On the explicit dead-time compensation for robust model predictive control

Computational simplicity is one of the most important aspects to take into account in robust model predictive control (MPC). In dead-time processes, it is common to use an augmented state-space representation in order to apply robust MPC strategies but, this procedure may affect computational aspects. In this paper, explicit dead-time compensation will be used to avoid augmented representation. This technique will be analyzed in terms of robust stability and constraint satisfaction for discrete-time linear systems. The results of this discussion will be applied to a robust tube-based MPC strategy which is able to guarantee robust stability and constraint satisfaction of a dead-time system by considering a prediction model without dead-time. Moreover, taking advantage of the proposed scheme, the robust MPC will be particularized for first-order plus dead-time models which simplifies significantly controller synthesis. The proposed dead-time compensation method will be applied to different robust MPC strategies in two case studies: (i) a simulated quadruple-tank system, and (ii) an experimental scaled laboratory heater process.     

Remarks on the L/sup p/-input converging-state property

Let X /spl sub/ /spl Ropf//sup N/ and consider a system x/spl dot/ = f(x,u), f : X /spl times/ /spl Ropf//sup M/ /spl rarr/ /spl Ropf//sup N/, with the property that the associated autonomous system x/spl dot/ = f (x,0) has an asymptotically stable compactum C with region of attraction A. Assume that x is a solution of the former, defined on [0,/spl infin/), corresponding to an input function u. Assume further that, for each compact K /spl sub/ X, there exists k > 0 such that |f(z,v) - f(z,0)| /spl les/ k|v| for all (z,v) /spl isin/ /spl times/ /spl Ropf//sup M/. A simple proof is given of the following L/sup p/-input converging-state property: if u /spl isin/ L/sup p/ for some p /spl isin/ [1,/spl infin/) and x has an /spl omega/-limit point in A, then x approaches C.     

L/sup p/ approximation of Sigma-Pi neural networks

A feedforward Sigma-Pi neural network with a single hidden layer of m neurons is given by /sup m//spl Sigma//sub j=1/c/sub j/g(n/spl Pi//sub k=1/x/sub k/-/spl theta//sub k//sup j///spl lambda//sub k//sup j/) where c/sub j/, /spl theta//sub k//sup j/, /spl lambda//sub k//spl isin/R. We investigate the approximation of arbitrary functions f: R/sup n//spl rarr/R by a Sigma-Pi neural network in the L/sup p/ norm. An L/sup p/ locally integrable function g(t) can approximate any given function, if and only if g(t) can not be written in the form /spl Sigma//sub j=1//sup n//spl Sigma//sub k=0//sup m//spl alpha//sub jk/(ln|t|)/sup j-1/t/sub k/.     

On the extraction of dead-time controllers and estimators from delay-free parametrizations

An approach to control design for dead-time (DT) systems is proposed. The underlying idea is to treat the DT element not as a part of the generalized plant, but rather as a (causality) constraint imposed upon the controller (estimator). This enables one to use well-understood parametrizations of all delay free controllers in the DT design. In particular, DT controllers can be extracted from such delay-free parametrizations. In the paper, the extraction procedures are developed in both H/sup 2/ and H/sup /spl infin// settings. It is shown that the proposed approach yields simple solution procedures and new transparent and intuitively appealing structures for the resulting controllers and estimators.     

On the delay margin of dead-time compensators

Dead-time compensators (DTCs) are frequently regarded as being excessively sensitive to uncertainty in the loop delay. Yet this claim is based mostly on empirical studies rather than on any rigorous analysis. In particular, despite existing literature on calculating the delay margin, μ _d, there appears to be no study of the underlying reasons of such a sensitivity. In this paper we address the latter issue. By applying Nyquist criterion arguments, we demonstrate that substantial deterioration of μ _d is caused by the crossover proliferation phenomenon, which, in turn, may be triggered by the use of DTC, especially when aggressive control strategies are used. We also show that crossover proliferation may give rise to the discontinuity of μ_d as a function of system parameters. We argue that the sensitivity of DTCs to delay uncertainty shows mainly through these discontinuity points, so that the robustness can be improved if the discontinuities are avoided.     

On ℋ∞ control for dead-time systems

A mixed sensitivity ℋ_∞ problem is solved for dead-time systems. It is shown that for a given bound on the ℋ_∞-norm causal stabilizing controllers exist that achieve this bound if and only if a related finite-dimensional Riccati equation has a solution with a certain nonsingularity property. In the case of zero time delay, the Riccati equation is a standard Riccati equation and the nonsingularity condition is that the solution be nonnegative definite. For nonzero time delay, the nonsingularity condition is more involved but still allows us to obtain controllers. All suboptimal controllers are parameterized, and the central controller is shown to be a feedback interconnection of a finite-dimensional system and a finite memory system, both of which can be implemented. Some ℋ_∞ problems are rewritten as pure rational ℋ _∞, problems using a Smith predictor parameterization of the controller     

Inducing NNC-trees with the R/sup 4/-rule

An NNC-Tree is a decision tree (DT) with each nonterminal node containing a nearest neighbor classifier (NNC). Compared with the conventional axis-parallel DTs (APDTs), the NNC-Trees can be more efficient, because the decision boundary made by an NNC is more complex than an axis-parallel hyperplane. Compared with single-layer NNCs, the NNC-Trees can classify given data in a hierarchical structure that is often useful for many applications. This paper proposes an algorithm for inducing NNC-Trees based on the R/sup 4/-rule, which was proposed by the author for finding the smallest nearest neighbor based multilayer perceptrons (NN-MLPs). There are mainly two contributions here. 1) A heuristic but effective method is given to define the teacher signals (group labels) for the data assigned to each nonterminal node. 2) The R/sup 4/-rule is modified so that an NNC with proper size can be designed automatically in each nonterminal node. Experiments with several public databases show that the proposed algorithm can produce NNC-Trees effectively and efficiently.     

On the practical stability of optimal stochastic control systems with dead-time

The practical stability of optimal stochastic control systems for processes having dead-times is considered. Previously obtained necessary conditions for practical stability of such systems are generalized using Pontryagin's theorem on the roots of two-variable polynomials. The conditions are expressed in terms of the relations between the orders of the process, the process model and the disturbance model.     

On the inf–sup Condition for the P mod 3 / P disc 2 Element

We consider a recently introduced triangular nonconforming finite element of third-order accuracy in the energy norm called P^mod₃ element. We show that this finite element is appropriate for approximating the velocity in incompressible flow problems since it satisfies an inf-sup condition for discontinuous piecewise quadratic pressures.     

On the design of linear multivariable feedback systems via constrained nondifferentiable optimization in H/sup infinity / spaces

The design discussed is of linear, lumped, time-invariant, multivariable feedback systems, subject to various frequency and time-domain performance specifications. The approach is based on the use of stabilizing controller parametrizations which result in the formulation of feedback system design problems as convex, nondifferentiable optimization problems. These problems are solvable by recently developed nondifferentiable optimization algorithms for the constrained minimization of regular, uniformly locally Lipschitz continuous functions in R/sup N/.<>     

On the modified Smith predictor for controlling a process with anintegrator and long dead-time

A dead-time compensator for controlling higher-order processes with integral action and long dead-time is proposed. Tuning formulas are derived. If the velocity gain and the dead-time are estimated experimentally, only one parameter, the time constant defining the speed of the closed-loop setpoint response, has to be tuned manually. The same setpoint response is obtained as in the modified Smith predictor, while the load disturbance rejection is considerably faster     

On the analysis of compensation correctness

One fundamental idea of service-oriented computing is that applications should be developed by composing already available services. Due to the long running nature of service interactions, a main challenge in service composition is ensuring correctness of transaction recovery. In this paper, we use a process calculus suitable for modelling long running transactions with a recovery mechanism based on compensations. Within this setting, we discuss and formally state correctness criteria for compensable processes compositions, assuming that each process is correct with respect to transaction recovery. Under our theory, we formally interpret self-healing compositions, that can detect and recover from faults, as correct compositions of compensable processes. Moreover, we develop an automated verification approach and we apply it to an illustrative case study.     

Reduced-order solutions for the singular H/sup /spl infin// filtering problem

We consider the filtering H/sup /spl infin// problem for linear time-varying systems. This problem has been already solved in the case when the direct feedthrough matrix F between the disturbance and the output vectors is full-row rank. Here, we consider the case when the problem is singular, that is when this feedthrough matrix is not full-row rank. We show that in this case a reduced-order observer can be designed to meet the desired performance. Moreover, we apply the obtained results to solve a particular H/sup /spl infin// singular output feedback problem.     

On the evaluation of illumination compensation algorithms

This paper presents a comparison framework for algorithms that can diminish the effects of illumination in images. Its main objective is to reveal the positive and negative characteristics of such algorithms, allowing researchers to select the most appropriate one for their target application. The proposed framework utilizes artificial illumination degradations on real images, which are then processed by the tested algorithms. The results are evaluated by an ensemble of performance metrics, highlighting the various characteristics of the algorithms across a range of different image attributes. The proposed framework represents a useful tool for the selection of illumination compensation algorithms due to a) its quantitative nature, b) its multifaceted analysis and c) its easy reproducibility. The validity of the proposed framework is tested by applying it to the enhancement results of four illumination compensation algorithms, which are used as preprocessing in two classic computer vision applications. The improvements brought about by the algorithms are in accordance with the predictions of the proposed framework.     

L1/2正则化Logistic回归

提出一种L1/2正则化Logistic回归模型,并针对此模型构造有效的求解算法.文中模型基于L1/2正则化理论建立,有效改善传统模型存在的变量选择与计算过拟合问题.文中算法基于"坐标下降"思想构造,快速有效.在一系列人工和实际数据集上的实验表明,文中算法在分类问题中具有良好的变量选择能力和预测能力,优于传统Logistic回归和L1正则化Logistic回归.     

On the M/Ck/1 queue

We obtain the exact analytic expression of the probability distribution of the number of units in a single server queue with Poisson arrivals and Coxian service time distribution (notated as M/C_k/1). A recursive procedure for calculating this probability distribution is given. The well-known queues M/E_k/1 and M/D/1 are re-derived as special cases of the M/C_k/1 queue. Finally, the cases of M/C₂/1 and M/C₃/1 are fully worked out.     

On the L(2, 1)-labelling of block graphs

The distance-two labelling problem of graphs was proposed by Griggs and Roberts in 1988, and it is a variation of the frequency assignment problem introduced by Hale in 1980. An L(2, 1)-labelling of a graph G is an assignment of non-negative integers to the vertices of G such that vertices at distance two receive different numbers and adjacent vertices receive different and non-consecutive integers. The L(2, 1)-labelling number of G, denoted by λ(G), is the smallest integer k such that G has a L(2, 1)-labelling in which no label is greater than k.

In this work, we study the L(2, 1)-labelling problem on block graphs. We find upper bounds for λ(G) in the general case and reduce those bounds for some particular cases of block graphs with maximum clique size equal to 3.     

On the parameterization H∞ controllers

The author clarifies some of the results of J.C. Doyle et al. (ibid., vol.34, no.8, p.831-47, Aug. 1989) and gives some new interpretations. In particular, the author parameterizes all suboptimal H_∞ controllers for the full information (FI) and state feedback control problems and indicates when this FI H_∞ control problem can or cannot be given a differential game saddle point interpretation