturbance attenuation with a fixed rate according to the H_∞ criterion is ensured. This is obtained thanks to the existence of a common quadratic Lyapunov function for all sub-systems. Finally, an academic example illustrates the efficiency of the developed approach.     

状态反馈极点配置问题的一个新算法

§1.引言 极点配置问题是控制理论中的一个重要的问题,描述如下: 问题(P1).给定A∈R~(n×n),B∈R~(n×m),Λ={λ_1,λ_2,…,λ_n},Λ在复共轭下封闭.求F∈R~(m×n),使得     

A simple method of chaos control for a class of chaotic discrete-time systems

In this paper, a simple method is proposed for chaos control for a class of discrete-time chaotic systems. The proposed method is built upon the state feedback control and the characteristic of ergodicity of chaos. The feedback gain matrix of the controller is designed using a simple criterion, so that control parameters can be selected via the pole placement technique of linear control theory. The new controller has a feature that it only uses the state variable for control and does not require the target equilibrium point in the feedback path. Moreover, the proposed control method cannot only overcome the so-called “odd eigenvalues number limitation” of delayed feedback control, but also control the chaotic systems to the specified equilibrium points. The effectiveness of the proposed method is demonstrated by a two-dimensional discrete-time chaotic system.     

LMI Approach to Output Feedback Control for Linear Uncertain Systems with D-Stability Constraints

This paper deals with the problem of designing output feedback controllers for linear uncertain continuous-time and discrete-time systems with circular pole constraints. The uncertainty is assumed to be norm bounded and enters into both the system state and input matrices. We focus on the design of a dynamic output feedback controller that, for all admissible parameter uncertainties, assigns all the closed-loop poles inside a specified disk. It is shown that the problem addressed can be recast as a convex optimization problem characterized by linear matrix inequalities (LMI); therefore, an LMI approach is developed to derive the necessary and sufficient conditions for the existence of all desired dynamic output feedback controllers that achieve the specified circular pole constraints. An effective design procedure for the expected controllers is also presented. Finally, a numerical example is provided to show the usefulness and applicability of the present approach.     

Modal exact linearization of a class of second-order switched nonlinear systems

This paper considers the problem of stabilizing single-input affine switched nonlinear systems. The main idea is to transform a switched nonlinear system to an equivalent controllable switched linear system. First, we define the notion of modal state feedback linearization. Then, we develop a set of conditions for modal state feedback linearizability of a certain class of second order switched nonlinear systems. Considering two special structures, easily verifiable conditions are proposed for the existence of suitable state transformations for modal feedback linearization. The results are constructive. Finally, the method is illustrated with two examples, including a Continuous Stirred Tank Reactor (CSTR) to demonstrate the applicability of the proposed approach.     

An efficient parallel processing optimal control scheme for a class of nonlinear composite systems

This article presents an efficient parallel processing approach for solving the optimal control problem of nonlinear composite systems. In this approach, the original high-order coupled nonlinear two-point boundary value problem (TPBVP) derived from the Pontryagin's maximum principle is first transformed into a sequence of lower-order decoupled linear time-invariant TPBVPs. Then, an optimal control law which consists of both feedback and forward terms is achieved by using the modal series method for the derived sequence. The feedback term specified by local states of each subsystem is determined by solving a matrix Riccati differential equation. The forward term for each subsystem derived from its local information is an infinite sum of adjoint vectors. The convergence analysis and parallel processing capability of the proposed approach are also provided. To achieve an accurate feedforward-feedback suboptimal control, we apply a fast iterative algorithm with low computational effort. Finally, some comparative results are included to illustrate the effectiveness of the proposed approach.     

Robust output feedback time optimal decomposed controllers for linear systems via moving horizon estimation

This paper studies the robust output feedback time optimal control (TOC) problem for linear discrete-time systems with state and input constraints. Bounded state disturbances are assumed. The moving horizon estimation (MHE) technique combined with a Luenberger observer is used to design a state estimator with which the state estimation error converges to and remains in some disturbance invariant set. A novel approach is proposed to reduce the computational complexity of TOC, in which the terminal controller comprises several predetermined local linear feedback laws, resulting in a large terminal set. Starting from this relatively large terminal set, a large domain of attraction of the proposed TOC controller can be obtained by using a short horizon, which consequently leads to a low on-line computational effort. A correction term, the output of the observer subtracted from the output of the plant and then multiplied by a design matrix, is added to the TOC controller, which aims at further correcting estimates of the state based on the present estimation error. Furthermore, by formulating a suitable cost function, as time evolves the TOC controller reaches the desired controller to obtain a good asymptotical behavior. A case study is used to illustrate the proposed approach.     

A novel feedforward–feedback suboptimal control of linear time-delay systems

This paper presents a new approach for solving the optimal control problem of linear time-delay systems with a quadratic cost functional. In this approach, a method of successive substitution is employed to convert the original time-delay optimal control problem into a sequence of linear time-invariant ordinary differential equations (ODEs) without delay and advance terms. The obtained optimal control consists of a linear state feedback term and a forward term. The feedback term is determined by solving a matrix Riccati differential equation. The forward term is an infinite sum of adjoint vectors, which can be obtained by solving recursively the above-mentioned sequence of linear non-delay ODEs. A fast-converging iterative algorithm for this purpose is presented which provides a promising possible reduction of computational efforts. Numerical examples demonstrating the efficiency, simplicity and high accuracy of the suggested technique have been included. Simulation results reveal that just a few iterations of the proposed algorithm are required to find an accurate enough feedforward–feedback suboptimal control.     

Partial pole assignment for the quadratic pencil by output feedback control with feedback designs

In this paper we study the partial pole assignment problem for the quadratic pencil by output feedback control where the output matrix is also a designing parameter. In addition, the input matrix is set to be the transpose of the output matrix. Under certain assumption, we give a solution to this partial pole assignment problem in which the unwanted eigenvalues are moved to desired values and all other eigenpairs remain unchanged. Copyright © 2005 John Wiley & Sons, Ltd.     

Robust dynamical compensator design for discrete-time linear periodic systems

This paper considers dynamical compensators design for purpose of pole assignment for discrete-time linear periodic systems. Similar to linear time-invariant systems, it is pointed out that the design of a periodic dynamical compensator can be converted into the design of a periodic output feedback controller for an augmented system. Utilizing the recent result on output feedback pole assignment, parametric solutions for this problem are obtained. The design approach can be used as a basis for the robust dynamical compensator design for this type of systems. Combined with a robustness index presented in this paper, robust dynamical compensator design problem is converted into a constrainted optimization problem. A numerical example is employed to illustrate the validity and feasibility of the methods.