A dynamic programming based approach for explicit model predictive control of hybrid systems

This work presents an algorithm for explicit model predictive control of hybrid systems based on recent developments in constrained dynamic programming and multi-parametric programming. By using the proposed approach, suitable for problems with linear cost function, the original model predictive control formulation is disassembled into a set of smaller problems, which can be efficiently solved using multi-parametric mixed-integer programming algorithms. It is also shown how the methodology is applied in the context of explicit robust model predictive control of hybrid systems, where model uncertainty is taken into account. The proposed developments are demonstrated through a numerical example where the methodology is applied to the optimal control of a piece-wise affine system with linear cost function.     

Mixed integer polynomial programming

The mixed integer polynomial programming problem is reformulated as a multi-parametric programming problem by relaxing integer variables as continuous variables and then treating them as parameters. The optimality conditions for the resulting parametric programming problem are given by a set of simultaneous parametric polynomial equations which are solved analytically to give the parametric optimal solution as a function of the relaxed integer variables. Evaluation of the parametric optimal solution for integer variables fixed at their integer values followed by screening of the evaluated solutions gives the optimal solutions.     

Multi-objective optimization with convex quadratic cost functions: A multi-parametric programming approach

In this note we present an approximate algorithm for the explicit calculation of the Pareto front for multi-objective optimization problems featuring convex quadratic cost functions and linear constraints based on multi-parametric programming and employing a set of suitable overestimators with tunable suboptimality. A numerical example as well as a small computational study highlight the features of the novel algorithm.     

Simultaneous design of explicit/multi-parametric constrained moving horizon estimation and robust model predictive control

In this work we present a rigorous methodology for the simultaneous design of moving horizon estimation (MHE) and robust model predictive control based on multi-parametric programming. First, an explicit/multi-parametric solution of the MHE is derived. Then, a novel method is presented that allows for the derivation of the estimation error dynamics, the bounding set of the estimation error, and the state estimate dynamic equations of constrained MHE. A framework is then presented for the design of robust explicit/multi-parametric model predictive control (MPC) controllers, based on tube-based MPC methods, which ensures that no constraints are violated due to the estimation error and the process noise in the system. This framework is first shown for the Kalman filter and unconstrained MHE and is then extended to the constrained MHE.     

Design of multi-parametric NCO tracking controllers for linear dynamic systems

A methodology for combining multi-parametric programming and NCO tracking is presented in the case of linear dynamic systems. The resulting parametric controllers consist of (potentially nonlinear) feedback laws for tracking optimality conditions by exploiting the underlying optimal control switching structure. Compared to the classical multi-parametric MPC controller, this approach leads to a reduction in the number of critical regions. It calls for the solution of more difficult parametric optimization problems with linear differential equations embedded, whose critical regions are potentially nonconvex. Examples of constrained linear quadratic optimal control problems with parametric uncertainty are presented to illustrate the approach.     

Integrated process design,scheduling, and model predictive control of batch processes with closed-loop implementation

Simultaneous evaluation of multiple time scale decisions has been regarded as a promising avenue to increase the process efficiency and profitability through leveraging their synergistic interactions. Feasibility of such an integral approach is essential to establish a guarantee for operability of the derived decisions. In this study, we present a modeling methodology to integrate process design, scheduling, and advanced control decisions with a single mixed-integer dynamic optimization (MIDO) formulation while providing certificates of operability for the closed-loop implementation. We use multi-parametric programming to derive explicit expressions for the model predictive control strategy, which is embedded into the MIDO using the base-2 numeral system that enhances the computational tractability of the integrated problem by exponentially reducing the required number of binary variables. Moreover, we apply the State Equipment Network representation within the MIDO to systematically evaluate the scheduling decisions. The proposed framework is illustrated with two batch processes with different complexities.     

Multi-parametric profiling network based on gene expression and phenotype data: a novel approach to developmental neurotoxicity testing

The establishment of more efficient approaches for developmental neurotoxicity testing (DNT) has been an emerging issue for children's environmental health. Here we describe a systematic approach for DNT using the neuronal differentiation of mouse embryonic stem cells (mESCs) as a model of fetal programming. During embryoid body (EB) formation, mESCs were exposed to 12 chemicals for 24 h and then global gene expression profiling was performed using whole genome microarray analysis. Gene expression signatures for seven kinds of gene sets related to neuronal development and neuronal diseases were selected for further analysis. At the later stages of neuronal cell differentiation from EBs, neuronal phenotypic parameters were determined using a high-content image analyzer. Bayesian network analysis was then performed based on global gene expression and neuronal phenotypic data to generate comprehensive networks with a linkage between early events and later effects. Furthermore, the probability distribution values for the strength of the linkage between parameters in each network was calculated and then used in principal component analysis. The characterization of chemicals according to their neurotoxic potential reveals that the multi-parametric analysis based on phenotype and gene expression profiling during neuronal differentiation of mESCs can provide a useful tool to monitor fetal programming and to predict developmentally neurotoxic compounds.     

Analysis of linear programming in model predictive control

The linear programming formulations of model predictive control are known to exhibit degenerate solution behavior. In this work, a multi-parametric linear programming technique is utilized to analyze the control laws that are generated from various linear programming based MPC routines. These various routines explore a number of factors, including objective function selection and constraint handling on the control laws generated from LP based MPC. A single input single output system is used to demonstrate that the use of input velocity penalties, input blocking, and ∞-norm objective functions can limit or eliminate this undesirable behavior. Finally, a paper machine cross directional control problem is used to demonstrate the control laws generated from LP based MPC for a multivariable example.     

Towards the integration of process design,control and scheduling: Are we getting closer?

The integration of design and control, control and scheduling and design, control and scheduling, all have been core PSE challenges. While significant progress has been achieved over the years, it is fair to say that at the moment there is not a generally accepted methodology and/or “protocol” for such an integration – it is also interesting to note that currently, there is not a commercially available software [or even in a prototype form] system to fully support such an activity.Here, we present the foundations for such an integrated framework and especially a software platform that enables such integration based on research developments over the last 25 years. In particular, we describe PAROC, a prototype software system which allows for the representation, modeling and solution of integrated design, scheduling and control problems. Its main features include: (i) a high-fidelity dynamic model representation, also involving global sensitivity analysis, parameter estimation and mixed integer dynamic optimization capabilities; (ii) a suite/toolbox of model approximation methods; (iii) a host of multi-parametric programming solvers for mixed continuous/integer problems; (iv) a state-space modeling representation capability for scheduling and control problems; and (v) an advanced toolkit for multi-parametric/explicit Model Predictive Control and moving horizon reactive scheduling problems. Algorithms that enable the integration capabilities of the systems for design, scheduling and control are presented on a case of a series of cogeneration units.     

Modelling and explicit model predictive control for PEM fuel cell systems

We present an analytical dynamic model and a general framework for the optima control design of a PEM fuel cell system. The mathematical model consists of a detailed model for the PEM fuel cell stack and simplified models for the compressor, humidifier and cooling system. The framework features (i) a detailed dynamic process model, (ii) a reduced order approximating model obtained by performing dynamic simulations of the system and (iii) the design of an explicit/multi-parametric model predictive controller. The derived explicit/multi-parametric controller is tested and validated off-line on several operating conditions.     

Off-line model reduction for on-line linear MPC of nonlinear large-scale distributed systems

Model predictive control (MPC) is an efficient method for the controller design of a large number of processes. However, linear MPC is often inappropriate for controlling nonlinear large-scale systems, while non-linear MPC can be computationally costly. The resulting optimization-based procedure can lead to local minima due to the, non-convexities that non-linear systems can exhibit. To overcome the excessive computational cost of MPC application for large-scale nonlinear systems, model reduction methodology in conjunction with efficient system linearizations have been exploited to enable the efficient application of linear MPC for nonlinear distributed parameter systems (DPS). An off-line model reduction technique, the proper orthogonal decomposition (POD) method, combined with a finite element Galerkin projection is first used to extract accurate non-linear low-order models from the large-scale ones. Trajectory Piecewise-Linear (TPWL) methodologies are subsequently developed to construct a piecewise linear representation of the reduced nonlinear model, both in a static and in a dynamic fashion. Linear MPC, based on quadratic programming, can then be efficiently performed on the resulting low-order, piece-wise affine system. Our combined methodology is readily applicable in combination with advanced MPC methodologies such as multi-parametric MPC (MP-MPC) (Pistikopoulos, 2009). The stabilisation of the oscillatory behaviour of a tubular reactor with recycle is used as an illustrative example to demonstrate our methodology.     

Nutritional metabonomics: an approach to promote personalized health and wellness

Nutritional research has emerged in the last century from the study of nutrients as a means of nourishment to the general population to the quest for wellness improvement through specific food components. Advances in nutrigenomics technologies have allowed nutrition scientists to be for the first time at the forefront of nutritional research. Such advances have given them the ability to discern new vital scientific discoveries specifically for the development of new tailored dietary patterns. In this, nutritional metabonomics has rapidly evolved into a very powerful bioanalytical tool able to assess multi-parametric metabolic responses of living organisms to specific dietary interventions. Nutritional metabonomics therefore provides a systematic approach through the comprehensive analysis of metabolites aiming today at the quest for homeostatic balance which is dependent not only on the host but also on the crucial metabolic interactions with microbial symbionts.     

基于模糊预测型线性规划模型的矿山产能配置

将线性规划与模糊数学及灰色理论有机结合,构建了与产能分配实际情况较为接近的模糊预测型线性规划模型.利用灰色预测理论对各灰色系数进行白化,将模糊预测型线性规划模型转化为模糊线性规划模型,利用最优判决条件进一步转化,得到以最大隶属度为目标函数的一般线性规划模型,求解得到了矿山的最优产能分配,以实现矿山产能的科学配置和效益的最大化.     

Reduced graphene oxide-ZnO hybrid composites as photocatalysts: The role of nature of the molecular target in catalytic performance

Spurred by controversial literature findings, we enwrapped reduced graphene oxide (rGO) in ZnO hierarchical microstructures (rGO loadings spanning from 0.01 to 2 wt%) using an in situ synthetic procedure. The obtained hybrid composites were carefully characterized, aiming at shining light on the possible role of rGO on the claimed increased performance as photocatalysts. Several characterization tools were exploited to unveil the effect exerted by rGO, including steady state and time resolved photoluminescence, electron microscopies and electrochemical techniques, in order to evaluate the physical, optical and electrical features involved in determining the catalytic degradation of rhodamine B and phenol in water.Several properties of native ZnO structures were found changed upon the rGO enwrapping (including optical absorbance, concentration of native defects in the ZnO matrix and double-layer capacitance), which are all involved in determining the photocatalytic performance of the hybrid composites. The findings discussed in the present work highlight the high complexity of the field of application of graphene-derivatives as supporters of semiconducting metal oxides functionality, which has to be analyzed through a multi-parametric approach.     

需求不确定下炼油企业生产计划优化混合规划模型

Abstract Production planning under uncertainty is considered as one of the most important problems in plant-wide optimization. In this article, first, a stochastic programming model with uniform distribution assumption is developed for refinery production planning under demand uncertainty, and then a hybrid programming model incorporating the linear programming model with the stochastic programming one by a weight factor is proposed. Subsequently, piecewise linear approximation functions are derived and applied to solve the hybrid programming model-under uniform distribution assumption. Case studies show that the linear approximation algorithm is effective to solve.the hybrid programming model, along with an error≤0.5% when the deviatiorgmean≤20%. The simulation results indicate that the hybrid programming model with an appropriate weight factor （0.1-0.2） can effectively improve the optimal operational strategies under demand uncertainty, achieving higher profit than the linear programming model and the stochastic programming one with about 1.3% and 0.4% enhancement, respectavely.     

露天矿剥采进度计划优化研究现状及发展趋势

对露天矿剥采进度优化研究的现状做了概括，对国内外有代表性的研究方法及数学模型（整数规划、目标规划、动态规划、系统模型法等）进行介绍与评价，并对该领域研究发展趋势（如人工智能法、综合方法）做了分析。     

线性规划实现动态优化的模型预测控制策略

为减小模型预测控制算法中动态优化部分的计算复杂度,提出了用线性规划而非二次规划解决模型预测控制动态优化方法。对单输入单输出和多输入多输出模型预测控制的情形,以控制增量、输出增量和偏移变量作为优化变量,建立线性等式约束和不等式约束,并引入线性目标函数,形成线性规划问题。通过加入多种软约束,可改善动态过程的性能指标,达到平稳控制的目的。最后通过一个实例验证了方法的有效性。     

Large scale mathematical programming systems

This survey covers the state of the art of large scale mathematical programming systems (MPS's) for solving problems which can be modeled using linear programming or its extensions, such as mixed integer and some types of nonlinear programming. Such models occur frequently in chemical engineering and in other types of process, manufacturing and distribution applications.     

Energy optimization in heat integrated water allocation networks

In this paper, linear programming formulations, complemented by concept based pinch analysis results, are developed to target the minimum energy requirements in a heat integrated fixed flow rate water allocation networks. These formulations can be applied for the cases of heat integration through isothermal and non-isothermal mixing in water allocation networks involving single as well as multiple contaminants. The earlier reported approaches are based on linear programming formulation for the case of isothermal mixing and either mixed integer non-linear programming or discontinuous non-linear programming formulations for the case of non-isothermal mixing. It has been observed that the earlier reported methodologies produce sub-optimal results for the case of non-isothermal mixing. However, the proposed methodologies produce the optimum results because of the rigorously proved linear formulation. Utility requirements for isothermal as well as for non-isothermal mixing cases are compared over a range of minimum approach temperatures, to evaluate the energy performance using illustrative examples.     

混杂系统基于参数规划的状态反馈预测控制

In this article, state feedback predictive controller for hybrid system via parametric programming is proposed. First, mixed logic dynamic （MLD） modeling mechanism for hybrid system is analyzed, which has a distinguished advantage to deal with the logic rules and constraints of a plant. Model predictive control algorithm with moving horizon state estimator （MHE） is presented. The estimator is adopted to estimate the current state of the plant with process disturbance and measurement noise, and the state estimated are utilized in the predictive controller for both regulation and tracking problems of the hybrid system based on MLD model. Off-line parametric programming is adopted and then on-line mixed integer programming problem can be treated as the parameter programming with estimated state as the parameters. A three tank system is used for computer simulation, results show that the proposed MHE based predictive control via parametric programming is effective for hybrid system with model/olant mismatch, and has a potential for the engineering applications.