Reduced-order LQG control of a Timoshenko beam model

We present a computational approach for the construction of reduced-order controllers for the Timoshenko beam model. By means of a space discretization of the Timoshenko equations, we obtain a large-scale, finite-dimensional dynamical system, for which we compute an LQG controller for closed-loop stabilization. The solutions of the algebraic Riccati equations characterizing the LQG controller are then used to construct a balancing transformation which allows the dimensional reduction of the large-scale dynamic compensator. We present numerical tests assessing the stability and performance of the approach.     

Reduced order controllers for distributed parameter systems: LQG balanced truncation and an adaptive approach

In this paper, two methods are reviewed and compared for designing reduced order controllers for distributed parameter systems. The first involves a reduction method known as LQG balanced truncation followed by MinMax control design and relies on the theory and properties of the distributed parameter system. The second is a neural network based adaptive output feedback synthesis approach, designed for the large scale discretized system and depends upon the relative degree of the regulated outputs. Both methods are applied to a problem concerning control of vibrations in a nonlinear structure with a bounded disturbance.     

Multi-Lagrange-Multiplier Problems: Desensitized Pole Assignment With Minimal Controller Matrix Norm for Networked Control Systems and Constraints in High-order Mechatronics

From a computational viewpoint, state controllers are implemented in fixed-point microcontrollers with matrices small in norm sense. Inaccuracies when implementing K in networked or remote control are anticipated by including a particular desensitization term. A direct approach for minimizing the Frobenius norm of the controller matrix is addressed including the conditions of predetermined eigenvalues of the closed-loop system. In mechatronics, there is a challenging demand on optimization augmented by a considerable number of conditions. The problem is solvable with several equality conditions included by Lagrange multipliers and interpolation techniques.     

Lead with closed-loop system compensation of a radically rotating elastic rod attached to a rigid body part I: A unified approach to the design of Llnear control system

Due to difficulties in modeling and poor knowledge of parameters, the behavior of flexible structures is subject to significant uncertainty. Hence it is essential that the control system provide an absolutely stable property in the presence of large variations. Over the years, many control laws—proportion and derivative (PD) control, nonlinear, linear-quadratic, adaptive, and linear quadratic Gaussian (LQG)—have been synthesized for flexible structures. The most commonly applied are the LQG controllers. In spite of its attractive qualities, the LQG controller is sensitive to parameter variations, and therefore its performance will deteriorate when the payload or typical parameters of the system vary with time. At the same time, the LQG controller does not guarantee general stability margins, and this is, perhaps, its main drawback. On the other hand, the PD is one kind of controller that ensures system stability to parameter variations within a certain bound. But a problem with the PD controller is evident; when high-frequency noise is present in the system, this noise will be amplified by the PD controller, which is generally unacceptable. In this paper, instead of using a PD controller, a passive lead compensator is employed, so that

• 1.(1) no additional power supplies are required and
• 2.(2) noise due to differentiation is reduced.

This lead compensator, together with a composite control strategy designed by the most popularly used sensors, potentiometer and tachometer, for the corresponding closed-loop system, has been shown with very good agreement in terms of system performance requirement. For the design of control system, it is practical to first design the controller based on the linear system model by neglecting the nonlinearities of the system. In Part I, the lead compensator, together with complementary control strategy and computer simulation modeling for a rotating flexible structure, with particular application to elastic rod system, is presented for the linear control system. Then the designed controller is applied to the nonlinear system model for evaluation and redesigned by computer simulation. This will be presented in Part II.     

Sector-condition-based results for adaptive control and synchronization of chaotic systems under input saturation

This paper addresses the design of adaptive feedback controllers for two problems (namely, stabilization and synchronization) of chaotic systems with unknown parameters by considering input saturation constraints. A novel generalized sector condition is developed to deal with the saturation nonlinearities for synthesizing the nonlinear and the adaptive controllers for the stabilization and synchronization control objectives. By application of the proposed sector condition and rigorous regional stability analysis, control and adaptation laws are formulated to guarantee local stabilization of a nonlinear system under actuator saturation. Further, simple control and adaptation laws are developed to synchronize two chaotic systems under uncertain parameters and input saturation nonlinearity. Numerical simulation results for Rössler and FitzHugh–Nagumo models are provided to demonstrate the effectiveness of the proposed adaptive stabilization and synchronization control methodologies.     

Sliding mode control for uncertain chaotic systems with input nonlinearity

For the sliding mode controller of uncertain chaotic systems subject to input nonlinearity, the upper bound of the norm of uncertainties is commonly used to determine the controller parameter. However, this will cause serious chattering. In order to overcome this drawback, two new sliding mode controllers are proposed to ensure robust synchronization for a classes of chaotic systems with input nonlinearities and external uncertainty. Compared with the existing results, the proposed controllers can effectively reduce the chattering nearby sliding mode and improve the dynamic performance of the systems. Simulation results are provided to verify the proposed methods.     

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.     

Principal powers of matrices with positive definite real part

We study principal powers of complex square matrices with positive definite real part, or with numerical range contained in a sector. We extend the notion of geometric mean to such matrices and we establish an operator norm bound in this context.     

Bounded controllers for robust exponential convergence

We consider the problem of stabilizing an uncertain system when the norm of the control input is bounded by a prespecified constant. We treat continuous-time dynamical systems whose nominal part is linear and whose uncertain part is norm-bounded by a known affine function of the norm of the system state and the norm of the control input. Given a prespecified rate of convergence and a ball containing the origin of the state space, we present controllers which guarantee that, for all allowable uncertainties and nonlinearities, there is a region of attraction from which all solutions converge to the given ball with the prespecified convergence rate.This research was supported by the National Science Foundation under Grant MSS-90-57079.     

Synchronization and anti-synchronization of chaotic oscillators under input saturation

This paper addresses the design of simple state feedback controllers for synchronization and anti-synchronization of chaotic oscillators under input saturation and disturbance. By employing sector condition, linear matrix inequality (LMI)-based sufficient conditions are derived to design (global or local) controllers for chaos synchronization. The proposed local synchronization strategy guarantees a region of stability in terms of difference between states of the master–slave systems. This region of stability can be enlarged by means of an LMI-based optimization algorithm, through which asymptotic synchronization of chaotic oscillators can be ensured for a large difference in their initial conditions. Further, a novel LMI-based robust control strategy is developed, for local synchronization of input-constrained chaotic oscillators, by providing an upper bound on synchronization error in terms of disturbance and initial conditions of chaotic systems. Moreover, the proposed robust state feedback control methodology is modified to provide an inaugural treatment for robust anti-synchronization of chaotic systems under input saturation and disturbance. The results of the proposed methodologies are verified through numerical simulations for synchronization and anti-synchronization of the master–slave chaotic Chua’s circuits under input saturation.     

Non-fragile robust stabilization and control for uncertain stochastic nonlinear time-delay systems

This paper deals with the problem of non-fragile robust stabilization and H_∞ control for a class of uncertain stochastic nonlinear time-delay systems. The parametric uncertainties are real time-varying as well as norm bounded. The time-delay factors are unknown and time-varying with known bounds. The aim is to design a memoryless non-fragile state feedback control law such that the closed-loop system is stochastically asymptotically stable in the mean square and the effect of the disturbance input on the controlled output is less than a prescribed level for all admissible parameter uncertainties. New sufficient conditions for the existence of such controllers are presented based on the linear matrix inequalities (LMIs) approach. Numerical example is given to illustrate the effectiveness of the developed techniques.     

Stochastic exponential synchronization of jumping chaotic neural networks with mixed delays

This paper deals with the exponential synchronization problem for a class of stochastic jumping chaotic neural networks with mixed delays and sector bounded nonlinearities. The mixed time delays under consideration comprise both discrete time-varying delays and distributed time delays. By applying the Finsler’s Lemma and constructing appropriate Lyapunov-Krasovskii functional based on delay partitioning, several improved delay-dependent feedback controllers with sector nonlinearities are developed to achieve the synchronization in mean square in terms of linear matrix inequalities. It is established theoretically that two special cases of the obtained criteria are less conservative than some existing results but including fewer slack variables. As the present conditions involve no free weighting matrices, the computational burden is largely reduced. One numerical example is provided to demonstrate the effectiveness of the theoretical results.     

LQG量测反馈最优控制的精细积分

对于线性二次型高斯(LQG)量测反馈最优控制问题,提出了精细积分解法。根据分离性原理,LQG控制问题可以分成为最优状态反馈控制问题以及最优状态估计问题,即:离线计算的两套黎卡提微分方程的求解以及状态向量的时变微分方程的在线积分解。该算法不仅适用于求解二点边值问题及其相应的黎卡提微分方程,也适用于求解状态估计的时变微分方程。精细积分高精度的特点,对控制和估计都是有利的。数值算例表明了算法的高精度及有效性。     

An extension of Radner's theorem

Radner's theorem states that the optimal solution for a static linear quadratic Gaussian (LQG) team is linear. In this paper, we find the optimal solution for a static LQG team in which each player knows which observations he has, but in which the observation set that a player receives (how many, which measuring device,etc.) is random before the team acts. Via the concept of nesting, the result extends to the dynamic case and includes teams in which the order of play of the team members as well as their sets of data are random. We also include random changes in the cost function which depend on the randomness of the observation system but are independent of the stochastic process that the team is observing and controlling.     

Nonlinear functional analysis and optimal economic growth

A problem of existence and characterization of solutions of optimal growth models in many sector economies is studied. The social utility to be optimized is a generalized form of a preference depending additively on consumption at the different dates of the planning period. The optimization is restricted to a set of admissible growth paths defined by production-investment-consumption relations described by a system of differential equations. Sufficient conditions are given for existence of a solution in a Hilbert space of paths, without convexity assumptions on either the utilities or the technology, using techniques of nonlinear functional analysis. A characterization is given of the utilities which are continuous with respect to the Hilbert space norm. Under convexity assumptions a characterization is also given of optimal and efficient solutions by competitive prices.     

求解非定常Lavrentiev迭代方程的多尺度配置法

本文采用多尺度配置法求解第一类弱扇形积分方程.将压缩配置法用于投影离散非定常迭代正则化方程,得到了近似解在Banach空间范数下误差估计,给出了迭代停止准则,确保近似解无穷范数下的最优收敛率.优点是确保了收敛率,减少了计算量.数值例子验证了算法的有效性.     

Explicit solution for a vector-valued LQG homing problem

In this note, a vector-valued LQG homing problem subject to a controlled stock-wealth process is formulated. Under certain conditions, the problem is solved explicitly via an auxiliary scalar LQG homing problem.     

Fractional-power semigroups of growth n

We characterize certain semigroups, in terms of growth properties, as fractional-power semigroups associated with special linear operators. Such a semigroup is holomorphic in a sector containing the positive reals. Its norm may grow as a negative power of distance from the origin, and may grow extremely rapidly with angular approach to the edges of the sector of definition. We show that a semigroup of this kind can be viewed as {exp(?w(?A)^a)}, where A is an operator whose resolvent is defined, with polynomial growth, in a region asymptotic, in a special sense, to a half-plane.