Prediction error method for identification of LPV models

This paper is concerned with identification of linear parameter varying (LPV) systems in an input-output setting with Box-Jenkins (BJ) model structure. Classical linear time invariant prediction error method (PEM) is extended to the LPV PEM. Under the new LPV framework, identification of two types of input-output LPV models is considered: one is based on parameter interpolation and the other is based on model interpolation. The effectiveness of the proposed solution is validated by comparison with other existing LPV identification approaches through simulation examples and demonstrated by experiment studies.     

Block models for scheduling jobs on two parallel machines with a single server

We consider the problem of scheduling a set of non-preemptable jobs on two identical parallel machines such that the makespan is minimized. Before processing, each job must be loaded on a machine, which takes a given setup time. All these setups have to be done by a single server which can handle at most one job at a time. For this problem, we propose a mixed integer linear programming formulation based on the idea of decomposing a schedule into a set of blocks. We compare the results obtained by the model suggested with known heuristics from the literature.     

Subspace identification of MIMO LPV systems using a periodic scheduling sequence

A novel subspace identification method is presented which is able to reconstruct the deterministic part of a multivariable state-space LPV system with affine parameter dependence, in the presence of process and output noise. It is assumed that the identification data is generated with the scheduling variable varying periodically during the course of the identification experiment. This allows to use methods from LTI subspace identification to determine the column space of the time-varying observability matrices. It is shown that the crucial step in determining the original LPV system is to ensure the obtained observability matrices are defined with respect to the same state basis. Once the LPV model has been identified, it is valid for other nonperiodic scheduling sequences as well.     

Model predictive control for LPV models with maximal stabilizable model range

This paper characterizes model predictive control (MPC) for linear parameter varying (LPV) models subject to state and input constraints, which is based on the homogeneous polynomially parameterized (HPP) Lyapunov function and HPP control law with tunable complexity degrees. The controller guarantees the closed‐loop asymptotic stability and finds the control move through the convex optimization. While it is known that this technique can improve the control performance and reduce conservatism, we suggest that it also enlarges, and maximizes with the sufficiently large complexity degrees, the stabilizable LPV model range. The computational burden becomes heavier when the complexity degrees increase. However, the main contributions of this paper are more on theory than on practice. It explores to what extent robust MPC can be applied for stabilization of LPV models. Numerical examples are provided to illustrate the effectiveness of the proposed technique.     

Refined instrumental variable methods for identification of LPV Box-Jenkins models

The identification of linear parameter-varying systems in an input-output setting is investigated, focusing on the case when the noise part of the data generating system is an additive colored noise. In the Box-Jenkins and output-error cases, it is shown that the currently available linear regression and instrumental variable methods from the literature are far from being optimal in terms of bias and variance of the estimates. To overcome the underlying problems, a refined instrumental variable method is introduced. The proposed approach is compared to the existing methods via a representative simulation example.     

Fault detection using interval LPV models in an open-flow canal

This paper proposes a new method of fault detection using Linear Parameter Varying (LPV) interval models and its application to an open-flow canal. The use of such models is motivated because the parameters and transport delay in the canal transfer function model vary with the operating point. LPV models allow to consider these variations by characterizing the parameters/delay variation law with the operating point while intervals are used to bound the parameter/delay uncertainty. Additionally, a LPV parameter estimation algorithm that allows to estimate parameter/delay uncertainty intervals is also proposed. As an application case study, an open-flow canal system based on the Lunax dam-gallery system located in France is used to show the effectiveness of the proposed method to detect faults. The satisfactory results obtained allow to assess the effectiveness of the proposed approach.     

基于多LPV 模型的调度离线鲁棒预测控制

针对一类具有大工作区域和快时变特性的约束非线性系统, 采用多个线性参数时变(LPV) 模型近似描述原非线性系统. 对于各LPV 模型, 设计基于参数独立Lyapunov 函数的局部离线预测控制器. 构造各局部控制器间的切换策略, 在保证切换稳定性的同时, 使相互重叠的稳定域覆盖期望的工作区域. 仿真结果表明, 相比于已有的调度预测控制方法, 所提出的方法不仅能够保证控制输入在给定的约束范围内, 而且在局部控制器切换次数少的情况下, 获得良好的控制性能.

     

Unbounded parallel-batching scheduling with two competitive agents

We consider the scheduling problems arising when two agents, each with a family of jobs, compete to perform their respective jobs on a common unbounded parallel-batching machine. The batching machine can process any number of jobs simultaneously in a batch. The processing time of a batch is equal to the maximum processing time of the jobs in the batch. Two main categories of batch processing based on the compatibility of job families or agents are distinguished. In the case where job families are incompatible, jobs from different families cannot be placed in the same processing batch while all jobs can be placed in the same processing batch when job families are compatible. The goal is to find a schedule for all jobs of the two agents that minimizes the objective of one agent while keeping the objective of the other agent below or at a fixed value Q. Polynomial-time and pseudo-polynomial-time algorithms are provided to solve various combinations of regular objective functions for the scenario in which job families are either incompatible or compatible.     

Bounded parallel-batching scheduling with two competing agents

We consider a scheduling problem in which two agents, each with a set of non-preemptive jobs, compete to perform their jobs on a common bounded parallel-batching machine. Each of the agents wants to minimize an objective function that depends on the completion times of its own jobs. The goal is to schedule the jobs such that the overall schedule performs well with respect to the objective functions of both agents. We focus on minimizing the makespan or the total completion time of one agent, subject to an upper bound on the makespan of the other agent. We distinguish two categories of batch processing according to the compatibility of the agents. In the case where the agents are incompatible, their jobs cannot be processed in the same batch, whereas all the jobs can be processed in the same batch when the agents are compatible. We show that the makespan problem can be solved in polynomial time for the incompatible case and is NP-hard in the ordinary sense for the compatible case. Furthermore, we show that the latter admits a fully polynomial-time approximation scheme. We prove that the total completion time problem is NP-hard and is polynomially solvable for the incompatible case with a fixed number of job types.     

Optimal scheduling of two competing queues with blocking

Consideration is given to the problem of optimal scheduling for two queues for service at a single station, where the queues have finite capacities and the service rate is class-dependent. The cost structure is linear in the number of holding customers in the queues, combined with blocking costs incurred whenever arrivals encounter a full queue. The authors derive the optimal policy minimizing this criterion when the blocking cost is larger than the holding cost for each queue. Then they show that the optimal policy is of the switching type. Numerical results are included to support the analytical findings     

Identification of LPV model for superheated steam temperature system using A-QPSO

Boiler superheated steam temperature control is of great importance for the safety and economy of thermal power unit. This article presents a nonlinear model identification method for the superheated steam temperature system, based on the unit load as a time-varying parameter. The linear parameter varying (LPV) model, which has been established by using the unit historical data, is suitable for control studies, and it can reflect the global dynamic characteristics of the object. To solve the model parameters estimation in high-dimensional problem, the evolutionary acceleration factor is introduced to the quantum particle swarm optimization (A-QPSO) algorithm to optimize the model parameters. The validity of the modified algorithm A-QPSO is verified through optimizing several classical high-dimensional standard test functions. The A-QPSO improved the optimization efficiency, and optimized result is very close to the optimal value. Finally, the proposed method is applied to the identification of a power plant superheated steam temperature process, and the results show that the optimized superheated steam temperature model is of high accuracy and the proposed method is feasible.     

Multi-queue scheduling of two tasks

Summary Scheduling in the central server queueing model, consisting of a CPU server and m I/O servers, is considered for the case of two customers. Optimal (maximal CPU utilization) CPU and I/O schedules are obtained. The best CPU schedule depends on the I/O schedule in effect; and is either Longest or Shortest-Expected-Remaining-Processing-Time-First. However, for certain I/O schedules the CPU schedule is immaterial. The best I/O schedule is always to process the longer CPU customer first.     

Estimation of global sensitivity indices for models with dependent variables

A novel approach for estimation variance-based sensitivity indices for models with dependent variables is presented. Both the first order and total sensitivity indices are derived as generalizations of Sobol? sensitivity indices. Formulas and Monte Carlo numerical estimates similar to Sobol? formulas are derived. A copula-based approach is proposed for sampling from arbitrary multivariate probability distributions. A good agreement between analytical and numerical values of the first order and total indices for considered test cases is obtained. The behavior of sensitivity indices depends on the relative predominance of interactions and correlations. The method is shown to be efficient and general.     

Optimal LPV control with hard constraints

This paper considers the optimal control of polytopic, discrete-time linear parameter varying (LPV) systems with a guaranteed ?₂ to ?_∞ gain. Additionally, to guarantee robust stability of the closed-loop system under parameter variations, H _∞ performance criterion is also considered as well. Controllers with a guaranteed ?₂ to ?_∞ gain and a guaranteed H _∞ performance (?₂ to ?₂ gain) are a special family of mixed H ₂=H _∞ controllers. Normally, H₂ controllers are obtained by considering a quadratic cost function that balances the output performance with the control input needed to achieve that performance. However, to obtain an optimal controller with a guaranteed ?₂ to ?_∞ gain (closely related to the physical performance constraint), the cost function used in the H₂ control synthesis minimizes the control input subject to maximal singular-value performance constraints on the output. This problem can be efficiently solved by a convex optimization with linear matrix inequality (LMI) constraints. The main contribution of this paper is the characterization of the control synthesis LMIs used to obtain an LPV controller with a guaranteed ?₂ to ?_∞ gain and >H _∞ performance. A numerical example is presented to demonstrate the effectiveness of the convex optimization.     

Semi-supervised PLVR models for process monitoring with unequal sample sizes of process variables and quality variables

As the key indicators of chemical processes, the quality variables, unlike process variables, are often difficult to obtain at the high frequency. Obtaining the data of quality variables is expensive, so the data are only collected as a small portion of the whole dataset. It is common to see in both continuous and batch processes that the sample sizes of process variables and quality variables are unequal. To effectively integrate two different observation sources, including quality variables collected at a low frequency and process variables sampled at a high rate, a semi-supervised probabilistic latent variable regression model (SSPLVR) is proposed in this article. It enhances the performance monitoring of the variations of process variables and quality variables. The proposed semi-supervised model is applied to continuous and batch processes respectively. The SSPLVR model calibrated by the expectation-maximization algorithm is derived and the corresponding statistics is also systematically developed for the fault detection. Finally, two simulated case studies, TE benchmark for a continuous process problem and the penicillin fermentation for a batch process problem, are presented to illustrate the effectiveness of the proposed method.     

Joint order and parameter estimation of multivariate autoregressive models using multi-model partitioning theory

In this paper the multi-model partitioning theory is used for simultaneous order and parameter estimation of multivariate autoregressive models. Simulation experiments show that the proposed method successfully selects the correct model order and estimates the parameters accurately, in very few steps, even with a small sample size. They also show that the proposed method performs equally well when the complexity of the model is increased. The results are compared to those obtained using well-established order selection criteria. Finally, it is shown that the method is also successful in tracking model order changes, in real time.