Model predictive control using an extended ARMarkov model

The original ARMarkov identification method explicitly determines the first μ Markov parameters from plant input–output data and approximates the slower dynamics of the process by an ARX model structure. In this paper, the method is extended to include a disturbance model and an ARIMAX structure is used to approximate the slower dynamics. This extended ARMarkov model is then used to formulate a predictive controller. As the number of Markov parameters in the model varies from one to P (prediction horizon)+1, the controller changes from generalized predictive control (GPC) to dynamic matrix control (DMC). The advantages of the proposed ARM-MPC are the consistency of the Markov parameters estimated by the ARMarkov method, independent tuning of the controller for servo and regulatory responses and the ability to combine the characteristics of GPC and DMC. The theoretical results are illustrated through simulation examples.     

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.     

Model predictive control for networked control systems

This paper investigates the problem of model predictive control for a class of networked control systems. Both sensor‐to‐controller and controller‐to‐actuator delays are considered and described by Markovian chains. The resulting closed‐loop systems are written as jump linear systems with two modes. The control scheme is characterized as a constrained delay‐dependent optimization problem of the worst‐case quadratic cost over an infinite horizon at each sampling instant. A linear matrix inequality approach for the controller synthesis is developed. It is shown that the proposed state feedback model predictive controller guarantees the stochastic stability of the closed‐loop system. Copyright © 2008 John Wiley & Sons, Ltd.     

Model predictive control of constrained LPV systems

This article considers robust model predictive control (MPC) schemes for linear parameter varying (LPV) systems in which the time-varying parameter is assumed to be measured online and exploited for feedback. A closed-loop MPC with a parameter-dependent control law is proposed first. The parameter-dependent control law reduces conservativeness of the existing results with a static control law at the cost of higher computational burden. Furthermore, an MPC scheme with prediction horizon ‘1’ is proposed to deal with the case of asymmetric constraints. Both approaches guarantee recursive feasibility and closed-loop stability if the considered optimisation problem is feasible at the initial time instant.     

Robust model predictive control of singular systems

This note is concerned with model predictive control for linear singular systems with time-varying uncertainties. A piecewise constant control sequence is calculated by minimizing the worst-case linear quadratic objective function. At each sample time, the sufficient conditions on the existence of the model predictive control are derived and expressed as linear matrix inequalities. The robust stability of the closed-loop systems is guaranteed by the proposed design method.     

Robust model predictive control of Wiener systems

Block-oriented models (BOMs) have shown to be appealing and efficient as nonlinear representations for many applications. They are at the same time valid and simple models in a more extensive region than time-invariant linear models. In this work, Wiener models are considered. They are one of the most diffused BOMs, and their structure consists in a linear dynamics in cascade with a nonlinear static block. Particularly, the problem of control of these systems in the presence of uncertainty is treated. The proposed methodology makes use of a robust identification procedure in order to obtain a robust model to represent the uncertain system. This model is then employed to design a model predictive controller. The mathematical problem involved in the controller design is formulated in the context of the existing linear matrix inequalities (LMI) theory. The main feature of this approach is that it takes advantage of the static nature of the nonlinearity, which allows to solve the control problem by focusing only in the linear dynamics. This formulation results in a simplified design procedure, because the original nonlinear model predictive control (MPC) problem turns into a linear one.     

非线性不对称系统的模型预测控制

针对基于正反方向上的两个线性模型分别设计 PID 控制器的缺陷,提出根据正反方向上的线性模型分别设计相应的状态反馈预测控制器.采用输入输出约束策略保证模型准确,并通过可行性分析确定最终的控制作用. pH 值控制的仿真实验表明,其对不对称非线性系统的控制效果明显优于传统的基于单一线性模型的预测控制及正反方向分别采用 PID 控制的控制效果.     

Model predictive control for perturbed max-plus-linear systems

Model predictive control (MPC) is a popular controller design technique in the process industry. Conventional MPC uses linear or nonlinear discrete-time models. Recently, we have extended MPC to a class of discrete event systems that can be described by a model that is “linear” in the (max,+) algebra. In our previous work, we have only considered MPC for the deterministic noise-free case without modeling errors. In this paper, we extend our previous results on MPC for max-plus-linear systems to cases with noise and/or modeling errors. We show that under quite general conditions the resulting optimization problems can be solved very efficiently.     

Stabilization of max-plus-linear systems using model predictive control: The unconstrained case

Max-plus-linear (MPL) systems are a class of event-driven nonlinear dynamic systems that can be described by models that are “linear” in the max-plus algebra. In this paper we derive a solution to a finite-horizon model predictive control (MPC) problem for MPL systems where the cost is designed to provide a trade-off between minimizing the due date error and a just-in-time production. In general, MPC can deal with complex input and states constraints. However, in this paper we assume that these are not present and it is only required that the input should be a nondecreasing sequence, i.e. we consider the “unconstrained” case. Despite the fact that the controlled system is nonlinear, by employing recent results in max-plus theory we are able to provide sufficient conditions such that the MPC controller is determined analytically and moreover the stability in terms of Lyapunov and in terms of boundedness of the closed-loop system is guaranteed a priori.     

基于Backstepping设计的不确定非线性系统的预测控制

本文的目的是针对一类带有不确定性的单输入单输出的仿射非线性系统,设计一种非线性预测控制器.用反步设计思想获得具有待定参数的控制器表达式,然后用预测控制在线优化获得控制器的参数.用这种方法设计的控制器更易使闭环系统稳定,且闭环系统具有良好的动态特性.连续发酵过程的仿真结果也验证了控制器是有效的.     

Robust model predictive control using tubes

A form of feedback model predictive control (MPC) that overcomes disadvantages of conventional MPC but which has manageable computational complexity is presented. The optimal control problem, solved on-line, yields a ‘tube’ and an associated piecewise affine control law that maintains the controlled trajectories in the tube despite uncertainty; computational complexity is linear (rather than exponential) in horizon length. Asymptotic stability of the controlled system is established.     

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.     

切换非线性系统的分布式模型预测控制

针对一类具有预先指定切换序列的切换非线性系统,研究了具有通信信道干扰和时滞测量的分布式模型预测控制问题.在每个子系统都存在镇定控制器的假设下,利用基于Lyapunov函数的模型预测控制器设计了分布式模型预测控制器,并给出了闭环切换非线性系统最终有界的充分条件.最后,通过仿真结果表明了分布式模型预测控制策略的有效性.     

Lyapunov-based model predictive control of stochastic nonlinear systems

In this work, we design a Lyapunov-based model predictive controller (LMPC) for nonlinear systems subject to stochastic uncertainty. The LMPC design provides an explicitly characterized region from where stability can be probabilistically obtained. The key idea is to use stochastic Lyapunov-based feedback controllers, with well characterized stabilization in probability, to design constraints in the LMPC that allow the inheritance of the stability properties by the LMPC. The application of the proposed LMPC method is illustrated using a nonlinear chemical process system example.     

Stabilizing decentralized model predictive control of nonlinear systems

This note presents a stabilizing decentralized model predictive control (MPC) algorithm for nonlinear discrete time systems. No information is assumed to be exchanged between local control laws. The stability proof relies on the inclusion of a contractive constraint in the formulation of the MPC problem.     

Formation control of multiple quadcopters using model predictive control

ABSTRACT

This paper presents the formation control of a fleet of three small quadcopters in a motion capture environment. The dynamic model of a single quadcopter is derived for model predictive control (MPC) and then constraints are explained and expressed in an adequate manner to be included in the cost function for the optimization problem to be solved by the C/GMRES method. Two control architectures, centralized and decentralized, were implemented in the ROS framework and tested on the CrazyFlie quadcopter. First performances are assessed for a static reference, the formation regulation problem, then for a dynamic reference, the formation tracking one. Finally, computational cost of the MPC controllers is evaluated.     

Model predictive control for linear parameter varying constrained systems using ellipsoidal set prediction

This paper proposes a new model predictive control (MPC) method for linear parameter varying systems with bounded parameter variation subject to input constraints. The method adopts closed-loop prediction and constructs ellipsoidal sets to predict the future states with reasonable computational effort. Then the information on the parameter variation rate is exploited to improve the accuracy of the prediction. Furthermore, a relaxed terminal condition, which guarantees the stability for infinite horizon, is introduced to enlarge the stabilizable region. It is shown that the feasibility of the MPC problem at the initial step ensures the stability of the closed-loop system. Finally, a simulation result illustrates the effectiveness of the proposed method.     

Model predictive control monitoring using multivariate statistics

Control loop monitoring has become an important research field over the past decade. Research has primarily targeted single-input single-output (SISO) feedback control systems with limited progress being made on the monitoring of multi-input multi-output (MIMO) control systems and large scale model predictive control (MPC) systems in particular. The size and complexity of MPC systems means that identifying and diagnosing problems with their operation can be challenging. This paper presents an MPC condition monitoring tool based on multivariate statistical process control (MSPC) techniques. The proposed tool uses intuitive charts to enable casual users of MPC technology to detect abnormal controller operation and to identify possible causes for this behaviour. Through its application to data collected from a large scale MPC system, the proposed technique is shown to be able to identify and diagnose poor control performance resulting from various issues including inappropriate interaction by process operators.     

Model predictive control using fuzzy decision functions

Fuzzy predictive control integrates conventional model predictive control with techniques from fuzzy multicriteria decision making, translating the goals and the constraints to predictive control in a transparent way. The information regarding the (fuzzy) goals and the (fuzzy) constraints of the control problem is combined by using a decision function from the theory of fuzzy sets. This paper investigates the use of fuzzy decision making (FDM) in model predictive control (MPG), and compares the results to those obtained from conventional MPG. Attention is also paid to the choice of aggregation operators for fuzzy decision making in control. Experiments on a nonminimum phase, unstable linear system, and on an air-conditioning system with nonlinear dynamics are studied. It is shown that the performance of the model predictive controller can be improved by the use of fuzzy criteria in a fuzzy decision making framework.     

约束非线性系统构造性模型预测控制

研究了连续时间约束非线性系统模型预测控制设计.利用控制Lyapunov函数离线构造单变量可调预测控制器,再根据性能指标在线优化可调参数,其中该参数近似于闭环系统的"衰减率".同时,控制Lyapunov函数保证了算法的可行性和闭环系统的稳定性.最后通过数值仿真验证了该算法的有效性.