Explicit stochastic predictive control of combustion plants based on Gaussian process models

Energy production is one of the largest sources of air pollution. A feasible method to reduce the harmful flue gases emissions and to increase the efficiency is to improve the control strategies of the existing thermoelectric power plants. This makes the Nonlinear Model Predictive Control (NMPC) method very suitable for achieving an efficient combustion control. Recently, an explicit approximate approach for stochastic NMPC based on a Gaussian process model was proposed. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation, which is an essential issue in safety-critical applications. This paper considers the application of an explicit approximate approach for stochastic NMPC to the design of an explicit reference tracking NMPC controller for a combustion plant based on its Gaussian process model. The controller brings the air factor (respectively the concentration of oxygen in the flue gases) on its optimal value with every change of the load factor and thus an optimal operation of the combustion plant is achieved.     

A nonlinear model predictive control system based on Wiener piecewise linear models

In this paper a nonlinear model predictive control (NMPC) based on a Wiener model with a piecewise linear gain is presented. This approach retains all the interested properties of the classical linear model predictive control (MPC) and keeps computations easy to solve due to the canonical structure of the nonlinear gain. Some guidelines for the identification of the nominal model as well as the uncertainty bounds are discussed, and two examples that show the possibility of application of this control scheme to real life problems are presented.     

Approximate explicit receding horizon control of constrained nonlinear systems

An algorithm for the construction of an explicit piecewise linear state feedback approximation to nonlinear constrained receding horizon control is given. It allows such controllers to be implemented via an efficient binary tree search, avoiding real-time optimization. This is of significant benefit in applications that requires low real-time computational complexity or low software complexity. The method has a priori guarantee of asymptotic stability with region of attraction being a close inner approximation to the stabilizable set. This is achieved by ensuring that the approximation error does not exceed the stability margin.     

Globally optimal nonlinear model predictive control based on multi-parametric disaggregation

Nonlinear model predictive control is appropriate for controlling highly nonlinear processes, particularly when operating conditions change frequently. If the problem is nonconvex, the controller must lead the process to a global, rather than a local optimum. This work deals with computation of the control actions which lead to the global optimum via the normalized multi-parametric disaggregation technique. The continuous process model is transformed into a nonlinear programming (NLP) problem via discretization which uses an implicit integration method. The NLP problem is relaxed into a mixed integer linear programming (MILP) model. Iterations between solving MILP (lower bound) and using its solution as a starting point for a local nonlinear optimizer (which computes the upper bound) continue until the gap is closed (an l₁-norm objective function is used). Controller performance is illustrated by several examples. Relative simplicity of the algorithm makes it possible to be implemented by a wide audience.     

Nonlinear predictive control of smooth nonlinear systems based on Volterra models. Application to a pilot plant

There is a large demand to apply nonlinear algorithms to control nonlinear systems. With algorithms considering the process nonlinearities, better control performance is expected in the whole operating range than with linear control algorithms. Three predictive control algorithms based on a Volterra model are considered. The iterative predictive control algorithm to solve the complete nonlinear problem uses the non‐autoregressive Volterra model calculated from the identified autoregressive Volterra model. Two algorithms for a reduced nonlinear optimization problem are considered for the unconstrained case, where an analytic control expression can be given. The performance of the three algorithms is analyzed and compared for reference signal tracking and disturbance rejection. The algorithms are applied and compared in simulation to control a Wiener model, and are used for real‐time control of a chemical pilot plant. Copyright © 2009 John Wiley & Sons, Ltd.     

Stabilizing low complexity feedback control of constrained piecewise affine systems

Piecewise affine (PWA) systems are powerful models for describing both non-linear and hybrid systems. One of the key problems in controlling these systems is the inherent computational complexity of controller synthesis and analysis, especially if constraints on states and inputs are present. In addition, few results are available which address the issue of computing stabilizing controllers for PWA systems without placing constraints on the location of the origin.This paper first introduces a method to obtain stability guarantees for receding horizon control of discrete-time PWA systems. Based on this result, two algorithms which provide low complexity state feedback controllers are introduced. Specifically, we demonstrate how multi-parametric programming can be used to obtain minimum-time controllers, i.e., controllers which drive the state into a pre-specified target set in minimum time. In a second segment, we show how controllers of even lower complexity can be obtained by separately dealing with constraint satisfaction and stability properties. To this end, we introduce a method to compute PWA Lyapunov functions for discrete-time PWA systems via linear programming. Finally, we report results of an extensive case study which justify our claims of complexity reduction.     

Explicit/multi-parametric model predictive control (MPC) of linear discrete-time systems by dynamic and multi-parametric programming

This work presents a new algorithm for solving the explicit/multi-parametric model predictive control (or mp-MPC) problem for linear, time-invariant discrete-time systems, based on dynamic programming and multi-parametric programming techniques. The algorithm features two key steps: (i) a dynamic programming step, in which the mp-MPC problem is decomposed into a set of smaller subproblems in which only the current control, state variables, and constraints are considered, and (ii) a multi-parametric programming step, in which each subproblem is solved as a convex multi-parametric programming problem, to derive the control variables as an explicit function of the states. The key feature of the proposed method is that it overcomes potential limitations of previous methods for solving multi-parametric programming problems with dynamic programming, such as the need for global optimization for each subproblem of the dynamic programming step.     

Multi-objective nonlinear predictive control of process systems: A dual-mode tracking control approach

There typically exist different and often conflicting control objectives, e.g., reference tracking, robustness and economic performance, in many chemical processes. The current work considers the multi-objective control problems of continuous-time nonlinear systems subject to state and input constraints and multiple conflicting objectives. We propose a new multi-objective nonlinear model predictive control (NMPC) design within the dual-mode paradigm, which guarantees stability and constraint satisfaction. The notions of utopia point and compromise solution are used to reconcile the confliction of the multiple objectives. The designed controller minimizes the distance of its cost vector to a vector of independently minimized objectives, i.e., the steady-state utopia point. Recursive feasibility is established via a particular terminal region formulation while stabilizing the closed-loop system to the compromise solution via the dual-mode control principle. In order to derive the terminal region as large as possible, a terminal control law with free-parameters is constructed by using the control Lyapunov functions (CLFs) technique. Two examples of multi-objective control of a CSTR and a free-radical polymerization process are used to illustrate the effectiveness of the new multi-objective NMPC and to compare their performance.     

Nolinear model predictive control using Hammerstein models

Nonlinear models that are composed of a linear dynamic element in series with a nonlinear static element prove to be very attractive in describing the behaviour of many chemical processes. In this paper, a model predictive control scheme is proposed using the Hammerstein model structure. Two simulation examples, a pH neutralization process and a binary distillation column, are used to demonstrate the effectiveness of the method.     

基于神经网络的非线性系统多步预测控制

针对离散非线性系统,利用非线性激励函数的局部线性表示,提出一种可用于非线性过程的神经网络多步预测控制方法,并给出了控制律的收敛性分析．该方法将非线性系统处理成简单的线性和非线性两部分,对复杂的非线性多步预测方程给出了直观而有效的线性形式,并用线性预测控制方法求得控制律,避免了复杂的非线性优化求解．仿真结果表明了该算法的有效性．     

基于神经网络的非线性系统预测函数控制

针对离散非线性系统,利用神经网络非线性激励函数的局部线性表示,提出一种可用于非线性过程的神经网络预测函数控制方法并给出了控制律的收敛性分析.该方法将复杂的神经网络非线性预测方程转化成直观而有效的线性形式,同时利用线性预测函数方法求得解析的控制律,避免了复杂的非线性优化求解,仿真结果表明了算法的有效性.     

基于神经网络的预测控制算法

针对某炼油厂油品车间柴油调和过程这个多输入多输出复杂对象进行了神经网络内模控制的仿真研究,其中在线优化算法采用线性规划的方法.神经网络预测控制正是克服了传统控制思想的束缚,通过对象的输入输出特性建立对象的数学模型,而不必通过复杂的系统辨识来建立过程的模型.对仿真结果进行了比较,结果表明神经网络预测控制算法对复杂对象具有较好的控制作用.     

Variational Bayesian learning of nonlinear hidden state-space models for model predictive control

This paper studies the identification and model predictive control in nonlinear hidden state-space models. Nonlinearities are modelled with neural networks and system identification is done with variational Bayesian learning. In addition to the robustness of control, the stochastic approach allows for various control schemes, including combinations of direct and indirect controls, as well as using probabilistic inference for control. We study the noise-robustness, speed, and accuracy of three different control schemes as well as the effect of changing horizon lengths and initialisation methods using a simulated cart–pole system. The simulations indicate that the proposed method is able to find a representation of the system state that makes control easier especially under high noise.     

Distributed nonlinear model predictive control based on contraction theory

A novel distributed model predictive control algorithm for continuous‐time nonlinear systems is proposed in this paper. Contraction theory is used to estimate the prediction error in the algorithm, leading to new feasibility and stability conditions. Compared to existing analysis based on Lipschitz continuity, the proposed approach gives a distributed model predictive control algorithm under less conservative conditions, allowing stronger couplings between subsystems and a larger sampling interval when the subsystems satisfy the specified contraction conditions. A numerical example is given to illustrate the effectiveness and advantage of the proposed approach.     

Application of an explicit min-max MPC to a scaled laboratory process

Min-max model predictive control (MMMPC) requires the on-line solution of a min-max problem, which can be computationally demanding. The piecewise affine nature of MMMPC has been proved for linear systems with quadratic performance criterion. This paper shows how to move most computations off-line obtaining the explicit form of this control law by means of a heuristic algorithm. These results are illustrated with an application to a scaled laboratory process with dynamics fast enough to preclude the use of numerical solvers.     

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.     

基于遗传算法的非线性模型预测控制方法

介绍了非线性模型预调控制算法结构，提出了基于遗传算法的非线性模型预测控制方法，将遗传算法作为优化技术用于受限非线性模型预测控制器的设计。算法采用双模控制策略，将保证预测控制算法稳定性的终点等式约束转化为终点不等式约束，以利于遗传算法的实施。基于不变集理论，给出了非线性模型预测控制算法的稳定性定理。仿真结果表明了所提出控制算法的可行性和有效性。     

Spacecraft attitude control using explicit model predictive control

In this paper, an explicit model predictive controller for the attitude of a satellite is designed. Explicit solutions to constrained linear MPC problems can be computed by solving multi-parametric quadratic programs (mpQP), where the parameters are the components of the state vector. The solution to the mpQP is a piecewise affine (PWA) function, which can be evaluated at each sample to obtain the optimal control law. The on-line computation effort is restricted to a table-lookup, and the controller can be implemented on inexpensive hardware as fixed-point arithmetics can be used. This is useful for systems with limited power and CPU resources. An example of such systems is micro-satellites, which is the focus of this paper. In particular, the explicit MPC (eMPC) approach is applied to the SSETI/ESEO micro-satellite, initiated by the European Space Agency (esa). The theoretical results are supported by simulations.     

Methodology for robust multi-parametric control in linear continuous-time systems

This paper presents an extension of the recent multi-parametric (mp-)NCO-tracking methodology by Sun et al. [Comput. Chem. Eng. 92 (2016) 64–77] for the design of robust multi-parametric controllers for constrained continuous-time linear systems in the presence of uncertainty. We propose a robust-counterpart formulation and solution of multi-parametric dynamic optimization (mp-DO), whereby the constraints are backed-off based on a worst-case propagation of the uncertainty using either interval analysis or ellipsoidal calculus and an ancillary linear state feedback. We address the case of additive uncertainty, and we discuss approaches to dealing with multiplicative uncertainty that retain tractability of the mp-NCO-tracking design problem, subject to extra conservativeness. In order to assist with the implementation of these controllers, we also investigate the use of data classifiers based on deep learning for approximating the critical regions in continuous-time mp-DO problems, and subsequently searching for a critical region during on-line execution. We illustrate these developments with the case studies of a fluid catalytic cracking (FCC) unit and a chemical reactor cascade.     

Extension of efficient predictive control to the nonlinear case

The combined use of the closed‐loop paradigm, an augmented autonomous state space formulation, partial invariance, local affine difference inclusion, and polytopic invariance are deployed in this paper to propose an NMPC algorithm which, unlike earlier algorithms that have to tackle online a nonlinear non‐convex optimization problem, requires the solution of a simple QP. The proposed algorithm is shown to outperform earlier algorithms in respect of size of region of attraction and online computational load. Conversely, for comparable computational loads, the proposed algorithm outperforms earlier algorithms in terms of optimality of dynamic performance. Copyright © 2005 John Wiley & Sons, Ltd.