Flood regulation using nonlinear model predictive control

In this paper the flood problem of the river Demer, a river located in Belgium, is discussed. First a simplified model of the Demer basin is derived based on the conceptual reservoir modeling concept. This model was calibrated to simulations results with a more detailed full hydrodynamic model. Afterwards, the focus is shifted to a nonlinear model predictive controller (NMPC) which is based on a new semi-condensed optimization procedure combined with a line search approach. Finally, simulations are performed based on historical data in which the NMPC is compared with the current control strategy used by the local water administration. Uncertainties are added to the rainfall predictions in order to assess the robustness of the NMPC.     

采用dsDNA-MC优化的非线性系统预测控制

将基于DNA双链结构的膜计算优化方法（dsDNA-MC）用于输入受限的非线性预测控制器设计,提出了基于dsDNA-MC优化的非线性系统预测控制算法。在对单输入单输出非线性系统预测控制分析的基础上,将非线性系统预测控制问题归结为具有输入约束的非线性系统优化问题,并采用dsDNA-MC算法来求解这一问题。仿真结果表明该算法可行、有效。     

Nested partitions for global optimization in nonlinear model predictive control

In Nonlinear Model Predictive Control (NMPC), the optimization problem may be nonconvex. It is important to find a global solution since a local solution may not be able to operate the process at desired setpoints. Also the solution must be available before the control input has to be applied to the process. In this paper, a stochastic algorithm called the Nested Partitions Algorithm (NPA) is used for global optimization. The NPA divides the search space into smaller regions and either concentrates search in one of these regions called the most promising region or backtracks to a larger region in the search space based on a performance index. To adapt the NPA to solve dynamic NMPC with continuous variables, a new partitioning scheme is developed that focuses on the first few control moves in the control horizon. The expected number of iterations taken by the NPA is presented. Convergence speed is improved by reducing the size of the starting most promising region based on a good starting point. The discrete sampling nature of the NPA may cause difficulty in finding the global solution in a continuous space. A gradient-based search is used with the NPA to overcome this difficulty. The solution quality is assessed in terms of the error from the actual global minimum. The algorithm is shown to give a feasible solution that provides asymptotic stability. Case studies are used to show the algorithm performance in terms of tracking setpoints, cost, solution quality and convergence time.     

Nonlinear model predictive control using trust-region derivative-free optimization

Gradient-based optimization may not be suited if the objective and constraint functions in a nonlinear model predictive control (NMPC) optimization problem are not differentiable. Some well-known derivative-free optimization (DFO)-algorithms are investigated, and a novel warm-start modification to the Wedge DFO-algorithm is proposed. Together with a gradient-based SQP-algorithm these are applied to the NMPC problem and compared in a single-shooting NMPC formulation to a subsea oil–gas separation process. The findings are that DFO is significantly more robust against the numerical issues, compared to a gradient-based SQP tested. Moreover, the warm-start modification reduces the computational complexity.     

Nonlinear model predictive control using deterministic global optimization

This paper presents a Nonlinear Model Predictive Control (NMPC) algorithm utilizing a deterministic global optimization method. Utilizing local techniques on nonlinear nonconvex problems leaves one susceptible to suboptimal solutions at each iteration. In complex problems, local solver reliability is difficult to predict and dependent upon the choice of initial guess. This paper demonstrates the application of a deterministic global solution technique to an example NMPC problem. A terminal state constraint is used in the example case study. In some cases the local solution method becomes infeasible, while the global solution correctly finds the feasible global solution. Increased computational burden is the most significant limitation for global optimization based online control techniques. This paper provides methods for improving the global optimization rates of convergence. This paper also shows that globally optimal NMPC methods can provide benefits over local techniques and can successfully be used for online control.     

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 formulation of nonlinear model predictive control using automatic differentiation

An efficient algorithm is developed to alleviate the computational burden associated with nonlinear model predictive control (NMPC). The new algorithm extends an existing algorithm for solutions of dynamic sensitivity from autonomous to non-autonomous differential equations using the Taylor series and automatic differentiation (AD). A formulation is then presented to recast the NMPC problem as a standard nonlinear programming problem by using the Taylor series and AD. The efficiency of the new algorithm is compared with other approaches via an evaporation case study. The comparison shows that the new algorithm can reduce computational time by two orders of magnitude.     

Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations

Optimization problems in chemical engineering often involve complex systems of nonlinear DAE as the model equations. The direct multiple shooting method has been known for a while as a fast off-line method for optimization problems in ODE and later in DAE. Some factors crucial for its fast performance are briefly reviewed. The direct multiple shooting approach has been successfully adapted to the specific requirements of real-time optimization. Special strategies have been developed to effectively minimize the on-line computational effort, in which the progress of the optimization iterations is nested with the progress of the process. They use precalculated information as far as possible (e.g. Hessians, gradients and QP presolves for iterated reference trajectories) to minimize response time in case of perturbations. In typical real-time problems they have proven much faster than fast off-line strategies. Compared with an optimal feedback control computable upper bounds for the loss of optimality can be established that are small in practice. Numerical results for the Nonlinear Model Predictive Control (NMPC) of a high-purity distillation column subject to parameter disturbances are presented.     

Reduced order optimization for model predictive control using principal control moves

In order to reduce the computational complexity of model predictive control (MPC) a proper input signal parametrization is proposed in this paper which significantly reduces the number of decision variables. This parametrization can be based on either measured data from closed-loop operation or simulation data. The snapshots of representative time domain data for all manipulated variables are projected on an orthonormal basis by a Karhunen-Loeve transformation. These significant features (termed principal control moves, PCM) can be reduced utilizing an analytic criterion for performance degradation. Furthermore, a stability analysis of the proposed method is given. Considerations on the identification of the PCM are made and another criterion is given for a sufficient selection of PCM. It is shown by an example of an industrial drying process that a strong reduction in the order of the optimization is possible while retaining a high performance level.     

Periodic optimal control of nonlinear constrained systems using economic model predictive control

In this paper, we consider the problem of periodic optimal control of nonlinear systems subject to online changing and periodically time-varying economic performance measures using model predictive control (MPC). The proposed economic MPC scheme uses an online optimized artificial periodic orbit to ensure recursive feasibility and constraint satisfaction despite unpredictable changes in the economic performance index. We demonstrate that the direct extension of existing methods to periodic orbits does not necessarily yield the desirable closed-loop economic performance. Instead, we carefully revise the constraints on the artificial trajectory, which ensures that the closed-loop average performance is no worse than a locally optimal periodic orbit. In the special case that the prediction horizon is set to zero, the proposed scheme is a modified version of recent publications using periodicity constraints, with the important difference that the resulting closed loop has more degrees of freedom which are vital to ensure convergence to an optimal periodic orbit. In addition, we detail a tailored offline computation of suitable terminal ingredients, which are both theoretically and practically beneficial for closed-loop performance improvement. Finally, we demonstrate the practicality and performance improvements of the proposed approach on benchmark examples.     

Wiener model based nonlinear predictive control

This paper addresses the problem of discrete-time nonlinear predictive control of W iener systems. Wiener-model-based nonlinear predictive control combines the advantages of linear-model-based predictive control and gain scheduling while retaining a moderate level of computational complexity. A clear relation is shown between an iteration in the optimization of the nonlinear control problem and the control problem of the underlying linear-model-based method. This relation has a simple form of gain scheduling, thus the properties of the nonlinear control system can be analysed from the comprehensible linear control aspect. Several disturbance rejection techniques are proposed and compared. The method was tested on a simulated model of a pH neutralization process. The performance was excellent also in the case of a considerable plant-tomodel mismatch. The method can be applied as a first next step in cases where the performance of linear control is unsatisfactory owing to process nonlinearity.     

采用预测控制的地铁节能优化控制算法

本文针对地铁列车自动运行系统(automatic train operation,ATO)一般运行情况以及晚点延迟发车情况下的节能问题,基于预测控制算法设计了地铁节能优化控制算法.利用预测控制算法的在线滚动优化特性,通过设计含有能量消耗趋势优化项的控制目标函数,控制算法能够针对节能目标实现快速动态调整.通过调节目标函数中各优化项权重的相对大小,节能算法可以在满足列车时间与路程运行指标的同时,达到降低能耗的目的.在MATLAB平台上利用真实车辆模型对提出的节能优化控制算法进行了仿真,在列车不延迟与延迟的情况下,算法都很好地平衡了跟踪目标与节能目标,为地铁能耗动态优化控制提供了可行方案.     

Economic optimization using model predictive control with a terminal cost

In the standard model predictive control implementation, first a steady-state optimization yields the equilibrium point with minimal economic cost. Then, the deviation from the computed best steady state is chosen as the stage cost for the dynamic regulation problem. The computed best equilibrium point may not be the global minimum of the economic cost, and hence, choosing the economic cost as the stage cost for the dynamic regulation problem, rather than the deviation from the best steady state, offers potential for improving the economic performance of the system. It has been previously shown that the existing framework for MPC stability analysis, which addresses to the standard class of problems with a regulation objective, does not extend to economic MPC. Previous work on economic MPC developed new tools for stability analysis and identified sufficient conditions for asymptotic stability. These tools were developed for the terminal constraint MPC formulation, in which the system is stabilized by forcing the state to the best equilibrium point at the end of the horizon. In this work, we relax this constraint by imposing a region constraint on the terminal state instead of a point constraint, and adding a penalty on the terminal state to the regulator cost. We extend the stability analysis tools, developed for terminal constraint economic MPC, to the proposed formulation and establish that strict dissipativity is sufficient for guaranteeing asymptotic stability of the closed-loop system. We also show that the average closed-loop performance outperforms the best steady-state performance. For implementing the proposed formulation, a rigorous analysis for computing the appropriate terminal penalty and the terminal region is presented. A further extension, in which the terminal constraint is completely removed by modifying the regulator cost function, is also presented along with its stability analysis. Finally, an illustrative example is presented to demonstrate the differences between the terminal constraint and the proposed terminal penalty formulation.     

Mean arterial pressure control system using model predictive control and particle swarm optimization

Microsystem Technologies - Linear controllers have been designed to regulate mean arterial pressure (MAP) in treating various cardiovascular diseases. For patients with hemodynamic fluctuations,...     

On optimality of nonlinear model predictive control

In this note the optimality property of nonlinear model predictive control (MPC) is analyzed. It is well known that the MPC approximates arbitrarily well the infinite horizon (IH) controller as the optimization horizon increases. Hence, it makes sense to suppose that the performance of the MPC is a not decreasing function of the optimization horizon. This work, by means of a counterexample, shows that the previous conjecture is fallacious, even for simple linear systems.     

Serial advanced-multi-step nonlinear model predictive control using an extended sensitivity method

Nonlinear model predictive control (NMPC) can directly handle multi-input multi-output nonlinear systems and explicitly consider input and state constraints. However, the computational load for nonlinear programming (NLP) of large-scale systems limits the range of possible applications and degrades NMPC performance. An NLP sensitivity based approach, advanced-step NMPC, has been developed to address the online computational load. In addition, for cases where the NLP solving time exceeds one sampling time, two types of advanced-multi-step NMPC (amsNMPC), parallel and serial, have been proposed. However, in previous studies, a serial amsNMPC could not be applied to large-scale problems because of the size of extended Karush–Kuhn–Tucker matrix and its Schur complement decomposition, and the robustness was analyzed under a conservative assumption for memory effects. In this paper, we propose a serial amsNMPC using an extended sensitivity method to increase the online computation speed further. We successfully apply it to a large-scale air separation unit using the sparse matrix handling packages of Python, Pyomo, and k_aug tools. Furthermore, an auxiliary NLP formulation is defined to analyze the robustness. Using this with the key properties of an extended sensitivity matrix, we can prove robustness while avoiding the memory effects term.     

Integration of real-time optimization and model predictive control

This paper proposes a controller design approach that integrates RTO and MPC for the control of constrained uncertain nonlinear systems. Assuming that the economic function is a known function of constrained system’s states, parameterized by unknown parameters and time-varying, the controller design objective is to simultaneously identify and regulate the system to the optimal operating point. The approach relies on a novel set-based parameter estimation routine and a robust model predictive controller that takes into the effect of parameter estimation errors. A simulation example is used to demonstrate the effectiveness of the design technique.     

Adaptive horizon economic nonlinear model predictive control

In this paper, we present a computationally efficient economic NMPC formulation, where we propose to adaptively update the length of the prediction horizon in order to reduce the problem size. This is based on approximating an infinite horizon economic NMPC problem with a finite horizon optimal control problem with terminal region of attraction to the optimal equilibrium point. Using the nonlinear programming (NLP) sensitivity calculations, the minimum length of the prediction horizon required to reach this terminal region is determined. We show that the proposed adaptive horizon economic NMPC (AH-ENMPC) has comparable performance to standard economic NMPC (ENMPC). We also show that the proposed adaptive horizon economic NMPC framework is nominally stable. Two benchmark examples demonstrate that the proposed adaptive horizon economic NMPC provides similar performance as the standard economic NMPC with significantly less computation time.     

Integrating dynamic economic optimization and model predictive control for optimal operation of nonlinear process systems

In this work, we propose a conceptual framework for integrating dynamic economic optimization and model predictive control (MPC) for optimal operation of nonlinear process systems. First, we introduce the proposed two-layer integrated framework. The upper layer, consisting of an economic MPC (EMPC) system that receives state feedback and time-dependent economic information, computes economically optimal time-varying operating trajectories for the process by optimizing a time-dependent economic cost function over a finite prediction horizon subject to a nonlinear dynamic process model. The lower feedback control layer may utilize conventional MPC schemes or even classical control to compute feedback control actions that force the process state to track the time-varying operating trajectories computed by the upper layer EMPC. Such a framework takes advantage of the EMPC ability to compute optimal process time-varying operating policies using a dynamic process model instead of a steady-state model, and the incorporation of suitable constraints on the EMPC allows calculating operating process state trajectories that can be tracked by the control layer. Second, we prove practical closed-loop stability including an explicit characterization of the closed-loop stability region. Finally, we demonstrate through extensive simulations using a chemical process model that the proposed framework can both (1) achieve stability and (2) lead to improved economic closed-loop performance compared to real-time optimization (RTO) systems using steady-state models.