Detecting infeasibility and generating cuts for mixed integer programming using constraint programming

We study a hybrid MIP/CP solution approach in which CP is used for detecting infeasibilities and generating cuts within a branch-and-cut algorithm for MIP. Our framework applies to MIP problems augmented by monotone constraints that can be handled by CP. We illustrate our approach on a generic multiple machine scheduling problem, and present a number of computational experiments.     

Robust control reconfiguration of resource allocation systems with Petri nets and integer programming

Supervisory control reconfiguration can handle the uncertainties including resource failures and task changes in discrete event systems. It was not addressed to exploit the robustness of closed-loop systems to accommodate some uncertainties in the prior studies. Such exploitation can cost-efficiently achieve reconfigurability and flexibility for real systems. This paper presents a robust reconfiguration method based on Petri nets (PNs) and integer programming for supervisory control of resource allocation systems (RASs) subject to varying resource allocation relationships. An allocation relationship is seen as a control specification while the execution processes requiring resources as an uncontrolled plant. First, a robust reconfiguration mechanism is proposed. It includes updating the P$P$-invariant-based supervisor and evolving the state of the closed-loop system. The latter adapts to the control specification changes by the self-regulation of the closed-loop system’s state. Next, two novel integer programming models for control reconfiguration are proposed, called a reconfiguration model with acceptability and reconfiguration one with specification correction. Since both models integrate the firability condition of transitions, no additional efforts are required for the state reachability analysis. Finally, a hospital emergency service system is used as an example to illustrate them.     

Robust multi-parametric model predictive control for LPV systems with application to anaesthesia

We present a multi-parametric model predictive controller (mpMPC) for discrete-time linear parameter-varying (LPV) systems based on the solution of the mpMPC problem for discrete-time linear time-invariant (LTI) systems. The control method yields a controller that adapts to parameter changes of the LPV system. This is accomplished by an add-on unit to the implementation of the mpMPC for LTI systems. No modification of the optimal mpMPC solution for LTI systems is needed. The mpMPC for LPV systems is entirely based on simple computational steps performed on-line. This control design method could improve the performance and robustness of a mpMPC for LPV systems with slowly varying parameters. We apply this method to process systems which suffer from slow variation of system parameters due, for example, to aging or degradation. As an illustrative example the reference tracking control problem of the hypnotic depth during intravenous anaesthesia is presented: the time varying system matrix mimics an external disturbance on the hypnotic depth. In this example the presented mpMPC for LPV systems shows a reduction of approximately 60% of the reference tracking error compared to the mpMPC for LTI systems.     

Efficient suboptimal parametric solutions to predictive control for PLC applications

The prime aim of this paper is to embed a predictive control (MPC) algorithm with constraint handling capabilities into a programmable logic controller (PLC). In order to achieve it, this paper develops parametric approaches to MPC but differs from more conventional approaches in that it predefines the complexity of the solution rather than the allowable suboptimality. The paper proposes a novel parameterisation of the parametric regions which allows efficiency of definition, effective spanning of the feasible region and also highly efficient search algorithms. Despite the suboptimality, the algorithm retains guaranteed stability, in the nominal case. A laboratory test was carried out to demonstrate the code on real hardware and the effectiveness of the solution.     

Affine and predictive control policies for a class of nonlinear systems

The input-state linear horizon (ISLH) for a nonlinear discrete-time system is defined as the smallest number of time steps it takes the system input to appear nonlinearly in the state variable. In this paper, we employ the latter concept and show that the class of constraint admissible N-step affine state-feedback policies is equivalent to the associated class of constraint admissible disturbance-feedback policies, provided that N is less than the system’s ISLH. The result generalizes a recent result in [Goulart, P. J., Kerrigan, E. C., Maciejowski, J. M. (2006). Optimization over state feedback policies for robust control with constraints. Automatica, 42(4), 523-533] and is significant because it enables one: (i) to determine a constraint admissible state-feedback policy by employing well-known convex optimization techniques; and (ii) to guarantee robust recursive feasibility of a class of model predictive control (MPC) policies by imposing a suitable terminal constraint. In particular, we propose an input-to-state stabilizing MPC policy for a class of nonlinear systems with bounded disturbance inputs and mixed polytopic constraints on the state and the control input. At each time step, the proposed MPC policy requires the solution of a single convex quadratic programme parameterized by the current system state.     

Constrained predictive pole-placement control with linear models

Predictive pole-placement (PPP) control is a continuous-time MPC using a particular set of basis functions leading to pole-placement behaviour in the unconstrained case. This paper presents two modified versions of the PPP controller which are each shown to have desirable stability properties when controlling systems with input, output and state constraints.     

Max-plus-linear model-based predictive control for constrained hybrid systems：linear programming solution

In this paper, a linear programming method is proposed to solve model predictive control for a class of hybrid systems. Firstly, using the （max, ＋） algebra, a typical subclass of hybrid systems called max-plus-linear （MPL） systems is obtained. And then, model predictive control （MPC） framework is extended to MPL systems. In general, the nonlinear optimization approach or extended linear complementarity problem （ELCP） were applied to solve the MPL-MPC optimization problem. A new optimization method based on canonical forms for max-min-plus-scaling （MMPS） functions （using the operations maximization, minimization, addition and scalar multiplication） with linear constraints on the inputs is presented. The proposed approach consists in solving several linear programming problems and is more efficient than nonlinear optimization. The validity of the algorithm is illustrated by an example.     

Max-plus-linear model-based predictive control for constrained hybrid systems: linear programming solution

In this paper, a linear programming method is proposed to solve model predictive control for a class of hybrid systems. Firstly, using the (max, +) algebra, a typical subclass of hybrid systems called max-plus-linear (MPL) systems is obtained. And then, model predictive control (MPC) framework is extended to MPL systems. In general, the nonlinear optimization approach or extended linear complementarity problem (ELCP) were applied to solve the MPL-MPC optimization problem. A new optimization method based on canonical forms for max-min-plus-scaling (MMPS) functions (using the operations maximization, minimization, addition and scalar multiplication) with linear constraints on the inputs is presented. The proposed approach consists in solving several linear programming problems and is more efficient than nonlinear optimization. The validity of the algorithm is illustrated by an example.     

Advanced-multi-step nonlinear model predictive control

Nonlinear model predictive control (NMPC) has gained widespread attention due to its ability to handle variable bounds and deal with multi-input, multi-output systems. However, it is susceptible to computational delay, especially when the solution time of the nonlinear programming (NLP) problem exceeds the sampling time. In this paper we propose a fast NMPC method based on NLP sensitivity, called advanced-multi-step NMPC (amsNMPC). Two variants of this method are developed, the parallel approach and the serial approach. For the amsNMPC method, NLP problems are solved in background multiple sampling times in advance, and manipulated variables are updated on-line when the actual states are available. We present case studies about a continuous stirred tank reactor (CSTR) and a distillation column to show the performance of amsNMPC. Nominal stability properties are also analyzed.     

A framework for hybrid model predictive control in mineral processing

Model Predictive Control (MPC) is an advanced technique for process control that has seen a significant and widespread increase in its use in the process industry since its introduction. In mineral processing, in particular, several applications of conventional MPC can be found for the individual processes of crushing, grinding, flotation, thickening, agglomeration, and smelting with varying degrees of success depending on the variables involved and the control objectives. Given the complexity of the processes normally found in mineral processing, there is also great interest in the design and development of advanced control techniques which aim to deal with situations that conventional controllers are unable to do. In this aspect, Hybrid MPC enables the representation of systems, incorporating logical variables, rules, and continuous dynamics. This paper firstly presents a framework for modeling and representation of hybrid systems, and the design and development of hybrid predictive controllers. Additionally, two application examples in mineral processing are presented. Results through simulation show that the control schemes developed under this framework exhibit a better performance when compared with conventional expert or MPC controllers, while providing a highly systematized methodology for the analysis, design, and development of hybrid MPC controllers.     

Stable redesign of predictive control

The paper deals with I/O versions of receding horizon controllers based on the minimization of multistep quadratic costs with the constraint that the terminal state goes to zero. The resulting control law yields stable closed-loop systems under sharp conditions. Simulation results are presented to both verify the theoretical analysis and relate the new control law with GPC     

Automatic structural identification and relaxation for integer programming

This research investigates the automatic identification of typical embedded structures in the Integer Programming (IP) models and automatic transformation of the problem to an adequate Lagrangian problem which can provide tight bounds within the acceptable run time. For this purpose, the structural distinctivenesses of variables, constants, blocks of terms, and constraint chunks are identified to specify the structure of the IP model. To assist the identification of the structural distinctiveness, the representation by the knowledge based IP model formulator, UNIK-IP, is adopted. To reason for the structural identification, the hybrid of bottom-up, top-down, and case-based approaches are proposed. A system UNIK-RELAX is developed to implement the approaches proposed in this research.     

Robust constrained predictive control using comparison model

This paper proposes a quadratic programming (QP) approach to robust model predictive control (MPC) for constrained linear systems having both model uncertainties and bounded disturbances. To this end, we construct an additional comparison model for worst-case analysis based on a robust control Lyapunov function (RCLF) for the unconstrained system (not necessarily an RCLF in the presence of constraints). This comparison model enables us to transform the given robust MPC problem into a nominal one without uncertain terms. Based on a terminal constraint obtained from the comparison model, we derive a condition for initial states under which the ultimate boundedness of the closed loop is guaranteed without violating state and control constraints. Since this terminal condition is described by linear constraints, the control optimization can be reduced to a QP problem.     

Computationally efficient model predictive control for convection dominated parabolic systems

Convection–diffusion–reaction processes widely exist in chemical engineering and other sectors of industry. In many cases, these systems are convection-dominated and can be modelled by parabolic partial differential equations (PDEs) with a relatively dominant convection term. The control of these systems using traditional solution methods requires demanding computation to achieve high control performance. In this paper, a predictive control approach is developed for these systems using a new solution technique that combines the method of characteristics and finite difference approximation. The study shows that the proposed control approach is able to provide a computationally efficient control for convection-dominant parabolic systems.     

混杂系统的预测控制

因混杂系统预测控制（PC-HS）具有在线处理控制量和状态量的约束等优点,而成为学术界研究的一个热点．系统地论述了PC-HS的发展和研究现状,在介绍混杂系统的背景和模型的基础上,重点讨论了PC-HS的各种算法、性能等几个前沿问题,并对PC-HS目前研究中存在的问题进行了分析,对未来的一些研究方向进行了展望．     

A neurofuzzy scheme to on-line identification in an adaptive–predictive control

A neurofuzzy scheme has been designed to carry out on-line identification, with the aim of being used in an adaptive–predictive dynamic matrix control (DMC) of unconstrained nonlinear systems represented by a transfer function with varying parameters. This scheme supplies to the DMC controller the linear model and the nonlinear output predictions at each sample instant, and is composed of two blocks. The first one makes use of a fuzzy partition of the external variable universe of discourse, which smoothly commutes between several linear models. In the second block, a recurrent linear neuron with interpretable weights performs the identification of the models by means of supervised learning. The resulting identifier has several main advantages: interpretability, learning speed, and robustness against catastrophic forgetting. The proposed controller has been tested both on simulation and on a real laboratory plant, showing a good performance.     

Robust constrained predictive control of uncertain norm-bounded linear systems

A novel robust predictive control algorithm is presented for uncertain discrete-time input-saturated linear systems described by structured norm-bounded model uncertainties. The solution is based on the minimization, at each time instant, of a semi-definite convex optimization problem subject to a number of LMI feasibility constraints which grows up only linearly with the control horizon length N. The general case of arbitrary N is considered. Closed-loop stability and feasibility retention over the time are proved and comparisons with robust multi-model (polytopic) MPC algorithms are reported.     

A new real-time perspective on non-linear model predictive control

This work presents a new formulation of continuous-time non-linear model predictive control (NMPC) in which the parameters defining the input trajectory are adapted continuously in real time. Continuous implementation of the control as the input parameterization is being optimized reduces the impact of computational delay, in particular in response to process disturbances. By eliminating the typical correspondence between the time partitions used for input parameterization and implementation, and instead parameterizing the input over arbitrary intervals of variable length, a means is provided to reduce the overall number of optimization parameters (and hence the dimension of the required gradient and Hessian calculations) without adversely affecting stability or optimality.     

On a generalized predictive control algorithm

Generalized predictive control algorithms with reference models on imputs and outputs of the process have been proposed recently in the literature. Thise algorithms are extended by introducing suitable weighting factors in the performance index and it is shown that such algorithms provide a combined feedback feedforward control resulting in pole-zero cancellation of poles which do not correspond to the reference model. Hence, the system behaves asymptotically as the reference model provided the cancelled poles are stable. Therefore, a careful analysis of the stability of those poles in still needed.     

一类非线性系统的多模型预测控制

讨论了基于多模型的预测控制方法.对于化工生产过程中具有高度非线性的连续搅拌反应釜（CSTR）,通过对覆盖工况的数据离线辨识建立多个局部模型,根据每个局部模型分别设计子GPC控制器,通过跟踪工况变化对子控制器加权以获得控制增量.仿真结果表明该方法可取得令人满意的控制效果.