Some manifold learning considerations toward explicit model predictive control

Model predictive control (MPC) is a de facto standard control algorithm across the process industries. There remain, however, applications where MPC is impractical because an optimization problem is solved at each time step. We present a link between explicit MPC formulations and manifold learning to enable facilitated prediction of the MPC policy. Our method uses a similarity measure informed by control policies and system state variables, to “learn” an intrinsic parametrization of the MPC controller using a diffusion maps algorithm, which will also discover a low-dimensional control law when it exists as a smooth, nonlinear combination of the state variables. We use function approximation algorithms to project points from state space to the intrinsic space, and from the intrinsic space to policy space. The approach is illustrated first by “learning” the intrinsic variables for MPC control of constrained linear systems, and then by designing controllers for an unstable nonlinear reactor.     

Distributed model predictive control of switched nonlinear systems with scheduled mode transitions

A method for the design of distributed model predictive control (DMPC) systems for a class of switched nonlinear systems for which the mode transitions take place according to a prescribed switching schedule is presented. Under appropriate stabilizability assumptions on the existence of a set of feedback controllers that can stabilize the closed‐loop switched, nonlinear system, a cooperative DMPC architecture using Lyapunov‐based model predictive control (MPC) in which the distributed controllers carry out their calculations in parallel and communicate in an iterative fashion to compute their control actions is designed. The proposed DMPC design is applied to a nonlinear chemical process network with scheduled mode transitions and its performance and computational efficiency properties in comparison to a centralized MPC architecture are evaluated through simulations. © 2013 American Institute of Chemical Engineers AIChE J, 59:860‐871, 2013     

Model predictive control for multivariable unstable processes with constraints on manipulated variables

The original MPC(Model Predictive Control) algorithm cannot be applied to open loop unstable systems, because the step responses of the open loop unstable system never reach steadystates. So when we apply MPC to the open loop unstable systems, first we have to stabilize them by state feedback or output feedback. Then the stabilized systems can be controlled by MPC. But problems such as valve saturation may occur because the manipulated input is the summation of the state feedback output and the MPC output. Therefore, we propose Quadratic Dynamic Matrix Control(QDMC) combined with state feedback as a new method to handle the constraints on manipulated variables for multivariable unstable processes. We applied this control method to a single-input-single-output unstable nonlinear system and a multi-input-multi-output unstable system. The results show that this method is robust and can handle the input constraints explicitly and also its control performance is better than that of others such as well tuned PI control. Linear Quadratic Regulator (LQR) with integral action.     

Model predictive control for multivariable unstable processes with constraints on manipulated variables

The original MPC(Model Predictive Control) algorithm cannot be applied to open loop unstable systems, because the step responses of the open loop unstable system never reach steady states. So when we apply MPC to the open loop unstable systems, first we have to stabilize them by state feedback or output feedback. Then the stabilized systems can be controlled by MPC. But problems such as valve saturation may occur because the manipulated input is the summation of the state feedback output and the MPC output. Therefore, we propose Quadratic Dynamic Matrix Control(QDMC) combined with state feedback as a new method to handle the constraints on manipulated variables for multivariable unstable processes. We applied this control method to a single-input-single-output unstable nonlinear system and a multi-input-multi-output unstable system. The results show that this method is robust and can handle the input constraints explicitly and also its control performance is better than that of others such as well tuned PI control. Linear Quadratic Regulator (LQR) with integral action.     

Economic model predictive control of nonlinear process systems using Lyapunov techniques

In this work, we develop model predictive control (MPC) designs, which are capable of optimizing closed‐loop performance with respect to general economic considerations for a broad class of nonlinear process systems. Specifically, in the proposed designs, the economic MPC optimizes a cost function, which is related directly to desired economic considerations and is not necessarily dependent on a steady‐state—unlike conventional MPC designs. First, we consider nonlinear systems with synchronous measurement sampling and uncertain variables. The proposed economic MPC is designed via Lyapunov‐based techniques and has two different operation modes. The first operation mode corresponds to the period in which the cost function should be optimized (e.g., normal production period); and in this operation mode, the MPC maintains the closed‐loop system state within a predefined stability region and optimizes the cost function to its maximum extent. The second operation mode corresponds to operation in which the system is driven by the economic MPC to an appropriate steady‐state. In this operation mode, suitable Lyapunov‐based constraints are incorporated in the economic MPC design to guarantee that the closed‐loop system state is always bounded in the predefined stability region and is ultimately bounded in a small region containing the origin. Subsequently, we extend the results to nonlinear systems subject to asynchronous and delayed measurements and uncertain variables. Under the assumptions that there exist an upper bound on the interval between two consecutive asynchronous measurements and an upper bound on the maximum measurement delay, an economic MPC design which takes explicitly into account asynchronous and delayed measurements and enforces closed‐loop stability is proposed. All the proposed economic MPC designs are illustrated through a chemical process example and their performance and robustness are evaluated through simulations. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Machine learning-based predictive control of nonlinear processes. Part I: Theory

This article focuses on the design of model predictive control (MPC) systems for nonlinear processes that utilize an ensemble of recurrent neural network (RNN) models to predict nonlinear dynamics. Specifically, RNN models are initially developed based on a data set generated from extensive open-loop simulations within a desired process operation region to capture process dynamics with a sufficiently small modeling error between the RNN model and the actual nonlinear process model. Subsequently, Lyapunov-based MPC (LMPC) that utilizes RNN models as the prediction model is developed to achieve closed-loop state boundedness and convergence to the origin. Additionally, machine learning ensemble regression modeling tools are employed in the formulation of LMPC to improve prediction accuracy of RNN models and overall closed-loop performance while parallel computing is utilized to reduce computation time. Computational implementation of the method and application to a chemical reactor example is discussed in the second article of this series.     

Predictive control of transport-reaction processes

This work focuses on the development of computationally efficient predictive control algorithms for nonlinear parabolic and hyperbolic PDEs with state and control constraints arising in the context of transport-reaction processes. We first consider a diffusion-reaction process described by a nonlinear parabolic PDE and address the problem of stabilization of an unstable steady-state subject to input and state constraints. Galerkin’s method is used to derive finite-dimensional systems that capture the dominant dynamics of the parabolic PDE, which are subsequently used for controller design. Various model predictive control (MPC) formulations are constructed on the basis of the finite dimensional approximations and are demonstrated, through simulation, to achieve the control objectives. We then consider a convection-reaction process example described by a set of hyperbolic PDEs and address the problem of stabilization of the desired steady-state subject to input and state constraints, in the presence of disturbances. An easily implementable predictive controller based on a finite dimensional approximation of the PDE obtained by the finite difference method is derived and demonstrated, via simulation, to achieve the control objective.     

Nonlinear model predictive control based on support vector machine and genetic algorithm

This paper presents a nonlinear model predictive control (NMPC) approach based on support vector machine (SVM) and genetic algorithm (GA) for multiple-input multiple-output (MIMO) nonlinear systems. Individual SVM is used to approximate each output of the controlled plant. Then the model is used in MPC control scheme to predict the outputs of the controlled plant. The optimal control sequence is calculated using GA with elite preserve strategy. Simulation results of a typical MIMO nonlinear system show that this method has a good ability of set points tracking and disturbance rejection.     

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.     

A Monte-Carlo based model approximation technique for linear model predictive control of nonlinear systems

In this paper we present a model approximation technique based on N-step-ahead affine representations obtained via Monte-Carlo integrations. The approach enables simultaneous linearization and model order reduction of nonlinear systems in the original state space thus allowing the application of linear MPC algorithms to nonlinear systems. The methodology is detailed through its application to benchmark model examples.     

Machine learning-based distributed model predictive control of nonlinear processes

This work explores the design of distributed model predictive control (DMPC) systems for nonlinear processes using machine learning models to predict nonlinear dynamic behavior. Specifically, sequential and iterative DMPC systems are designed and analyzed with respect to closed-loop stability and performance properties. Extensive open-loop data within a desired operating region are used to develop long short-term memory (LSTM) recurrent neural network models with a sufficiently small modeling error from the actual nonlinear process model. Subsequently, these LSTM models are utilized in Lyapunov-based DMPC to achieve efficient real-time computation time while ensuring closed-loop state boundedness and convergence to the origin. Using a nonlinear chemical process network example, the simulation results demonstrate the improved computational efficiency when the process is operated under sequential and iterative DMPCs while the closed-loop performance is very close to the one of a centralized MPC system.     

On improving accuracy of computationally efficient nonlinear predictive control based on neural models

For nonlinear processes the classical model predictive control (MPC) algorithm, in which a linear model is used, usually does not give satisfactory closed-loop performance. In such nonlinear cases a suboptimal MPC strategy is typically used in which the nonlinear model is successively linearised on-line for the current operating point and, thanks to linearisation, the control policy is calculated from a quadratic programming problem. Although the suboptimal MPC algorithm frequently gives good results, for some nonlinear processes it would be beneficial to further improve control accuracy. This paper details a computationally efficient nonlinear MPC algorithm in which a neural model is linearised on-line along the predicted trajectory in an iterative way. The algorithm needs solving on-line only a series of quadratic programming problems. Advantages of the discussed algorithm are demonstrated in the control system of a high-purity ethylene–ethane distillation column for which the classical linear MPC algorithm does not work and the classical suboptimal MPC algorithm is slow. It is shown that the discussed algorithm can give practically the same control accuracy as the algorithm with on-line nonlinear optimisation and, at the same time, the algorithm is significantly less computationally demanding.     

Composite fast‐slow MPC design for nonlinear singularly perturbed systems

The design of a composite control system for nonlinear singularly perturbed systems using model predictive control (MPC) is described. Specifically, a composite control system comprised of a “fast” MPC acting to regulate the fast dynamics and a “slow” MPC acting to regulate the slow dynamics is designed. The composite MPC system uses multirate sampling of the plant state measurements, i.e., fast sampling of the fast state variables is used in the fast MPC and slow‐sampling of the slow state variables is used in the slow MPC. Using singular perturbation theory, the stability and optimality of the closed‐loop nonlinear singularly perturbed system are analyzed. A chemical process example which exhibits two‐time‐scale behavior is used to demonstrate the structure and implementation of the proposed fast–slow MPC architecture in a practical setting. © 2012 American Institute of Chemical Engineers AIChE J, 58: 1802–1811, 2012     

Encrypted model predictive control design for security to cyberattacks

In recent years, cyber-security of networked control systems has become crucial, as these systems are vulnerable to targeted cyberattacks that compromise the stability, integrity, and safety of these systems. In this work, secure and private communication links are established between sensor–controller and controller–actuator elements using semi-homomorphic encryption to ensure cyber-security in model predictive control (MPC) of nonlinear systems. Specifically, Paillier cryptosystem is implemented for encryption-decryption operations in the communication links. Cryptosystems, in general, work on a subset of integers. As a direct consequence of this nature of encryption algorithms, quantization errors arise in the closed-loop MPC of nonlinear systems. Thus, the closed-loop encrypted MPC is designed with a certain degree of robustness to the quantization errors. Furthermore, the trade-off between the accuracy of the encrypted MPC and the computational cost is discussed. Finally, two chemical process examples are employed to demonstrate the implementation of the proposed encrypted MPC design.     

基于自适应模糊神经网络的非线性系统模型预测控制

针对非线性动态系统的控制问题,提出了一种基于自适应模糊神经网络(adaptive fuzzy neural network,AFNN)的模型预测控制(model predictive control, MPC)方法。首先,在离线建模阶段,AFNN采用规则自分裂技术产生初始模糊规则,采用改进的自适应LM学习算法优化网络参数;然后,在实时控制过程,AFNN根据系统输出和预测输出之间的误差调整网络参数,从而为MPC提供一个精确的预测模型;进一步,AFNN-MPC利用带有自适应学习率的梯度下降寻优算法求解优化问题,在线获取非线性控制量,并将其作用到动态系统实施控制。此外,给出了AFNN-MPC的收敛性和稳定性证明,以保证其在实际工程中的成功应用。最后,利用数值仿真和双CSTR过程进行实验验证。结果表明,AFNN-MPC能够取得优越的控制性能。     

Online machine learning modeling and predictive control of nonlinear systems with scheduled mode transitions

This work develops a model predictive control (MPC) scheme using online learning of recurrent neural network (RNN) models for nonlinear systems switched between multiple operating regions following a prescribed switching schedule. Specifically, an RNN model is initially developed offline to model process dynamics using the historical operational data collected in a small region around a certain steady-state. After the system is switched to another operating region under a Lyapunov-based MPC with suitable constraints to ensure satisfaction of the prescribed switching schedule policy, RNN models are updated using real-time process data to improve closed-loop performance. A generalization error bound is derived for the updated RNN models using the notion of regret, and closed-loop stability results are established for the switched nonlinear system under RNN-based MPC. Finally, a chemical process example with the operation schedule that requires switching between two steady-states is used to demonstrate the effectiveness of the proposed RNN-MPC scheme.     

Demand reduction in building energy systems based on economic model predictive control

This paper proposes and demonstrates the effectiveness of an economic model predictive control (MPC) technique in reducing energy and demand costs for building heating, ventilating, and air conditioning (HVAC) systems. A simulated multi-zone commercial building equipped with of variable air volume (VAV) cooling system is built in Energyplus. With the introduced Building Controls Virtual Test Bed (BCVTB) as middleware, real-time data exchange between Energyplus and a Matlab controller is realized by sending and receiving sockets. System identification is performed to obtain zone temperature and power models, which are used in the MPC framework. The economic objective function in MPC accounts for the daily electricity costs, which include time-of-use (TOU) energy charge and demand charge. In each time step, a min–max optimization is formulated and converted into a linear programming problem and solved. In a weekly simulation, a pre-cooling effect during off-peak period and a cooling discharge from the building thermal mass during on-peak period can be observed. Cost savings by MPC are estimated by comparing with the baseline and other open-loop control strategies. The effect of several experimental factors in the MPC configuration is investigated and the best scenario is selected for future practical tests.     

Predictive control of transport-reaction processes

This work focuses on the development of computationally efficient predictive control algorithms for nonlinear parabolic and hyperbolic PDEs with state and control constraints arising in the context of transport-reaction processes. We first consider a diffusion-reaction process described by a nonlinear parabolic PDE and address the problem of stabilization of an unstable steady-state subject to input and state constraints. Galerkin’s method is used to derive finite-dimensional systems that capture the dominant dynamics of the parabolic PDE, which are subsequently used for controller design. Various model predictive control (MPC) formulations are constructed on the basis of the finite dimensional approximations and are demonstrated, through simulation, to achieve the control objectives. We then consider a convection-reaction process example described by a set of hyperbolic PDEs and address the problem of stabilization of the desired steady-state subject to input and state constraints, in the presence of disturbances. An easily implementable predictive controller based on a finite dimensional approximation of the PDE obtained by the finite difference method is derived and demonstrated, via simulation, to achieve the control objective.     

Multivariable model predictive control of a novel rapid pressure swing adsorption system

A multivariable model predictive control (MPC) algorithm is developed for the control and operation of a rapid pressure swing adsorption (RPSA)‐based medical oxygen concentrator. The novelty of the approach is the use of all four step durations in the RPSA cycle as independent manipulated variables in a truly multivariable context. The RPSA has a complex, cyclic, nonlinear multivariable operation that requires feedback control, and MPC provides a suitable framework for controlling such a multivariable system. The multivariable MPC presented here uses a quadratic optimization program with integral action and a linear model identified using subspace system identification techniques. The controller was designed and tested in simulation using a complex, highly coupled, nonlinear RPSA process model. The model was developed with the least restrictive assumptions compared to those reported in the literature, thereby providing a more realistic representation of the underlying physical phenomena. The resulting MPC effectively tracks set points, rejects realistic process disturbances and is shown to outperform conventional PID control. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1234–1245, 2018