Robust model predictive control for continuous uncertain systems with state delay

This paper is concerned with robust model predictive control for linear continuous uncertain systems with state delay and control constraints. A piecewise constant control sequence is calculated by minimizing the upper-bound of the infinite horizon quadratic cost function. At each sampling time, the sufficient conditions for the existence of the model predictive control are derived, and expressed as a set of linear matrix inequalities. The robust stability of the closed-loop systems is guaranteed by the proposed design method. A numerical example is given to illustrate the main results.     

时延网络控制系统的模型预测控制

针对有输入约束的不确定时延网络控制系统,提出鲁棒模型预测控制方法;其中,将不确定时延建模为范数有界的输入矩阵的不确定性．给出了鲁棒性能指标的上界和系统渐近稳定的充分条件,通过在线求解LMI凸优化问题得到状态反馈控制律．仿真例子验证了该方法的有效性．     

带有状态和输入时滞的不确定广义系统的鲁棒预测控制

针对一类同时具有状态和输入时滞的不确定广义系统, 研究其鲁棒预测控制问题, 给出了鲁棒预测控制器的综合方法. 运用Lyapunov稳定性理论和线性矩阵不等式方法, 近似求解无穷时域二次性能指标优化问题, 从而得到鲁棒预测控制器存在的充分条件和显式表达式. 证明了优化问题在初始时刻的可行解, 可以保证广义闭环时滞系统是渐近稳定且正则无脉冲的. 仿真算例验证了所提出方法的有效性.     

一类具有非线性扰动的多重时滞不确定系统鲁棒预测控制

针对一类具有非线性扰动且同时存在多重状态和输入时滞的不确定系统, 提出 一种鲁棒预测控制器设计方法. 基于预测控制滚动优化原理, 运用Lyapunov稳定性 理论和线性矩阵不等式 (Linear matrix inequalities, LMIs)方法, 首先近似求解无限时域二次性能指标优化问题, 然后优化非 线性扰动项所应满足的最大上界, 定量地研究鲁棒预测控制在范数有界意义下的扰动抑制 问题, 并给出了鲁棒预测控制器存在的充分条件. 最后通过仿真验证了所提方法的有效性.     

Tube‐based robust nonlinear model predictive control

This paper extends tube‐based model predictive control of linear systems to achieve robust control of nonlinear systems subject to additive disturbances. A central or reference trajectory is determined by solving a nominal optimal control problem. The local linear controller, employed in tube‐based robust control of linear systems, is replaced by an ancillary model predictive controller that forces the trajectories of the disturbed system to lie in a tube whose center is the reference trajectory thereby enabling robust control of uncertain nonlinear systems to be achieved. Copyright © 2011 John Wiley & Sons, Ltd.     

An improved robust model predictive control approach to systems with linear fractional transformation perturbations

In this paper, a robust model predictive control approach is proposed for a class of uncertain systems with time-varying, linear fractional transformation perturbations. By adopting a sequence of feedback control laws instead of a single one, the control performance can be improved and the region of attraction can be enlarged compared with the existing model predictive control (MPC) approaches. Moreover, a synthesis approach of MPC is developed to achieve high performance with lower on-line computational burden. The effectiveness of the proposed approach is verified by simulation examples.     

基于输出反馈的不确定连续系统的鲁棒预测控制

运用线性矩阵不等式方法,研究一类基于输出反馈的线性连续时间范数有界参数不确定系统的鲁棒预测控制问题．基于变量变换的思想,将无限时域“最小—最大”优化问题转化为线性规划问题,得出分段连续的输出反馈控制律,并给出了控制律存在的充分条件,证明了优化问题在初始时刻的可行解保证闭环系统渐近稳定．仿真实例验证了此方法的有效性．     

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.     

基于多面体描述系统的鲁棒非线性预测控制

针对一类具有持续有界扰动的离散时间非线性系统, 提出一种基于多面体描述系统的鲁棒非线性模型预测控制策略. 首先利用泰勒级数构造多面体描述系统包裹原系统. 其次, 对该多面体描述系统构造鲁棒终端不变集和仿射输入型预测控制律. 进一步, 利用离散系统的输入状态实际稳定性(Input-to-state practical stability, ISpS)概念证明了闭环系统的鲁棒稳定性. 最后, 通过仿真验证了本结果的有效性.     

一类离散不确定系统的Tube不变集离线鲁棒模型预测控制

针对一类输入和状态受限的离散线性不确定系统,提出了一种基于Tube不变集的离线鲁棒模型预测控制方法.首先针对输入和状态约束线性时不变标准系统,设计了改进的基于多面体不变集的离线模型预测控制算法,并证明了稳定性.其次对于存在未知有界干扰的实际不确定系统,引入了Tube不变集策略,通过设计对应标准模型的最优控制序列和状态轨迹,给出了实际不确定系统的离线Tube不变集控制策略,保证系统状态鲁棒渐近稳定,并收敛于终端干扰不变集.仿真结果验证了该控制方法的有效性.     

ROBUST MODEL PREDICTIVE CONTROL FOR INPUT SATURATED AND SOFTENED STATE CONSTRAINTS

This paper starts with a brief review of robust model predictive control (RMPC) algorithsms for uncertain systems using linear matrix inequalities (LMIs) subject to input and/or output saturated constraints. However when RMPC has both input and state constraints, a difficulty will arise due to the inability of the optimizer to satisfy the state constraints due to the constraints on inputs. Therefore, a novel RMPC scheme is presented that softens the state constraints as penalty terms are added to its objective function. These terms maintain state violation at low values until a constrained solution is returned. The state violation can be regulated by changing the value of the weighting factor. A novel robust predictive controller for input saturated and softened state constraints for linear time varying (LTV) systems with polytopic model uncertainties is presented.     

Output feedback model predictive control for LPV systems based on quasi-min–max algorithm

This paper proposes a robust output feedback model predictive control (MPC) scheme for linear parameter varying (LPV) systems based on a quasi-min–max algorithm. This approach involves an off-line design of a robust state observer for LPV systems using linear matrix inequality (LMI) and an on-line robust output feedback MPC algorithm using the estimated state. The proposed MPC method for LPV systems is applicable for a variety of systems with constraints and guarantees the robust stability of the output feedback systems. A numerical example for an LPV system subject to input constraints is given to demonstrate its effectiveness.     

Design of an RMPC with a time‐varying terminal constraint set for tracking problem

This paper presents a robust model predictive control algorithm with a time‐varying terminal constraint set for systems with model uncertainty and input constraints. In this algorithm, the nonlinear system is approximated by a linear model where the approximation error is considered as an unstructured uncertainty that can be represented by a Lipschitz nonlinear function. A continuum of terminal constraint sets is constructed off‐line, and robust stability is achieved on‐line by using a variable control horizon. This approach significantly reduces the computational complexity. The proposed robust model predictive controller with a terminal constraint set is used in tracking set‐points for nonlinear systems. The effectiveness of the proposed method is illustrated with a numerical example. Copyright © 2015 John Wiley & Sons, Ltd.     

Synthesizing scheduled robust model predictive control with target tracking

Systems with large operating regions and non-zero state target tracking have limited the industrial application of robust model predictive control (RMPC) with synthetic action. To overcome the problem, this paper presents a novel formulation of synthesizing scheduled RMPC for linear time varying (LTV) systems. Off-line, we compute the matrix that transforms target output into steady state first. Then a set of stabilizing state feedback laws which are corresponding to a set of estimated regions of stability covering the desired operating region are provided. On-line, these control laws are implemented as a single scheduled state feedback model predictive control (MPC) which switches between the set of local controllers and achieve the desired target at last. Finally, the algorithm is illustrated with an example.     

Multi-step Predictive Control of a PDF-shaping Problem

A predictive control strategy is proposed for the shaping of the output probability density function (PDF) of linear stochastic systems. The B-spline neural network is used to set up the output PDF model and therefore converts the PDF-shaping into the control of B-spline weights vector. The Diophantine equation is then introduced to formulate the predictive PDF model, based on which a moving-horizon control algorithm is developed so as to realize the predictive PDF tracking performance.     

一类不确定模糊模型的输出反馈鲁棒预测控制

针对一类满足扇形界条件的不确定模糊模型描述的非线性系统,提出一种输出反馈鲁棒预测控制方法．该方法将鲁棒预测控制的Min-Max优化问题转化为具有LMI约束的线性目标最小化问题,并且不需系统状态完全可测,仅仅利用系统测量输出和不可测状态的界限值来确定保证闭环系统鲁棒稳定的输出反馈控制器．仿真实验证明了该方法的有效性．     

输出概率密度函数形状的多步预测控制

A predictive control strategy is proposed for the shaping of the output probability density function (PDF) of linear stochastic systems. The B-spline neural network is used to set up the output PDF model and therefore converts the PDF-shaping into the control of B-spline weights vector. The Diophantine equation is then introduced to formulate the predictive PDF model, based on which a moving-horizon control algorithm is developed so as to realize the predictive PDF tracking performance.     

Designing of non-fragile robust model predictive control for constrained uncertain systems and its application in process control

A non-fragile robust model predictive control (RMPC) is designed in the uncertain systems under bounded control signals. To this aim, a class of the nonlinear systems with additive uncertainty is considered in its general form. The RMPC synthesis could lead to the proper selection of the controller’s gains. Thus, the non-fragile RMPC design is translated into a minimization problem subjected to some constraints in terms of linear matrix inequality (LMI). Hence, the controller’s gains are computed by solving such a minimization problem. In some numerical examples, the suggested non-fragile RMPC is compared with the other methods. The simulation results demonstrate the effectiveness of the proposed RMPC in comparison with similar techniques.     

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.     

Efficient algorithms for online tracking of set points in robust model predictive control

This paper presents some computationally efficient algorithms for online tracking of set points in robust model predictive control context subject to state and input constraints. The nonlinear systems are represented by a linear model along with an additive nonlinear term which is locally Lipschitz. As an unstructured uncertainty, this term is replaced in the robust stability constraint by its Lipschitz coefficient. A scheduled control technique is employed to transfer the system to desired set points, given online, by designing local robust model predictive controllers. This scheme includes estimating the regions of feasibility and stability of the related equilibriums and online switching among the local controllers. The proposed optimisation problems for calculating the regions of feasibility and stability are defined as linear matrix inequalities that can be solved in polynomial time. The effectiveness of the proposed algorithms is illustrated by an example.