Discrete-time Linear Model Research Articles

Out-of-Home Placement of Children and Economic Factors: An Empirical Analysis

In this paper, we use data from the National Longitudinal Survey of Youth (NLSY) to estimate the effects of income, maternal employment, family structure, and public policies on several measures of children’s living arrangements. We use both linear probability models and discrete-time event history models to explore the effects of these factors on: (1) the probability that a child is living out-of-home in a given year; (2) the probability that a child is removed from home in a given year, conditional on the child living at home in the previous year; (3) the probability that a child is removed from home for the first time; (4) the probability that a child is reunified with his/her biological parent(s) given that the child was living out-of-home in the previous year. We also analyze whether these estimates differ by types of out-of-home placements. Our results suggest that children from lower-income, single-mother, and mother–partner families are considerably more likely both to be living out-of-home and to be removed from home. A change in family structure also tends to place a child at higher risk of an out-of-home living arrangement, unless this transition functions to bring a child’s father back into the household. Maternal work appears to increase the probability that a child lives at home. Additionally, once a removal has taken place, we do not find a relationship between income and the probability of a family reunification, but we do find that single-mother and mother–partner families are less likely to reunify. Finally, our analyses provide some evidence that welfare benefit levels are negatively related to out-of-home placements.

Kalman-Filter Based Control and Performance Monitoring Systems

This paper addresses the problem to design control and performance monitoring systems for robotic manipulators. Basically three control schemes are proposed. The first one is a modification of the computed torque method where the input torques necessary to drive the robotic manipulator are on-line computed as functions of the optimal – unbiased, minimum variance – estimates of the joint coordinates and velocities, and the corrected accelerations. The optimal state estimator based on a stochastic discrete-time linear dynamic model and previous observations is generated the discrete Kalman filter. The idea of the second control system is to use a better reference trajectory for linearization in each working cycle. Two ways are given to perform this relinearization process: the relinearization is performed around the estimated trajectory, and the extended Kalman filter. The third novel control method addresses the problem to design a nonlinear feedback controller in case of uncertain dynamical parameters and other disturbances. Monitoring schemes for real-time detection and isolation of failures in robotic manipulators are outlined in the second part of the paper. The problem of fault detection is formulated as a problem in Hypothesis Testing by regarding the normal operation of the robot manipulator as the null hypothesis.

Identification of linear parameter-varying state-space models with application to helicopter rotor dynamics

A considerable amount of work has been dedicated in the past to the problem of the system identification of helicopter flight dynamics, while much less activity has been oriented to the goal of developing suitable identification procedures for rotor dynamics, mainly because of the difficulties associated with the task. This paper shows that subspace and optimization based identification techniques can be used to determine discrete-time linear parameter-varying models that have the potential to provide accurate descriptions for the (intrinsically time-varying) dynamics of a rotor blade. The identification techniques are presented and applied to simulated data generated by a physical model that describes the out-of-plane bending dynamics of a helicopter rotor blade.

A positive linear discrete-time model of capacity planning and its controllability properties

One of the most important concepts in production planning is that of the establishment of an overall or aggregate production plan. In this paper, the problem of establishing an aggregate production plan for a manufacturing plant is considered. A new dynamic discrete-time model of capacity planning utilizing concepts arising in positive linear systems (PLS) theory is proposed and its controllability property is analyzed. Controllability is a fundamental property of the system with direct implications not only in dynamic optimization problems (such as those arising in inventory and production control) but also in feedback control problems. Some new open problems regarding controllability of stationary and nonstationary PLS with linear constraints are posed in the paper. An optimal control problem for capacity planning is formulated and discussed.

Adaptive model predictive control for max-plus-linear discrete event input-output systems

Model predictive control (MPC) is a popular controller design technique in the process industry. Conventional MPC uses linear or nonlinear discrete-time models. Recently, MPC has been extended to a class of discrete-event systems that can be described by a model that is ‘linear’ in max-plus algebra. An adaptive scheme for the time-varying case, based on parameter estimation of input-output models is presented. In a simulation example it is shown that the combined parameter-estimation/MPC algorithm gives a good closed-loop behaviour.

Model predictive control for perturbed max-plus-linear systems: a stochastic approach

Model predictive control (MPC) is a popular controller design technique in the process industry. Conventional MPC uses linear or non-linear discrete-time models. Recently, we have extended MPC to a class of discrete event systems that can be described by a model that is ‘linear’ in the (max, +) algebra. In our previous work we have only considered MPC for the perturbations-free case and for the case with bounded noise and/or modelling errors. In this paper we extend these results on MPC for max-plus-linear systems to a stochastic setting. We show that under quite general conditions the resulting optimization problems turn out to be convex and can thus be solved very efficiently.

Global Predictive Regulation of a Class of Nonlinear Cascaded Systems with Bounded Input

A predictive control algorithm globally asymptotically stabilizing a class of input-saturated nonlinear cascaded systems is presented. The developed predictive control law, which is calculated off-line as an unconstrained direct state feedback using a discrete-time linear model, is applied to the plant by means of an iterative procedure. In this way, closed-loop stability is guaranteed without increasing the computational complexity and the input constraints can be handled using projection. Moreover, the computational complexity does not depend on the length of the prediction horizon and therefore stability and regulating performance are achieved with a reduced computational burden. Finally, an example is given for illustration purposes.

Linear Time-Invariant Milling Models Applicable to Chatter Suppression System Design

Milling models, applicable to chatter suppression system design, are derived by transforming an established nonlinear milling model into linear constant coefficient discrete time models. The derivation initially utilizes either a modified Tustin or zero-order-hold approximation to create a discrete time approximation of the original model. The resulting periodically time varying system, which includes time delays, is then transformed into a system with constants coefficient and no time delays by adding delay states to the system and computing the system's monodromy matrix. The resulting linear models are then compared to the established nonlinear model. The linear models, while of high order, can be used directly to design chatter suppression systems with traditional linear control system design techniques. An example chatter control system is designed using an optimal regulator. The example controller reduces chatter in a milling system with a four tooth cutter in an up-milling configuration.

A reverse logistics cost minimization model for the treatment of hazardous wastes

This study presents a cost-minimization model for a multi-time-step, multi-type hazardous-waste reverse logistics system. A discrete-time linear analytical model is formulated that minimizes total reverse logistics operating costs subject to constraints that take into account such internal and external factors as business operating strategies and governmental regulations. Application cases are presented to demonstrate the feasibility of the proposed approach. By using the proposed model coupled with operational strategies, it is shown that the total reverse logistics costs for the applications cases can be reduced by more than 49%. � 2002 Elsevier Science Ltd. All rights reserved.

OPTIMAL CONTROL OF SWITCHED CONTINUOUS SYSTEMS USING MIXED-INTEGER PROGRAMMING

The paper presents an optimization-based approach to compute controllers for a class of hybrid systems with switched dynamics. The starting point is a representation as a hybrid automaton which models autonomous switching between different nonlinear dynamics and includes discrete as well as continuous control inputs. The automaton is transformed into a linear discrete-time model in equation-based form. The task of generating an optimal control law to drive the system from an initial state into a target region (while avoiding forbidden states) is solved by mixed-integer programming performed in a moving-horizon setting with variable time steps.

Properties of MPC for Max-Plus-Linear Systems

Model predictive control (MPC) is a very popular controller design method in the process industry. One of the main advantages of MPC is that it can handle constraints on the inputs and outputs. Usually MPC uses linear discrete-time models. Recently, we have extended this framework to max-plus-linear discrete event systems. In this paper, we further explore this topic. More specifically, we focus on implementation and timing aspects, closed-loop behavior and tuning rules for model predictive control of max-plus-linear (MPL) systems.

DISTURBED FAULT DETECTION AND ISOLATION PROBLEMS FOR LINEAR STATE MODELS IN A NOISY ENVIRONMENT

In this paper we afford the fault detection and isolation problem in the context of linear discrete-time state-space models whose state equation is affected both by faults and by disturbances. Model as well as measurement errors, described as zero-mean white gaussian noises, are also assumed to additively act both on the state and on the output equations.Upon introducing several deterministic and stochastic goals, which constitute the mathematical formalization of very natural and practical requirements, necessary and sufficient conditions for the existence of an observer-based fault detector and isolator, which achieves the aforementioned goals, are finally derived.

Model predictive control for perturbed max-plus-linear systems

Model predictive control (MPC) is a popular controller design technique in the process industry. Conventional MPC uses linear or nonlinear discrete-time models. Recently, we have extended MPC to a class of discrete event systems that can be described by a model that is “linear” in the (max,+) algebra. In our previous work, we have only considered MPC for the deterministic noise-free case without modeling errors. In this paper, we extend our previous results on MPC for max-plus-linear systems to cases with noise and/or modeling errors. We show that under quite general conditions the resulting optimization problems can be solved very efficiently.

Minimum entropy deconvolution of pulse-echo signals acquired from attenuative layered media.

In this article deconvolution of ultrasonic pulse-echo data acquired from attenuative layered media is considered. The problem is divided in two subproblems: treating the sparse reflection sequence caused by the layered structure of the media and treating the frequency-dependent attenuation. The first subproblem is solved by means of joint maximum a posteriori estimation of the assumed zero mean, white, nonstationary reflection sequence and its corresponding sequence of unknown standard deviations. This approach leads to an algorithm that seeks minimum entropy solutions for the reflection sequence and therefore the algorithm serves as a novel link between the classical Wiener filter and methods for sparse or minimum entropy deconvolution. The second subproblem is solved by introducing a new signal processing-oriented, linear discrete-time model for frequency-dependent attenuation in isotropic and homogeneous media. The deconvolution algorithm is tested using simulated data and its performance for real normal incidence pulse-echo data from a composite material is also demonstrated. The results show that the algorithm, in combination with the attenuation model, yields estimates that reveal the internal structure of the composite and, thus, simplify the interpretation of the ultrasonic data.

Model predictive control for max-plus-linear discrete event systems

Model predictive control (MPC) is a very popular controller design method in the process industry. A key advantage of MPC is that it can accommodate constraints on the inputs and outputs. Usually MPC uses linear discrete-time models. In this paper we extend MPC to a class of discrete-event systems that can be described by models that are “linear” in the max-plus algebra, which has maximization and addition as basic operations. In general, the resulting optimization problem are nonlinear and nonconvex. However, if the control objective and the constraints depend monotonically on the outputs of the system, the model predictive control problem can be recast as problem with a convex feasible set. If in addition the objective function is convex, this leads to a convex optimization problem, which can be solved very efficiently.

Multivariable feedback relevant system identification of a wafer stepper system

This paper discusses the approximation and feedback relevant parametric identification of a positioning mechanism present in a wafer stepper. The positioning mechanism in a wafer stepper is used in chip manufacturing processes for accurate positioning of the silicon wafer on which the chips are to be produced. The accurate positioning requires a robust and high-performance feedback controller that enables a fast throughput of silicon wafers. A control relevant set of multivariable finite dimensional linear time invariant discrete-time models is formulated and estimated on the basis of closed-loop experiments. The set of models is shown to be suitable for model-based robust control design of the positioning mechanism. This is illustrated by a successful design and implementation of a robust controller.

Parametric modelling and dynamic characterization of a two-degree-of-freedom twin-rotor multi-input multi-output system

A mathematical model for the dynamic characterization of a two-degree-of-freedom (2 DOF) twin-rotor multi-input multi-output (MIMO) system (TRMS) in hover is extracted using a black box system identification technique. The behaviour of the TRMS, in certain aspects, resembles that of a helicopter, with a significant cross-coupling between longitudinal and lateral directional motions. Hence, it is an interesting identification and control problem. Identification for a 2 DOF, rigid-body, discrete-time linear model is presented in detail. The extracted model has a good degree of prediction capability. The modelling approach presented is suitable for complex new-generation air vehicles.

Modeling and identification of electrohydraulic servos

In general, design of adaptive controllers requires a proper model of the actual plant. This is normally done by considering a discrete-time linear model and estimating its unknown parameters, periodically. In this note, we discuss some practical issues concerning the identification of electrohydraulic actuators, using discrete-time linear models.

Set-Membership Estimation with the Trace Criterion made Simpler than with the Determinant Criterion

The problem considered is outer ellipsoidal bounding of the state of a MIMO linear discrete-time model with bounded process perturbations and measurement noise. In the literature, two main measures of the size of bounding ellipsoids have been considered, namely the determinant and trace criteria. The determinant criterion is directly related to the volume of the ellipsoid and has been employed most frequently. It may, however, lead to narrow elongated ellipsoids. The trace algorithm tends to avoid this drawback, but has earned a reputation for complexity. We show that it can be made even simpler globally than the determinant algorithm. A complete filter based on the trace criterion is presented.

A Study on Identification of State-Space Model for Refuse Incineration Plant

This paper identifies a discrete-time linear combustion model of Refuse Incineration Plant(RIP) which characterizes steam generation quantity, where the RIP is considered as a MIMO system with thirteen-inputs and one-output. The structure of RIP model is described as an ARX model which are analytically obtained from the combustion dynamics. Furthermore, using the Instrumental Variable(IV) identification algorithm, model structure and unknown parameters are identified from experimental input-output data sets, In result, it is shown that the identified ARX model well approximates the input-output combustion characteristics given by experimental data sets.