Local differentiable pole assignment

Given a general local differentiable family of pairs of matrices, we obtain a local differentiable family of feedbacks solving the pole assignment problem, that is to say, shifting the spectrum into a prefixed one. We point out that no additional hypothesis is needed. In fact, simple approaches work in particular cases (controllable pairs, constancy of the dimension of the controllable subspace, and so on). Here the general case is proved by means of Arnold's techniques: the key point is to reduce the construction to a versal deformation of the central pair; in fact to a quite singular miniversal one for which the family of feedbacks can be explicitly constructed. As a direct application, a differentiable family of stabilizing feedbacks is obtained, provided that the central pair is stabilizable.     

无界单输入分布参数系统的一秩扰动和极点配置

本文考虑一类带有无界单输入元的分布参数系统的无条件基扰动和极点配置问题,推广了文［1－4］的结果,同时亦解决了文［5］中提出的一个猜想．     

A new algorithm for pole assignment of single-input linear systems using state feedback

In this paper we present a new algorithm for the single-input pole assignment problem using state feedback. This algorithm is based on the Schur decomposition of the closed-loop system matrix, and the numerically stable unitary transformations are used whenever possible, and hence it is numerically reliable.The good numerical behavior of this algorithm is also illustrated by numerical examples.     

Dissipativity for Lur’e distributed parameter control systems

In this work, dissipativity of Lur’e distributed parameter control systems has been addressed. Delay-dependent sufficient conditions for the dissipativity with respect to the infinite-dimensional version of energy supply rate (Q₁,S₁,R₁) characterized exclusively by unbounded operator Q₁ are established in terms of linear operator inequalities (LOIs). Finally, the heat equation illustrates our result.     

Gossip based asynchronous and randomized distributed task assignment with guaranteed performance on heterogeneous networks

The main contribution of this paper is a novel distributed algorithm based on asynchronous and randomized local interactions, i.e., gossip based, for task assignment on heterogeneous networks. We consider a set of tasks with heterogeneous cost to be assigned to a set of nodes with heterogeneous execution speed and interconnected by a network with unknown topology represented by an undirected graph. Our objective is to minimize the execution time of the set of tasks by the networked system. We propose a local interaction rule which allows the nodes of a network to cooperatively assign tasks among themselves with a guaranteed performance with respect to the optimal assignment exploiting a gossip based randomized interaction scheme. We first characterize the convergence properties of the proposed approach, then we propose an edge selection process and a distributed embedded stop criterion to terminate communications, not only task exchanges, while keeping the performance guarantee. Numerical simulations are finally presented to corroborate the theoretical results.     

Absolutely exponential stability of Lur’e distributed parameter control systems

In this work, absolutely exponential stability of Lur’e distributed parameter control systems with delayed state has been addressed. Delay-dependent sufficient conditions for the absolutely exponential stability in Hilbert spaces are established in terms of linear operator inequalities (LOIs). Finally, the wave equation is given to illustrate our result.     

D-optimal design of a monitoring network for parameter estimation of distributed systems

This paper addresses the design of a network of observation locations in a spatial domain that will be used to estimate unknown parameters of a distributed parameter system. We consider a setting where we are given a finite number of possible sites at which to locate a sensor, but cost constraints allow only some proper subset of them to be selected. We formulate this problem as the selection of the gauged sites so as to maximize the log-determinant of the Fisher information matrix associated with the estimated parameters. The search for the optimal solution is performed using the branch-and-bound method in which an extremely simple and efficient technique is employed to produce an upper bound to the maximum objective function. Its idea consists in solving a relaxed problem through the application of a simplicial decomposition algorithm in which the restricted master problem is solved using a multiplicative algorithm for optimal design. The use of the proposed approach is illustrated by a numerical example involving sensor selection for a two-dimensional convective diffusion process.     

Empirical Gramian-based spatial basis functions for model reduction of nonlinear distributed parameter systems

Correct selection of spatial basis functions is crucial for model reduction for nonlinear distributed parameter systems in engineering applications. To construct appropriate reduced models, modelling accuracy and computational costs must be balanced. In this paper, empirical Gramian-based spatial basis functions were proposed for model reduction of nonlinear distributed parameter systems. Empirical Gramians can be computed by generalizing linear Gramians onto nonlinear systems, which results in calculations that only require standard matrix operations. Associated model reduction is described under the framework of Galerkin projection. In this study, two numerical examples were used to evaluate the efficacy of the proposed approach. Lower-order reduced models were achieved with the required modelling accuracy compared to linear Gramian-based combined spatial basis function- and spectral eigenfunction-based methods.     

Input-to-state stability for Lur’e stochastic distributed parameter control systems

In this work, the stochastic input-to-state stability (SISS) of Lur’e distributed parameter control systems has been addressed. Using a comparison principle, delay-dependent sufficient conditions for the stochastic input-to-state stability in Hilbert spaces are established in terms of linear operator inequalities (LOIs). Finally, the stochastic wave equation illustrates our result.     

Periodic measurement strategies for distributed parameter systems filtering

This paper deals with the optimization of the output matrix for a discrete time linear stochastic system. The output matrix varies as a periodic function of time, and its values are constrained to belong to a finite prescribed set. The aim is to minimize the average variance of the Kalman filter estimation error in the periodic steady state. The application regards the optimization both of the measurement points and of the scanning sequence for a distributed parameter system (DPS) of parabolic type. A modal approximation is used to reduce the DPS to finite dimension. The proposed solution algorithm makes use of heuristic rules that enable to overcome the difficulties arising from the cardinality of the admissible set, the possible slow convergence of the relevant Riccati equation and the high dimensionality of the lumped approximate model of the DPS. The numerical applications show that the periodic scanning policies, found by the optimization algorithm, cause a great improvement of the filter performance, with respect to the case where a single fixed sensor is used.     

Procedure for asymptotic state and parameter estimation of nonlinear distributed parameter bioreactors

Due to measurement problem in biological variables, such as the biomass concentration and its specific growth rate, the on-line measurement of these variables is not ensured and this presents a great difficulty, especially when we consider the control problem. This paper presents and analyses an approach for estimating these biological variables through an example of a nonlinear distributed parameter bioreactor. An orthogonal collocation method is applied in the distributed system to obtain a system of ordinary differential equations. A simulation study shows the feasibility and the robustness of the estimator used for this nonlinear process.     

Absolute mean square exponential stability of Lur’e stochastic distributed parameter control systems

In this work the absolute mean square exponential stability of Lur’e stochastic distributed parameter control systems has been addressed. Delay-dependent sufficient conditions for the stochastic stability in Hilbert spaces are established in terms of linear operator inequalities (LOIs). Finally, the stochastic wave equation illustrates our result.     

The region of attainability of nonlinear systems with unbounded controls

In this work, we give a characterization of the topological boundary and the interior of the reachable set for a family of vector fields of the formX ⁰+aX ⁱ , wherea andi belongs to an arbitrary set of indices. The methods considered in this article are applied to various problems in control theory.The authors wish to express their gratitude to Professor Felix Albrecht for his precious comments on the first version of this work.     

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.     

Stabilization of linear distributed control systems with unbounded delay

In this paper we study the asymptotic stabilization of linear distributed parameter control systems with unbounded delay. Assuming that the semigroup of operators associated with the uncontrolled and nondelayed equation is compact and that the phase space is a uniform fading memory space, we characterize those systems that can be stabilized using a feedback control. As consequence we conclude that every system of this type is stabilizable with an appropriated finite dimensional control.     

On the pole assignment for single-input systems with time-delays

A design procedure is put forward for pole allocation for single-input systems with time delays. A relationship is obtained which allows a straightforward calculation of the feedback matrix to attain prescribed closed-loop pole positions. Numerical examples are given to illustrate the method.     

Least squared estimation for distributed parameter systems with uncertain observations: Part 1: linear prediction and filtering

The least mean squared error linear one-stage predictor and filter are derived for discrete-time distributed parameter systems with uncertain observations. The measurements are taken at several fixed points of the spatial domain. We have used an orthogonal projection approach. © 1998 John Wiley & Sons, Ltd.     

Stabilization and control of distributed systems with time-dependent spatial domains

This paper considers the problem of the stabilization and control of distributed systems with time-dependent spatial domains. The evolution of the spatial domains with time is described by a finite-dimensional system of ordinary differential equations, while the distributed systems are described by first-order or second-order linear evolution equations defined on appropriate Hilbert spaces. First, results pertaining to the existence and uniqueness of solutions of the system equations are presented. Then, various optimal control and stabilization problems are considered. The paper concludes with some examples which illustrate the application of the main results.This work was supported by the Air Force Office of Scientific Research, Grant No. AFOSR 86-0132, by the National Science Foundation, Grant No. 87-18473, and by the Jet Propulsion Laboratory, Pasadena, California.