A parametric solution to the pole assignment problem using dynamicoutput-feedback

A technique is presented for pole placement of linear time-invariant systems using dynamic feedback. A previously developed method for partial pole assignment using constant feedback is generalized to the dynamic output-feedback case. Subject to a mild assumption on the number of complex conjugate poles to be assigned, it is almost always possible to arbitrarily assign all the closed-loop system poles using a compensator of order [(n-φ)/max(m,l)] using this new method. Here, n, m, and l are the order of the system, and the number of inputs and outputs, respectively, and φ Δ/=max(m,l)+[max(m,l)/2]+…+[max(m,l)/min(m,l)] where [x] denotes the nearest integer lower than or equal to x (i.e., floor (x)), and [x] denotes the nearest integer greater than or equal to x (i.e., ceiling (x)). An equivalent result is that using a compensator of order q, it is almost always possible to arbitrarily assign min(n+q,(max(m,l)+1)q+φ) closed-loop system poles. Only the normal procedures of linear algebra are required to implement the technique. Note that φ⩾l+m-1 and, therefore, the result is stronger than previous exact pole assignment results. Since it does not involve iteration or any other numerical techniques, it is possible to implement the method symbolically and, therefore, to obtain general parametric solutions to the pole assignment problem. The freedom in this design approach can also often be used to guarantee the internal stability and/or robustness of the resulting closed-loop system     

A parametric programming solution to the F-policy queue with fuzzy parameters

This paper investigates the F-policy queue using fuzzy parameters, in which the arrival rate, service rate, and start-up rate are all fuzzy numbers. The F-policy deals with the control of arrivals in a queueing system, in which the server requires a start-up time before allowing customers to enter. A crisp F-policy queueing system generalised to a fuzzy environment would be widely applicable; therefore, we apply the α-cuts approach and Zadeh's extension principle to transform fuzzy F-policy queues into a family of crisp F-policy queues. This study presents a mathematical programming approach applicable to the construction of membership functions for the expected number of customers in the system. Furthermore, we propose an efficient solution procedure to compute the membership function of the expected number of customers in the system under different levels of α. Finally, we give an example of the proposed system as applied to a case in the automotive industry to demonstrate its practicality.     

A logarithmic-time solution to the point location problem for parametric linear programming

The optimiser of a (multi) parametric linear program (pLP) is a piecewise affine function defined over a polyhedral subdivision of the set of feasible states. Once this affine function has been pre-calculated, the optimal solution can be computed for a particular parameter by determining the region that contains it. This is the so-called point location problem. In this paper, we show that this problem can be written as an additively weighted nearest neighbour search that can be solved in time linear in the dimension of the state space and logarithmic in the number of regions.

It is well-known that linear model predictive control (MPC) problems based on linear control objectives (e.g., 1- or ∞-norm) can be posed as pLPs, and on-line calculation of the control law involves the solution to the point location problem. Several orders of magnitude sampling speed improvement are demonstrated over traditional MPC and closed-form MPC schemes using the proposed scheme.     

A framework for robust parametric set membership identification

This paper proposes a new framework for studying robust parametric set membership identification. The authors derive some new results on the fundamental limitations of algorithms in this framework, given a particular model structure. The new idea is to quantify uncertainty only with respect to the (finite dimensional) parametric part of the model and not the (fixed size) unmodeled dynamics. Thus, the measure of uncertainty is different from the measures used in previous robust identification work where system norms are used to quantify uncertainty. As an example, the results are used to assess the fidelity of a certain approximate robust parametric set membership identification algorithm     

A set of standard modeling commands for the history-based parametric approach

The current version of STEP standard cannot exchange the parametric information of CAD models. Only pure boundary representations that cannot be parametrically edited are transferable [Geometric Modeling: Theory and Practice (1997)]. There are two approaches for the exchange of design intents such as parameters, features, and constraints. The first is an explicit approach based on constraints between pre-defined parameters and features. The second is a procedural approach based on the sequence of operations issued to construct the models. The authors have previously proposed a macro-parametric approach [International Journal of CAD/CAM 2 (2002) 23], which is a variation of the procedural approach. In this approach, CAD models can be exchanged in the form of macro files, which include the history of modeling commands. To exchange CAD models using the macro-parametric approach, a set of standard modeling commands should be defined. This paper introduces a set of standard commands and explains the process of developing the set.     

Solvers for the verified solution of parametric linear systems

We present a newly developed version of our solvers for the verified solution of dense parametric linear systems, i.e. linear systems whose system matrix and right-hand side depend affine-linearly on parameters that vary inside prescribed intervals. The solvers use our C++ class library for reliable computing, C-XSC. The C-XSC library provides many features, especially easy to handle data types for dense and sparse matrices and vectors and the ability to compute dot products and dot product expressions in arbitrary precision. The new solvers can use either sparse or dense matrices as the coefficient matrices for the parameters. The use of sparse coefficient matrices can result in huge improvements in both performance and memory consumption. BLAS and LAPACK routines are used where applicable, and OpenMP is used for the parallelization on multi-core and multi-processor systems. The solvers also provide the ability to compute not only an outer but also a componentwise inner enclosure of the solution set of the system and to choose between two versions of the algorithm, one being very fast and one giving sharp results and extending the range of solvable systems. We give some examples for parametric linear systems (also from real world examples such as worst-case tolerance analysis of linear electric circuits), give performance measurements of our solvers and also demonstrate that they scale very well when using multiple cores or processors.     

The parametric solution of underdetermined linear ODEs

The purpose of this paper is twofold. An immediate practical use of the presented algorithm is its applicability to the parametric solution of underdetermined linear ordinary differential equations (ODEs) with coefficients that are arbitrary analytic functions in the independent variable. A second conceptual aim is to present an algorithm that is in some sense dual to the fundamental Euclids algorithm, and thus an alternative to the special case of a Gröbner basis algorithm as it is used for solving linear ODE-systems. In the paper Euclids algorithm and the new “dual version” are compared and their complementary strengths are analysed on the task of solving underdetermined ODEs. An implementation of the described algorithm is interactively accessible under [7].     

Comparison of direct to shooting enclosures for an inverse-monotone boundary value problem with locally steep solution

For an inverse-monotone boundary value problem with the nonlinear ODE –ɛu" + sinh(u)=1,ɛ>0, u(0)=u(1)=0, applications of the following enclosure methods are presented and discussed:

The solution set of the mixed ls-tls problem

Although the least squares (LS) problem and the total least squares (TLS) problem have received much attention, the mixed LS-TLS problem still remains to be investigated. In this paper, we study the necessary and sufficient solvability conditions for the mixed LS-TLS problem in Frobenius norm. The solution set, the minimum Frobenius norm solution and an algorithm to obtain the solution are also given. Further we propose the mixed LS-TLS problem in spectral norm and present the solvability condition.     

动态仿真模型的参数曲面族包络体表示

为建立系统仿真中运动单元的动态模型,首先根据仿真单元起始位置和终止位置的部分表面以及运动轨迹推导了包络面族的方程,然后根据包络面形成时与任意两个运动曲面的公切求取曲面族包络的瞬时接触线,为仿真干涉校验算法中计算各运动单元部件扫描体交集提供了理论依据。     

The minimal disturbance invariant set: Outer approximations via its partial sums

This paper is concerned with outer approximations of the minimal disturbance invariant set (MDIS) of a discrete-time linear system with an additive set-bounded disturbance. The k-step disturbance reachable sets (Minkowski partial sums) are inner approximations of MDIS that converge to MDIS. Enlarged by a suitable scaling, they can lead to outer approximations of MDIS. Three families of approximations, each based on partial sums, are considered. Theoretical properties of the families are proved and interrelated. Algorithmic questions, including error bounds, are addressed. The results are illustrated by computational data from several examples.     

Estimation of algebraic solution by limiting the solution set of an interval linear system

In this paper, we introduce a new method for estimating the algebraic solution of an interval linear system (ILS) whose coefficient matrix is real-valued and right-hand side vector is interval-valued. In the proposed method, we first apply the interval Gaussian elimination procedure to obtain the solution set of an interval linear system and then by limiting the solution set of related ILS by the limiting factors, we get an algebraic solution of ILS. In addition, we prove that the obtained solution by our method satisfies the related interval linear system. Finally, based on our method, an algorithm is proposed and numerically demonstrated.     

A uniform solution to the independent set problem through tissue P systems with cell separation

Membrane computing is an emergent branch of natural computing, which is inspired by the structure and the functioning of living cells, as well as the organization of cells in tissues, organs, and other higher order structures. Tissue P systems are a class of the most investigated computing models in the framework of membrane computing, especially in the aspect of efficiency. To generate an exponential resource in a polynomial time, cell separation is incorporated into such systems, thus obtaining so called tissue P systems with cell separation. In this work, we exploit the computational efficiency of this model and construct a uniform family of such tissue P systems for solving the independent set problem, a well-known NP-complete problem, by which an efficient solution can be obtained in polynomial time.     

On the stability of solution mapping for parametric generalized vector quasiequilibrium problems

In this paper, we study the solution stability for a class of parametric generalized vector quasiequilibrium problems. By virtue of the parametric gap function, we obtain a sufficient and necessary condition for the Hausdorff lower semicontinuity of the solution mapping to the parametric generalized vector quasiequilibrium problem. The results presented in this paper generalize and improve some main results of Chen et al. (2010) [34], and Zhong and Huang (2011) [35].