This work presents an unsupervised learning-based approach to approximate the controller of the Lyapunov-based Model Predictive Control (MPC) for a class of continuous-time nonlinear systems. The proposed design aims to produce an optimal control input by aligning the objectives and constraints of the learning problem with those of the MPC. The MPC is approximated by a deep feedforward neural network (DFNN) whose output can strictly satisfy the system constraints. A sufficient condition is provided under which the stability of the closed-loop system with the approximation DFNN control implemented in a sampling-and-hold fashion can be guaranteed. Additionally, we define a polyhedral Lyapunov function to shape the domain of attraction, allowing it to approach the shape of the state boundary defined by polyhedral state constraints, thereby providing potential for enlarging the domain of attraction. The implementation of the proposed method on a permanent magnet synchronous generator wind turbine and a continuous stirred tank reactor illustrates the effectiveness and performance of the designed approximation controller.

In response to the tenets of Industry 4.0, operation optimization in industrial processes has become a significant research topic. However, the uncertainties prevailing in the process pose challenges to production operations, especially the feedstock properties. In this work, the operation optimization study is performed on a distillation unit (DU), a typical plant in the industrial process. To enhance production performance, a modeling and operation optimization strategy based on feedstock property and production features is presented. One of the difficulties is how to uncover features from high-dimensional and imperfect data, where imperfect data refers to product quality data that is unavailable online. In the strategy, we inject the inherent characteristic of the process into the data-driven method to extract the feedstock property in a data-based and knowledge-oriented manner. Further, optimal feature representation and process modeling can be achieved by customizing the network structure. The operation optimization problem is formulated to adjust the top temperature of the distillation column (TTDC) to achieve satisfactory production under varying feedstock properties. Experimental results illustrate that the process model based on feedstock property and production features (PM-FP-PF) can better fit the physical process mechanism even based on incomplete information in industrial data. Industrial experiments have shown the proposed strategy has advanced generalization ability to the different feedstock properties. The proposed operation optimization strategy (OOS) improves the product qualification rate and has broad application prospects in industrial processes with similar features. Note to Practitioners—Industrial processes suffer from a variety of disturbances that interrupt the smooth operation of the system, such as varying feedstock properties. How to deal with them is the key to improve the product qualification rate. In this work, we propose a data-driven modeling and operation optimization framework to improve product quality under varying feedstock properties. The dynamic variation characteristics of the feedstock properties can be obtained by analyzing the physical properties of the production unit. This is used as a basis for representing and extracting feedstock properties in a data-driven way. Further, a process model based on feedstock property and production features (PM-FP-PF) is built to predict product quality. An operation optimization strategy with production capacity consideration is established. It can determine the optimal operation action required by the current system, mitigating the uncertainty of feedstock property. This operation optimization system has been applied to a distillation unit in the hydrofining process. The application results show that the process model achieves satisfactory estimation accuracy, and the operation optimization strategy has improved production performance.

This paper aims to design a stabilized Adaptive Model Predictive Control (MPC) for nonlinear continuous systems with unknown dynamics at the start time. The proposed method is based on the Lyapunov MPC (LMPC) where the derivative of the Lyapunov function of the closed-loop system is limited to be less than that under an auxiliary Lyapunov controller. Different from the existing LMPC methods, this paper provides an online constraint updating strategy, which gradually reduces the conservation of the constraint. Specifically, the piece-wise linear (PWL) model updated by the Set-Membership (SM) identification method is adopted in the constraint and the auxiliary controller design, which can result in a non-increasing boundary of the model error. Then, a sufficient condition that guarantees the stabilization of the closed-loop system is deduced, which takes the effect of sample-and-hold implementation and the error boundary of the PWL model into account. By this condition, an optimization problem to update the Lyapunov controller for relaxing the constraints of MPC is proposed. We prove that, by the proposed method, the states will eventually converge to a small region around the equilibrium, both this small region and the conservatism of MPC decrease with the increasing of the accuracy of the PWL model. The application of the proposed method to a chemical process demonstrates the effectiveness of the proposed method. Note to Practitioners—The control problem of nonlinear continuous systems with unknown dynamics has attracted the attention of researchers. This article develops an Adaptive MPC for this kind of system, which updates the boundary of uncertainties according to the measurement, and updates the constraints of MPC according to the updated uncertainty boundary. It provides a guaranteed stabilization and continuously relaxed constraint design for MPC where machine learning-based models are employed to predict the future trajectory. In the process of implementation, the method solves two optimization problems: one is to get the parameters of constraints which is based on the PWL model, and the other is used to optimize the future trajectory with the updated constraints. To proceed, the initial boundary of the uncertainty should be given at the initial instant, the initialization of PWL models and constraints can be configured based on it. The proposed method can be used for tracking control of chemical processes, power systems, robots, etc., where the accurate dynamics are not provided in advance and an improved performance is required.

This work presents a learning-based approximation scheme to improve the computational burden of general distributed model predictive control (DMPC). Under the framework of dual decomposition, an independent neural network approximator with rectified linear unit is designed for each subsystem. The primal and Lagrangian dual analysis indicates that this error-containing approximation is a suboptimal solution of the global DMPC optimization problem. In addition, the distributed conditions designed to guarantee the feasibility and stability of global system, which inspired by an explicit-implicit procedure to approximate an MPC law, are derived from an decoupling process using dual decomposition. In cases with infeasible approximator output or the distributed conditions are violated, an backup controller will used to promote the implementation of approximation. The proposed learning-based DMPC approximator with feasibility and stability guarantees is finally employed to a reactor-separator process, and simulation results demonstrate the efficiency and superior performance of proposed strategy.

This article proposes a distributed model predictive control (DMPC) strategy for a class of large-scale systems composed of several interacting subsystems. When a certain subsystem is required to be removed or inserted, the topology change of the system network can lead to the infeasibility of interacting local controllers due to the existence of the interactions among subsystems. In this article, the interactions among subsystems are presented as state trajectory estimations of interacting subsystems, and the estimations are involved in each local MPC. To deal with the influence resulted from the change of system topology, optimization schemes for removal and plugging-in are designed and employed in the proposed strategy. They optimize related subsystems’ reference trajectories, which are used to approximate the interacting state trajectories here, to reduce the time it takes to drive the system states and reference trajectories to a region. This region ensures that the system topology change can be conducted with all controllers having feasible solutions. The proposed DMPC algorithm has the following characteristics: 1) all the optimization problems in each MPC are solved in a noniterative manner and each controller only communicates with its neighbors and 2) it guarantees the feasibility of all controllers throughout the topology change process and the convergence of the system after the topology change. Simulation results show the effectiveness of the proposed DMPC algorithm.Note to Practitioners—The DMPC algorithm proposed in this article is designed for networked systems where certain subsystems may be removed or inserted. The purpose is to obtain a fast response to this topology change of system. An integrated algorithm is provided for the application of the strategy. First, the parameters of the MPCs are initialized. Then, before the command of a switch in topology is given, local controllers for normal situations provide the real-time inputs. Once the switch of topology is commanded, additional optimization problems are solved in the related subsystems’ controllers to guarantee the feasibility of removal or plugging-in operation. The optimization problems involved in each MPCs can be solved by adopting efficiently quadratic programming solvers supported by MATLAB. Note that although the topology change is commanded, all the subsystems are still operated normally until the topology change is conducted. In general, the strategy introduced in this article can be applied to control a class of large-scale networked systems, where each subsystem-based controller can exchange information with its neighbors.

Designing a stabilized distributed model predictive control (DMPC) with constraints is an open and important problem for a class of large-scale distributed systems, which are composed by both weakly and strongly coupled subsystems. This paper proposes a design of DMPC network to stabilize this class of large-scale systems. A coupling degree-based clustering method is first designed to classify subsystems into some middle-scale subsystems (M-subsystem) off-line according to the adjacent matrix, so that these M-subsystems are weakly coupled with each other. Then, each M-subsystem is controlled by a virtual model predictive control (MPC), which is realized by several individual controllers with running iterative cooperative DMPC algorithm, since the solution of cooperative DMPC is able to converge to a fixed point without coupling constraints. Each MPC communicates with the corresponding interacted M-subsystems' MPCs once in a control period for exchanging future state evolution estimation. All the subsystem-based MPCs are composed of the proposed peer-to-peer DMPC network. In addition, an additional consistency and stabilization constraints are added to guarantee the recursive feasibility and stability of the overall system. The convergence of the iterative DMPC algorithm for each M-subsystem and the stabilization analysis of the overall system are provided. The simulation results show the efficiency of the proposed method.

For a large-scale distributed system, distributed model predictive control (DMPC) is a method of choice because of its ability to explicitly accommodate constraints and to achieve good dynamic performance. In the design of a DMPC, guaranteeing stability with a strong global performance is known to be a challenge. In this paper, we consider a large-scale distributed system whose input is constrained to given sets in their respective spaces and propose a stabilizing DMPC design, where each subsystem-based model predictive control (MPC) optimizes the cost function of the entire system over the region it directly impacts on. Consistency constraints and stability constraints, which bound the estimation errors of the interaction sequences among subsystems, are designed to guarantee that, if an initially feasible solution can be found, subsequent feasibility of the algorithm is guaranteed at every update, and that the closed-loop system is asymptotically stable. A key feature of the proposed DMPC is that it coordinates the MPCs of the subsystems by redefining the impact region of a subsystem according to the coordination strategy. Simulation results show that the performance of the proposed DMPC is very close to that of a centralized MPC.

Fractional order differential equations (FODE) provides a more flexible approach to describe dynamic systems. However, the extra flexibility poses a difficult problem in system identification, which requires not only the estimation of model coefficients but also the determination of fractional orders. They are coupled nonlinearly. In addition, the model coefficients in a FODE are shown nonlinearly coupled with respect to the often used Sum Squared Error (SSE) objective function. In this article, a two-layer approach is designed to estimate fractional orders and model coefficients iteratively. An intermediate step that estimates model coefficients is also introduced to address the nonlinear coupling of coefficients in a SSE. In the subsequent simulation for electrochemical systems, it is found that prior knowledge on physical systems being modeled is necessary to create optimization constraints and justify the results.

In accelerated & controlled cooling (ACC) process, the relationship between plate point's temperature and the manipulated variable, plate velocity, is complicate and nonlinear with a time delay. A novel Model Predictive Control (MPC) is developed for precise control of the plate point's final temperature (FT) with fast computational speed. The control objective of time-temperature curve (plate temperature evolution) is converted into a space distribution of plate temperature along cooling line, which simplifies the ACC model to a linear model then does beneficial to employ MPC directly for optimizing the FT of plate points. The predictive horizon and control horizon of MPC is reduced to one or two sample time since the space distribution of plate temperature contains the future information of plate point's temperature, then dramatically reduce the computational burden. The simulation result shows the efficiency of the proposed method.