An algorithmic method for the selection of multivariable process control structures

In process systems, the selection of suitable sets of manipulated and controlled variables and the design of their interconnection, known as the control structure selection problem, is an important structural optimisation problem. The operating performance of a plant depends on the control structure selected as well as the characteristics of the disturbances acting on the plant. The economic penalty associated with the variability of main process variables close to active constraints is used in this work in order to develop a quantitative measure for the ranking of alternative control structures. Based on this measure, a general methodology is presented for the generation of promising control structures where general centralised, linear time invariant, output feedback controllers are used to form the closed loop system. The special case of optimal static output feedback controllers is further investigated in this paper. Furthermore, the problem of selecting proper weights in forming quadratic integral performance indices in designing optimal multivariable controllers is addressed. The validity and usefulness of the method is demonstrated through a number of case studies.     

Profitable and dynamically feasible operating point selection for constrained processes

The operating point of a typical chemical process is determined by solving a non-linear optimization problem where the objective is to minimize an economic cost subject to constraints. Often, some or all of the constraints at the optimal solution are active, i.e., the solution is constrained. Though it is profitable to operate at the constrained optimal point, it might lead to infeasible operation due to uncertainties. Hence, industries try to operate the plant close to the optimal point by “backing-off” to achieve the desired economic benefits. Therefore, the primary focus of this paper is to present an optimization formulation for solving the dynamic back-off problem based on an economic cost function. In this regard, we work within a stochastic framework that ensures feasible dynamic operating region within the prescribed confidence limit. In this work, we aim to reduce the economic loss due to the back-off by simultaneously solving for the operating point and a compatible controller that ensures feasibility. Since the resulting formulation is non-linear and non-convex, we propose a novel two-stage iterative solution procedure such that a convex problem is solved at each step in the iteration. Finally, the proposed approach is demonstrated using case studies.     

Optimal mean–variance control for discrete-time linear systems with Markovian jumps and multiplicative noises

In this paper, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noises under two criteria. The first one is an unconstrained mean–variance trade-off performance criterion along the time, and the second one is a minimum variance criterion along the time with constraints on the expected output. We present explicit conditions for the existence of an optimal control strategy for the problems, generalizing previous results in the literature. We conclude the paper by presenting a numerical example of a multi-period portfolio selection problem with regime switching in which it is desired to minimize the sum of the variances of the portfolio along the time under the restriction of keeping the expected value of the portfolio greater than some minimum values specified by the investor.     

无人机辅助的无线传感网络AoI最小化方案研究

针对无线传感器网络中海量数据处理过程中信息新鲜度问题,基于无人机飞行速度、高度、避碰和可靠传输等约束,以系统信息年龄AoI为考核参数提出了一种联合采集点选择、轨迹优化及无人机工作时间权衡的AoI最小化非凸优化方案。以一个多无人机在同频段条件下为多个传感器节点传输能量并收集传感数据为场景,对多架无人机在三维空间中的信息采集过程进行模拟验证。通过SCA优化算法将建立的非凸问题转化为一个凸优化问题进行求解,最终得到无人机飞行过程中的最优采集点、最优飞行策略及能量输送时间与信息传输时间分配权衡指数,使系统性能达到最优,实验结果表明,所提方案求得的最优解可有效实现系统AoI最小化。     

Steady-state target optimization designs for integrating real-time optimization and model predictive control

In industrial practice, the optimal steady-state operation of continuous-time processes is typically addressed by a control hierarchy involving various layers. Therein, the real-time optimization (RTO) layer computes the optimal operating point based on a nonlinear steady-state model of the plant. The optimal point is implemented by means of the model predictive control (MPC) layer, which typically uses a linear dynamical model of the plant. The MPC layer usually includes two stages: a steady-state target optimization (SSTO) followed by the MPC dynamic regulator. In this work, we consider the integration of RTO with MPC in the presence of plant-model mismatch and constraints, by focusing on the design of the SSTO problem. Three different quadratic program (QP) designs are considered: (i) the standard design that finds steady-state targets that are as close as possible to the RTO setpoints; (ii) a novel optimizing control design that tracks the active constraints and the optimal inputs for the remaining degrees of freedom; and (iii) an improved QP approximation design were the SSTO problem approximates the RTO problem. The main advantage of the strategies (ii) and (iii) is in the improved optimality of the stationary operating points reached by the SSTO-MPC control system. The performance of the different SSTO designs is illustrated in simulation for several case studies.     

Convex formulations for optimal selection of controlled variables and measurements using Mixed Integer Quadratic Programming

The appropriate selection of controlled variables is important for operating a process optimally in the presence of disturbances. Self-optimizing control provides a mathematical framework for selecting the controlled variables as combinations of measurements, c = Hy, with the aim to minimize the steady state loss from optimal operation. In this paper, we present (i) a convex formulation to find the optimal combination matrix H for a given measurement set and (ii) a Mixed-Integer Quadratic Programming (MIQP) methodology to select optimal measurement subsets that result in minimal loss. The methods presented in this paper are exact for quadratic problems with linear measurement relations. The MIQP methods can handle additional structural constraints compared to the branch and bound (BAB) methods reported in literature. The MIQP methods are evaluated on a toy test problem, an evaporator example, a binary distillation column example with 41 stages and a Kaibel column with 71 stages.     

基于模糊控制的线性最优励磁控制系统权矩阵的优化选取

传统线性最优励磁控制系统的加权矩阵,通常是根据正常运行工况下系统对状态变量的约束程度选取的,因此在平衡点附近控制系统具有较好的动态品质,而当系统受到的扰动过大或者过小时,调节性能会变差.模糊控制器可以跟踪系统运行工况,依据在线插值法所细化的规则库输出目标反馈增益矩阵,进而利用灵敏度分析综合考虑目标反馈增益的物理可实现性与权值对动态性能的影响,通过迭代求出优化权矩阵.仿真结果表明基于模糊控制的权矩阵优化选取,使线性最优励磁控制系统表现出更加优良的动态品质.     

输入变量关联约束对约束优化控制的影响特性分析

过程工业控制中除了存在常见的输入变量和输出变量幅值高低限约束, 由于工艺或者控制的需要也可能具有关于输入变量线性函数的关联约束. 不同约束条件之间的矛盾可能会造成约束条件无法全部满足, 失去了实施预测控制的基础. 从凸体顶点角度, 将具有输入关联约束的约束优化控制的可行性判定转化为凸多面集是否非空的问题. 为保证具有输入关联约束预测控制的有效实施, 本文将输入关联约束纳入到预测控制控制律的求解当中. 基于Newton控制框架, 考虑具有输入关联约束条件下, 得到基于区间控制思想的预测控制律的解析表达式, 从而分析输入关联约束条件对控制的影响. 通过典型系统模型的控制仿真实验, 验证以上方法的有效性.     

Novel developments in process optimisation using predictive control

In industrial practice, constrained steady state optimisation and predictive control are separate, albeit closely related functions within the control hierarchy. This paper presents a method which integrates predictive control with on-line optimisation with economic objectives. A receding horizon optimal control problem is formulated using linear state space models. This optimal control problem is very similar to the one presented in many predictive control formulations, but the main difference is that it includes in its formulation a general steady state objective depending on the magnitudes of manipulated and measured output variables. This steady state objective may include the standard quadratic regulatory objective, together with economic objectives which are often linear. Assuming that the system settles to a steady state operating point under receding horizon control, conditions are given for the satisfaction of the necessary optimality conditions of the steady-state optimisation problem. The method is based on adaptive linear state space models, which are obtained by using on-line identification techniques. The use of model adaptation is justified from a theoretical standpoint and its beneficial effects are shown in simulations. The method is tested with simulations of an industrial distillation column and a system of chemical reactors.     

Weiner and Kalman filters for systems with random parameters

A linear stationary optimal filtering problem is considered in which the plant dynamics and noise covariances are incompletely known. Unknown plant parameters in the plant model, such as gains and time constants, are treated as random variables with specified means and variances. Generalized Wiener and Kalman-Bucy filters are derived on the basis of transfer-function matrix or state-space representations of the plant, respectively. An application of the generalized filter to the linear quadratic optimal control of plants with unknown disturbances is also described and a certainty equivalence principle is shown to apply.     

Short-time parameter optimization with flight control application

A design approach is presented for systems operating over a relatively short period of time about various operating points with state variable constraints. This class of problems is especially relevant to certain flight control problems. The design approach is applied to a simplified model of longitudinal dynamics of the F-4 aircraft operating in three widely separated flight conditions. A linear model is assumed about each operating point. Control is achieved via constrained state feedback. The basic problem is then to minimize a suitable integral quadratic performance measure subject to state variable constraints. The main theoretical result is theorem 1 which supplies the inequality constraints required to guarantee short-time stability. The short-time optimization problem is ultimately reduced to a nonlinear programming problem with inequality constraints.     

Using variable reduction strategy to accelerate evolutionary optimization

In this study, we introduce a novel approach of variable reduction and integrate it into evolutionary algorithms in order to reduce the complexity of optimization problems. We develop reduction processes of variable reduction for derivative unconstrained optimization problems (DUOPs) and constrained optimization problems (COPs) with equality constraints and active inequality constraints. Variable reduction uses the problem domain knowledge implied when investigating optimal conditions existing in optimization problems. For DUOPs, equations involving derivatives are considered while for COPs, we discuss equations expressing the equality constraints. From the relationships formed in this way, we obtain relationships among the variables that have to be satisfied by optimal solutions. According to such relationships, we can utilize some variables (referred to as core variables) to express some other variables (referred to as reduced variables). We show that the essence of variable reduction is to produce a minimum collection of core variables and a maximum number of reduced variables based on a system of equations. We summarize some application-oriented situations of variable reduction and stress several important issues related to the further application and development of variable reduction. Essentially, variable reduction can reduce the number of variables and eliminate equality constraints, thus reducing the dimensionality of the solution space and improving the efficiency of evolutionary algorithms. The approach can be applied to unconstrained, constrained, continuous and discrete optimization problems only if there are explicit variable relationships to be satisfied in the optimal conditions. We test variable reduction on real-world and synthesized DUOPs and COPs. Experimental results and comparative studies point at the effectiveness of variable reduction.     

Optimal sizing,scheduling and shift policy of the grinding section of a ceramic tile plant

This paper addresses the optimal design of the grinding section of a ceramic tile plant operating in a cyclic mode with the units (mills) following a batch sequence. The optimal design problem of this single product plant is formulated with a fixed time horizon of one week, corresponding to one cycle of production, and using a discrete-time resource task network (RTN) process representation. The size of the individual units is restricted to discrete values, and the plant operates with a set of limited resources (workforce and equipment). The goal is to determine the optimal number and size of the mills to install in the grinding section, the corresponding production schedule, and shift policy. This problem involves labor/semi-labor intensive (LI/SLI) units with a depreciation cost of the same order as that of the operation cost. The optimal design of the grinding section comprises the trade-off between these two costs. The resulting optimization formulation is of the form of a mixed integer linear programming (MILP) problem, solved using a branch and bound solver (CPLEX 9.0.2). The optimal solution is analyzed for various ceramic tile productions and different shift policies.     

Enforcing Service-Level Constraints in Supply Chains With Assembly Operations

We study a feedforward supply network that involves assembly operations. We compute optimal stock levels which minimize inventory costs and maintain stockout probabilities below given desirable levels (service-level constraints). To that end, we develop large deviations approximations for inventory costs and service level constraints and formulate the stock level selection problem as a nonlinear programming problem which can be solved using standard techniques. This results in significant computational savings when compared to exhaustive search using simulation. Our distributional assumptions are general enough to include temporal dependencies in the demand and production processes. We leverage the solution of the inventory control problem in the design of supply contracts under explicit service-level constraints     

State-space constrained optimal control problems with control variables appearing linearly

This paper deals with the state-space constrained optimal control problems with control variables appearing linearly by the concept of decomposition. To solve this continuous optimal control problem, we first discretize the time and replace the system of differential equations by difference equations. For this resulting discrete optimal control problem, fixing the value of state variables reduces the given problem to a finite number of independent linear programming problems which are parameterized by the value of state variables. From this point of view, after para. meterizing by the value of state variables, we outer-linearize the resulting itifimal valuo functions in the minimond and apply the relaxation strategy to the new constraints arising as a consequence of outer-linearization. An algorithm is proposed which requires baek-and-forth iteration between a master problem and a finite number of linear programming subproblems. Finite convergence of this algorithm follows directly from the finite number of constraints of the master problem.     

An efficient algorithm for solving optimal control problems with linear terminal constraints

The optimization of nonlinear systems subject to linear terminal state variable constraints is considered. A technique for solving this class of problems is proposed that involves a piecewise polynomial parameterization of the system variables. The optimal control problem is thereby reduced to a linearly constrained parameter optimization problem which can be solved efficiently using the quadratically convergent Gold-farb-Lapidus algorithm. Illustrative numerical examples are presented.     

A memetic algorithm for cardinality-constrained portfolio optimization with transaction costs

A memetic approach that combines a genetic algorithm (GA) and quadratic programming is used to address the problem of optimal portfolio selection with cardinality constraints and piecewise linear transaction costs. The framework used is an extension of the standard Markowitz mean–variance model that incorporates realistic constraints, such as upper and lower bounds for investment in individual assets and/or groups of assets, and minimum trading restrictions. The inclusion of constraints that limit the number of assets in the final portfolio and piecewise linear transaction costs transforms the selection of optimal portfolios into a mixed-integer quadratic problem, which cannot be solved by standard optimization techniques. We propose to use a genetic algorithm in which the candidate portfolios are encoded using a set representation to handle the combinatorial aspect of the optimization problem. Besides specifying which assets are included in the portfolio, this representation includes attributes that encode the trading operation (sell/hold/buy) performed when the portfolio is rebalanced. The results of this hybrid method are benchmarked against a range of investment strategies (passive management, the equally weighted portfolio, the minimum variance portfolio, optimal portfolios without cardinality constraints, ignoring transaction costs or obtained with L₁ regularization) using publicly available data. The transaction costs and the cardinality constraints provide regularization mechanisms that generally improve the out-of-sample performance of the selected portfolios.     

A Dantzig–Wolfe decomposition algorithm for linear economic model predictive control of dynamically decoupled subsystems

This paper presents a warm-started Dantzig–Wolfe decomposition algorithm tailored to economic model predictive control of dynamically decoupled subsystems. We formulate the constrained optimal control problem solved at each sampling instant as a linear program with state space constraints, input limits, input rate limits, and soft output limits. The objective function of the linear program is related directly to the cost of operating the subsystems, and the cost of violating the soft output constraints. Simulations for large-scale economic power dispatch problems show that the proposed algorithm is significantly faster than both state-of-the-art linear programming solvers, and a structure exploiting implementation of the alternating direction method of multipliers. It is also demonstrated that the control strategy presented in this paper can be tuned using a weighted ℓ₁-regularization term. In the presence of process and measurement noise, such a regularization term is critical for achieving a well-behaved closed-loop performance.     

Formulations and relaxations for a multi-echelon capacitated location–distribution problem

We consider a multi-echelon location–distribution problem arising from an actual application in fast delivery service. We present and compare two formulations for this problem: an arc-based model and a path-based model. We show that the linear programming (LP) relaxation of the path-based model provides a better bound than the LP relaxation of the arc-based model. We also compare the so-called binary relaxations of the models, which are obtained by relaxing the integrality constraints for the general integer variables, but not for the 0–1 variables. We show that the binary relaxations of the two models always provide the same bound, but that the path-based binary relaxation appears preferable from a computational point of view, since it can be reformulated as an equivalent simple plant location problem (SPLP), for which several efficient algorithms exist. We also show that the LP relaxation of this SPLP reformulation provides a better bound than the LP relaxation of the path-based model.