A COMPARATIVE STUDY ON COMPUTATIONAL SCHEMES FOR NONLINEAR MODEL PREDICTIVE CONTROL

This paper briefly reviews development of nonlinear model predictive control (NMPC) schemes for finite horizon prediction and basic computational algorithms that can solve the stable real‐time implementation of NMPC in space state form with state and input constraints. In order to ensure stability within a finite prediction horizon, most NMPC schemes use a terminal region constraint at the end of the prediction horizon — a particular NMPC scheme using a terminal region constraint, namely quasi‐infinite horizon, that guarantees asymptotic closed‐loop stability with input constraints is presented. However, when nonlinear processes have both input and state constraints, difficulty arises from failure to satisfy the state constraints due to constraints on input. Therefore, a new NMPC scheme without a terminal region constraint is developed using soften state constraints. A brief comparative simulation study of two NMPC schemes: quasi‐infinite horizon and soften state constraints is done via simple nonlinear examples to demonstrate the ability of the soften state constraints scheme. Finally, some features of future research from this study are discussed.     

Dual closed‐loop tracking control for wheeled mobile robots via active disturbance rejection control and model predictive control

A dual closed‐loop tracking control is proposed for a wheeled mobile robot based on active disturbance rejection control (ADRC) and model predictive control (MPC). In the inner loop system, the ADRC scheme with an extended state observer (ESO) is proposed to estimate and compensate external disturbances. In the outer loop system, the MPC strategy is developed to generate a desired velocity for the inner loop dynamic system subject to a diamond‐shaped input constraint. Both effectiveness and stability analysis are given for the ESO and the dual closed‐loop system, respectively. Simulation results demonstrate the performances of the proposed control scheme.     

液压釜温度自适应预测控制

详细介绍了液压釜温度系统自适应控制方案、误差分析及实际应用调试情况.应用 全系数自适应控制理论及模型预测控制原理设计了一种新的自适应预测控制方案,并给出了 控制算法的稳定性证明及闭环系统稳态误差和动态特性分析.实际应用表明,该方法对建模 误差、系统延时及测量噪声具有较好的鲁棒性.     

液压釜温度自适应预测控制

详细介绍了液压釜温度系统自适应控制方案、误差分析及实际应用调试情况．应用全系数自适应控制理论及模型预测控制原理设计了一种新的自适应预测控制方案,并给出了控制算法的稳定性证明及闭环系统稳态误差和动态特性分析．实际应用表明,该方法对建模误差、系统延时及测量噪声具有较好的鲁棒性．     

Synthesis of Mixed Objective Output Feedback Robust Model Predictive Control

Aiming at the constrained polytopic uncertain system with energy‐bounded disturbance and unmeasurable states, a novel synthesis scheme to design the output feedback robust model predictive control(MPC)is put forward by using mixed H₂/H_∞ design approach. The proposed scheme involves an offline design of a robust state observer using linear matrix inequalities(LMIs)and an online output feedback robust MPC algorithm using the estimated states in which the desired mixed objective robust output feedback controllers are cast into efficiently tractable LMI‐based convex optimization problems. In addition, the closed‐loop stability and the recursive feasibility of the proposed robust MPC are guaranteed through an appropriate reformulation of the estimation error bound (EEB). A numerical example subject to input constraints illustrates the effectiveness of the proposed controller.     

Nussbaum‐type function–based attitude control of spacecraft with actuator saturation

This paper investigates the attitude stabilization problem of spacecraft subject to external disturbances and actuator saturation. A novel attitude control scheme is technically proposed by incorporating the Nussbaum gain technique into backstepping design. The key idea behind this is to introduce a special Nussbaum‐type function in order to compensate for the time‐varying nonlinear terms arising from input saturation. By exploiting the dynamic surface control technique, the problem of “explosion of terms” inherent in traditional backstepping designs is effectively eliminated and the computational burden is significantly reduced. Additionally, based on the selected Nussbaum‐type function, a constructive analysis methodology is presented, which plays an important role in analyzing the stability properties of the closed‐loop system. It is then proved that the proposed control scheme can guarantee the boundedness of all closed‐loop signals. Furthermore, the unwinding phenomenon is given a simple and effective remedy by resorting to suitable choices of the attitude error variable and the virtual control law. Finally, simulation experiments are carried out to assess the effectiveness and demonstrate the advantages of the proposed control scheme.     

Input‐to‐state stability of min‐max MPC scheme for nonlinear time‐varying delay systems

This paper studies the robustness problem of the min–max model predictive control (MPC) scheme for constrained nonlinear time‐varying delay systems subject to bounded disturbances. The notion of the input‐to‐state stability (ISS) of nonlinear time‐delay systems is introduced. Then by using the Lyapunov–Krasovskii method, a delay‐dependent sufficient condition is derived to guarantee input‐to‐state practical stability (ISpS) of the closed‐loop system by way of nonlinear matrix inequalities (NLMI). In order to lessen the online computational demand, the non‐convex min‐max optimization problem is then converted to a minimization problem with linear matrix inequality (LMI) constraints and a suboptimal MPC algorithm is provided. Finally, an example of a truck‐trailer is used to illustrate the effectiveness of the proposed results. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

基于2维性能参考模型的2维模型预测迭代学习控制策略

将迭代学习控制(Iterative learning control, ILC)系统看作一类具有2维动态特性的控制系统,根据模型预测控制(Model predictive control, MPC)和性能参考模型控制思想, 提出了一种基于2维性能参考模型的2维模型预测迭代学习控制系统设计方案.在该控制系统设计方案中,可以通过选择适当的2 维性能参考模型来构造2 维动态变化的设定值信号和预测控制信号,从而引导迭代学习控制系统收敛到合理的控制性能,并有效避 免系统性能收敛过程中控制输入可能发生的剧烈波动.通过对控制系统的结构分析可知,所得的迭代学习控制器本质上是由沿时 间指标的参考模型预测控制器和沿周期指标的迭代学习控制器组成,闭环系统的收敛性等价于一个2维滤波系统的稳定性.数值仿 真结果证明了该设计方案的有效性和鲁棒性.     

A stable block model predictive control with variable implementation horizon

In this paper, we present a stable model predictive control method for discrete-time nonlinear systems. The standard MPC scheme is modified to incorporate (1) a block implementation scheme where a sub-string of the optimized input sequence is applied instead of a single value; (2) an additional constraint which guarantees that a Lyapunov function will decrease over time; (3) a variable implementation window that facilitates the stability constraint enforcement. Stability of the closed-loop system with the proposed algorithm is established. Examples are given to illustrate the effectiveness of the control scheme. The impacts of several key design parameters on the overall performance are also analyzed and discussed.     

Examples when nonlinear model predictive control is nonrobust

We consider nominal robustness of model predictive control for discrete-time nonlinear systems. We show, by examples, that when the optimization problem involves state constraints, or terminal constraints coupled with short optimization horizons, the asymptotic stability of the closed loop may have absolutely no robustness. That is to say, it is possible for arbitrarily small disturbances to keep the closed loop strictly inside the interior of the feasibility region of the optimization problem and, at the same time, far from the desired set point. This phenomenon does not occur when using model predictive control for linear systems with convex constraint sets. We emphasize that a necessary condition for the absence of nominal robustness in nonlinear model predictive control is that the value function and feedback law are discontinuous at some point(s) in the interior of the feasibility region.     

液压釜温度自适应预测控制1)

This paper introduces the details of the adaptive control scheme,error analysis and field adjustment of a hydraulic cauldron control system.A kind of new adaptive predictive control scheme is designed based on the all-coefficient adaptive control theory and model predictive control theory.The stability of this control algorithm is proved,and the analysis of error in stable stage and analysis of dynamic performance in the closed loop system are given.The actual application shows that the method proposed in this paper has good robustness to model error,system delay and measure noise.     

An improved robust model predictive control for linear parameter‐varying input‐output models

This paper describes a new robust model predictive control (MPC) scheme to control the discrete‐time linear parameter‐varying input‐output models subject to input and output constraints. Closed‐loop asymptotic stability is guaranteed by including a quadratic terminal cost and an ellipsoidal terminal set, which are solved offline, for the underlying online MPC optimization problem. The main attractive feature of the proposed scheme in comparison with previously published results is that all offline computations are now based on the convex optimization problem, which significantly reduces conservatism and computational complexity. Moreover, the proposed scheme can handle a wider class of linear parameter‐varying input‐output models than those considered by previous schemes without increasing the complexity. For an illustration, the predictive control of a continuously stirred tank reactor is provided with the proposed method.     

Robust event‐triggered model predictive control for cyber‐physical systems under denial‐of‐service attacks

This paper investigates the resilient control problem for constrained continuous‐time cyber‐physical systems subject to bounded disturbances and denial‐of‐service (DoS) attacks. A sampled‐data robust model predictive control law with a packet‐based transmission scheduling is taken advantage to compensate for the loss of the control data during the intermittent DoS intervals, and an event‐triggered control strategy is designed to save communication and computation resources. The robust constraint satisfaction and the stability of the closed‐loop system under DoS attacks are proved. In contrast to the existing studies that guarantee the system under DoS attacks is input‐to‐state stable, the predicted input error caused by the system constraints can be dealt with by the input‐to‐state practical stability framework. Finally, a simulation example is performed to verify the feasibility and efficiency of the proposed strategy.     

Control design of timed continuous Petri nets via model predictive constant control

This paper addresses the problem of control design for timed continuous Petri net (TCPN) systems. The problem is studied using model predictive control that determines the control vector, under some constraints, to drive a TCPN from an initial marking to a steady state by minimising certain cost functions. In order to reduce the computational complexity, a new cost function is first proposed and additional constrains that enforce constant control sequences are considered. An adaptive prediction horizon is also proposed. Then, the main contribution is to reduce the actuator solicitation by combining a new weighted term, which takes into account the flow variations, and an online adaptation of the weighting factor with a terminal constraint that ensures the asymptotic stability of the closed-loop system.     

Robust stability of nonlinear model predictive control with extended Kalman filter and target setting

This work deals with the closed‐loop robust stability of nonlinear model predictive control (NMPC) coupled with an extended Kalman filter (EKF). First, we point out the gaps between the practical formulations and theoretical research. Then, we show that the estimation error dynamics of an EKF are input‐to‐state stable (ISS) in the presence of nonvanishing perturbations. Moreover, a target setting optimization problem is proposed to solve the target state corresponding to the desired set points, which are used in the objective function in NMPC formulation. Thus, the objective function is a Lyapunov function candidate, and the input‐to‐state practical stability (ISpS) of the closed‐loop system can be established. Moreover, we see that the stability property deteriorates because of the estimation error. Simulation results of the proposed scheme are presented.Copyright © 2012 John Wiley & Sons, Ltd.     

Feedback Stabilization of Singularly Perturbed Systems Under Information Constraints

The quantized feedback control for a class of singularly perturbed systems is addressed, in which the controlled system and the controller are connected via a limited capacity communication channel. First, a proper coder–decoder pair is presented such that the transmission error decays to zero exponentially under information constraints. Then, a control law in terms of linear matrix inequalities is constructed to render the resulting closed‐loop system input‐to‐state stable with regard to the transmission error. Thus the asymptotic stability of the closed‐loop system is guaranteed. It is shown that the proposed method is simple and easy to operate. Moreover, an upper bound of the small perturbation parameter for the stability of systems can be explicitly estimated with a workable computational way. Finally, two examples are presented to show the effectiveness of the proposed method.     

无人直升机的姿态增强学习控制设计与验证

针对小型无人直升机的姿态控制问题,考虑到现有基于模型的控制方法对直升机动力学模型的先验信息依赖较大,以及未建模动态系统的影响等问题,设计了一种基于增强学习(RL)的飞行控制算法.仅利用直升机的在线飞行数据,补偿了未建模不确定性的影响.同时为了抑制外界扰动,提高系统的鲁棒性,设计了一种基于误差符号函数积分的鲁棒(RISE)控制算法.将两种算法结合,并利用基于Lyapunov分析的方法,证明了无人机姿态控制误差的半全局渐近收敛.最后在无人直升机飞行控制实验平台上,进行了姿态控制的实时实验验证.实验结果表明,本文提出的控制方法具有良好的控制效果,对系统不确定性和外界风扰具有良好鲁棒性.     

A closed‐loop nonlinear control and sliding mode estimation strategy for fluid flow regulation

Novel sliding mode observer (SMO) and robust nonlinear control methods are presented, which are shown to achieve finite‐time state estimation and asymptotic regulation of a fluid flow system. To facilitate the design and analysis of the closed‐loop active flow control (AFC) system, proper orthogonal decomposition–based model order reduction is utilized to express the Navier‐Stokes partial differential equations as a set of nonlinear ordinary differential equations. The resulting reduced‐order model contains a measurement equation that is in a nonstandard mathematical form. This challenge is mitigated through the detailed design and analysis of an SMO. The observer is shown to achieve finite‐time estimation of the unmeasurable states of the reduced‐order model using direct sensor measurements of the flow field velocity. The estimated states are utilized as feedback measurements in a closed‐loop AFC system. To address the practical challenge of actuator bandwidth limitations, the control law is designed to be continuous. A rigorous Lyapunov‐based stability analysis is presented to prove that the closed‐loop flow estimation and control method achieves asymptotic regulation of a fluid flow field to a prescribed state. Numerical simulation results are also provided to demonstrate the performance of the proposed closed‐loop AFC system, comparing 2 different designs for the SMO.     

Robust nonlinear MPC without terminal constraint for tracking changing setpoints in the presence of non-additive unknown disturbance

This paper develops a novel robust tracking model predictive control (MPC) without terminal constraint for discrete-time nonlinear systems capable to deal with changing setpoints and unknown non-additive bounded disturbances. The MPC scheme without terminal constraint avoids difficult computations for the terminal region and is thus simpler to design and implement. However, the existence of disturbances and/or sudden changes in a setpoint may lead to feasibility and stability issues in this method. In contrast to previous works that considered changing setpoints and/or additive slowly varying disturbance, the proposed method is able to deal with changing setpoints and non-additive non-slowly varying disturbance. The key idea is the addition of tightened input and state (tracking error) constraints as new constraints to the tracking MPC scheme without terminal constraints based on artificial references. In the proposed method, the optimal tracking error converges asymptotically to the invariant set for tracking, and the perturbed system tracking error remains in a variable size tube around the optimal tracking error. Closed-loop input-to-state stability and recursive feasibility of the optimization problem for any piece-wise constant setpoint and non-additive disturbance are guaranteed by tightening input and state constraints as well as weighting the terminal cost function by an appropriate stabilizing weighting factor. The simulation results of the satellite attitude control system are provided to demonstrate the efficiency of the proposed predictive controller.