Noncausal minimax linear state estimation for systems with uncertain second-order statistics

This note considers the problem of minimax state estimation of the states of a linear time-invariant system which is driven by and observed in the presence of noise processes with uncertain second-order statistics. When the process noise and observations are scalars, the problem is shown to be equivalent to a scalar minimax estimation problem. The existence of a minimax solution is thereby established, and the minimax filter is shown to be a linear transformation of the minimax filter for the scalar problem.     

Topological entropy and data rate for practical stability: a scalar case

A special class of nonlinear systems, i.e. expanding piecewise affine discrete‐time scalar systems with limited data rate, is used to investigate the role of topological entropy and date rate in a practical stability problem. This special class of nonlinear system as an abstract model is an extension of discrete‐time unstable scalar systems, a well‐known model for quantized feedback design. For such systems with finite quantization levels, how to design a quantized feedback controller to achieve practical stability is considered as a boundability problem. Unlike the existing results about topological entropy for nonlinear stabilization and optimal control for linear systems, for the boundability problem under consideration, the feedback topological entropy defined in this paper is not equal to the minimum number of the quantization interval (i.e. the minimal information rate) and only provides a necessary condition for the boundability of our system under some condition. A necessary and sufficient condition for the boundability is also presented in terms of an inequality related to data rate and the minimum number of quantization intervals. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A constrained scalar control for the motion of a system of oscillators with damping residual oscillations

The problem of scalar control of a finite or countable system of oscillators mounted on a common base is considered. The control is conducted by a scalar bounded force applied to the base. A wide circle of control problems for systems with distributed parameters and many-mass systems can be reduced to the considered statement. A method for solving the problem of constructing a control bounded in modulus that steers the base from a given state to the origin for a finite time and provides that there are no residual oscillations is developed.     

On the optimum timing of observations for linear control systems with unknown initial state

A linear system with a cost function that is quadratic in the control and terminal position error is given. The initial state is unknown and noise-corrupted observations are taken. Due to the cost of taking the observations, they are limited to a given number. Using the tools of optimum stochastic control theory, the optimum timing of the available observations is determined (minimizing the expected value of the loss function). For the cases considered, the locations can be determined a priori, and do not depend on the values of previous observations. Graphs of the optimum observation locations for several scalar cases are given. Graphs of the true cost, as a function of the locations of the observations, are also given for several scalar cases. The change in cost for small variations from the optimum location is usually not significant.     

单参数离散时间非线性系统的可镇定性定理

本文对基本的离散时间非线性单参数随机系统建立了可镇定性定理. 该定理推进了文献[1]的结果, 进一步完 善了关于离散时间自适应控制的反馈能力刻画. 离散时间单参数系统可镇定的一个重要非线性临界常数是4, 用以刻画 关于幂函数类系统的反馈能力. 而作为本文定理的应用, 本文对一类典型的单参数离散时间非线性随机系统发现了新的 可镇定临界常数2.     

Minimum sensitivity design of linear multivariable feedback control systems by matrix spectral factorization

A scalar measure of system sensitivity to plant parameter variations is employed in the design of linear lumped stationary multivariable feedback control systems. The plant parameters are treated as random variables, and design formulas are derived which lead to systems with the smallest expected value for the chosen scalar sensitivity measure. The design formulas give physically realizable feedback and tandem compensation network transfer function matrices provided the overall system transfer function matrix is properly specified. The solution of the minimum sensitivity design problem is obtained by first solving the multivariable semi-free-configuration Wiener problem.     

Optimum experimental designs for dynamic systems in the presence of correlated errors

The problem of determining an optimal measurement time schedule for identification of unknown parameters in multiresponse systems when correlations between observations occur is considered. The measurement process is performed by collecting data at discrete time instants from several outputs. An observation plan is proposed based on a scalar measure of the Fisher information matrix as the design criterion quantifying the accuracy of parameter estimators. A numerical procedure is proposed to determine approximations of optimum designs in the case of correlated measurement errors. The approach is illustrated with an example of the multi-output system of equations describing a chemical kinetic reaction.     

Optimal measurement policies for control purposes

A method is presented for off-line calculation of optimal measurement subsets to be used during implementation of optimal feedback control for linear stochastic systems. It is seen that feedback control imposes a penalty on noisy measurements which must be included with measurement cost in the optimization. The combinatorial problem involved with subset selection is avoided by creating a non-linear ‘ optimal control ’ problem which can be solved using available algorithms. Results for a scalar example show that, with costly measurements, it is most economical to use a number of short measurement periods.     

A necessary and sufficient condition for feedback stabilization in a factorial ring

The necessity for a coprime fractional representation of a plant, in order to completely parametrize all stabilizing compensators by the Youla theory, is examined. It is shown that the coprimeness is necessary for systems in a factorial ring, a class inclusive of multidimensional scalar systems. Some observations on partial-state transfer functions in the feedback configuration are found to be useful in showing the necessity.     

The Brockett Problem for Linear Discrete Control Systems

The Brockett problem for linear discrete control systems is studied. A method for designing time-varying stabilizing feedback is developed. The Brockett problem for second-order systems with scalar feedback and nondegenerate transfer function is shown to have a positive solution.     

Disturbance Decoupled Observers for Systems With Unknown Inputs

This note deals with the design of reduced-order disturbance decoupled scalar functional observers for linear systems with unknown inputs. Based on a parametric approach, existence conditions are derived and a design procedure for finding reduced-order scalar functional observers is given. The derived existence conditions are relaxed and the procedure can find first-order disturbance decoupled scalar functional observers for some cases where the number of unknown inputs is more than the number of outputs. Also, the observer matching condition, which is the necessary requirement for the design of state observers for linear systems with unknown inputs, is not required. Numerical examples are given to illustrate the attractiveness of the proposed design method.      

A new fusion formula and its application to continuous-time linear systems with multisensor environment

The problem of fusion of local estimates is considered. An optimal mean-square linear combination (fusion formula) of an arbitrary number of local vector estimates is derived. The derived result holds for all dynamic systems with measurements. In particular, for scalar uncorrelated local estimates, the fusion formula represents the well-known result in statistics. The fusion formula is applied to fusion of local Kalman estimates in multisensor filtering problem. Examples demonstrate high accuracy of the proposed fusion formula.     

Multispace and multilevel BDDC

The Balancing Domain Decomposition by Constraints (BDDC) method is the most advanced method from the Balancing family of iterative substructuring methods for the solution of large systems of linear algebraic equations arising from discretization of elliptic boundary value problems. In the case of many substructures, solving the coarse problem exactly becomes a bottleneck. Since the coarse problem in BDDC has the same structure as the original problem, it is straightforward to apply the BDDC method recursively to solve the coarse problem only approximately. In this paper, we formulate a new family of abstract Multispace BDDC methods and give condition number bounds from the abstract additive Schwarz preconditioning theory. The Multilevel BDDC is then treated as a special case of the Multispace BDDC and abstract multilevel condition number bounds are given. The abstract bounds yield polylogarithmic condition number bounds for an arbitrary fixed number of levels and scalar elliptic problems discretized by finite elements in two and three spatial dimensions. Numerical experiments confirm the theory.     

Performance Analysis of Scalar DC–QIM for Zero-Bit Watermarking

Quantization-based schemes, such as scalar distortion compensated quantization index modulation (DC-QIM), have demonstrated some performance merits in data hiding, which is mainly a transmission problem. However, a number of applications can be stated in terms of the watermark detection problem (also named zero-bit watermarking), and this situation has been seldom addressed in the literature for quantization-based techniques. In this context, we carry out a complete performance analysis of dithered uniform quantizer-based QIM with DC under additive white Gaussian noise. Using large deviation theory, performance is evaluated according to the receiver operating characteristic (ROC) and the total probability of detection error. Under the white Gaussian host signal assumption, scalar DC-QIM is compared with other existing watermarking methods, including quantized projection (QP), spread spectrum (SS) and improved SS (ISS, for which zero-bit watermarking performances with correlation detector are also proposed). Among the compared methods, it is shown that dithered scalar DC-QIM is the more relevant choice to address zero-bit watermarking, due to its host independent performance. A short comparison is also provided with respect to the corresponding transmission problem, thus evaluating the loss in performance due to the detection. We conclude in measuring the performance gain that could be provided by the use of more sophisticated lattice quantizers than the cubic structure     

Canonical state space representations for multivariable systems

The problem of state space representations for multiple-input, multiple-output linear time-invariant systems is considered. The known definitions of the first and second canonical forma for scalar systems are used to facilitate the derivation of explicit canonical expressions for multivariable systems.     

Petrov invariants of Hamiltonian systems with a control parameter

The problem is considered of the classification of Hamiltonian systems with a scalar control parameter relative to feedback transformations. Differential invariants of these systems, which are called Petrov invariants, are set up. The dimensions of algebras of these invariants are found. The conditions of global equivalence of regular Hamiltonian systems with the control parameter are found in terms of Petrov invariants.     

多变量时滞系统Dahlin控制器的设计

在现代鲁棒控制理论基础上,提出一种多变量Dahlin控制器多目标优化设计方法. 利用线性分解变换,多变量Dahlin控制器设计问题被转化为标准的H∞优化问题,通过对标 准的H∞优化问题求解得到了最终的控制器.它同时具有时滞补偿,解耦和控制的作用.与已 有的方法相比,该方法不但直观,而且兼顾了系统的性能和鲁棒性.     

Stability analysis of interconnected systems with possibly unstable subsystems

A direct method is presented for stability analysis of nonlinear interconnected dynamical systems. A new scalar Lyapunov function is considered as weighted sum of individual Lyapunov functions for each free subsystem and individual scalar functions related separately to each connection. Sufficient conditions are obtained for asymptotic stability of the equilibrium state by testing the definity of two constant square matrices whose dimension is equal to the number of subsystems. This method can assure stability of systems with possible unstable subsystems. A simple numerical example is included to illustrate this theory.