An off-line robust MPC algorithm for uncertain polytopic discrete-time systems using polyhedral invariant sets

In this paper, an off-line synthesis approach to robust model predictive control (MPC) using polyhedral invariant sets is presented. Most of the computational burdens are moved off-line by computing a sequence of state feedback control laws corresponding to a sequence of polyhedral invariant sets. At each sampling time, the smallest polyhedral invariant set that the currently measured state can be embedded is determined. The corresponding state feedback control law is then implemented to the process. The controller design is illustrated with two examples. Comparisons between the proposed algorithm and an ellipsoidal off-line robust MPC algorithm have been undertaken. The proposed algorithm yields a substantial expansion of the stabilizable region. Therefore, it can achieve less conservative result as compared to an ellipsoidal off-line robust MPC algorithm.     

Robust output feedback model predictive control using off-line linear matrix inequalities

A fundamental question about model predictive control (MPC) is its robustness to model uncertainty. In this paper, we present a robust constrained output feedback MPC algorithm that can stabilize plants with both polytopic uncertainty and norm-bound uncertainty. The design procedure involves off-line design of a robust constrained state feedback MPC law and a state estimator using linear matrix inequalities (LMIs). Since we employ an off-line approach for the controller design which gives a sequence of explicit control laws, we are able to analyze the robust stabilizability of the combined control laws and estimator, and by adjusting the design parameters, guarantee robust stability of the closed-loop system in the presence of constraints. The algorithm is illustrated with two examples.     

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.     

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.     

基于多面体不变集的离线鲁棒预测控制器综合

提出一种基于多面体不变集的离线鲁棒预测控制器综合算法.该算法离线确定一组反馈控制律及其对应的不变集,在线控制时根据当前状态所处的位置选择相应的控制律,不仅扩大了初始可行域,还能在一定程度上改善控制性能.仿真结果表明了采用多面体不变集的优越性.     

鲁棒模型预测控制在变风量空调系统中的应用

在变风量空调系统中二次泵压差控制可以有效地减少空调能耗,为克服二次泵模型的不确定性,提高二次泵变频调速控制的响应速度和精度,采用基于线性矩阵不等式的鲁棒预测控制策略。算法分为离线和在线两个部分,离线时首先用传统算法得出目标函数上界,以此为已知量重新优化得到一系列较大的渐近稳定的不变椭圆集。在线时,每个采样周期用三个相邻的椭圆集优化来对状态变量进行精确定位,并给出控制量。给出在线优化的理论证明。通过和传统算法的仿真比较,表明该算法的有效性。二次泵压差控制的实验表明该算法可得到较大的可行域,系统响应快,控制效果好。     

Adaptive model predictive control for a class of constrained linear systems based on the comparison model

This paper proposes an adaptive model predictive control (MPC) algorithm for a class of constrained linear systems, which estimates system parameters on-line and produces the control input satisfying input/state constraints for possible parameter estimation errors. The key idea is to combine the robust MPC method based on the comparison model with an adaptive parameter estimation method suitable for MPC. To this end, first, a new parameter update method based on the moving horizon estimation is proposed, which allows to predict an estimation error bound over the prediction horizon. Second, an adaptive MPC algorithm is developed by combining the on-line parameter estimation with an MPC method based on the comparison model, suitably modified to cope with the time-varying case. This method guarantees feasibility and stability of the closed-loop system in the presence of state/input constraints. A numerical example is given to demonstrate its effectiveness.     

Nonlinear system modeling and robust predictive control based on RBF-ARX model

An integrated modeling and robust model predictive control (MPC) approach is proposed for a class of nonlinear systems with unknown steady state. First, the nonlinear system is identified off-line by RBF-ARX model possessing linear ARX model structure and state-dependent Gaussian RBF neural network type coefficients. On the basis of the RBF-ARX model, a combination of a local linearization model and a polytopic uncertain linear parameter-varying (LPV) model are built to approximate the present and the future system's nonlinear behavior, respectively. Subsequently, based on the approximate models, a min–max robust MPC algorithm with input constraint is designed for the output-tracking control of the nonlinear system with unknown steady state. The closed-loop stability of the MPC strategy is guaranteed by the use of parameter-dependent Lyapunov function and the feasibility of the linear matrix inequalities (LMIs). Simulation study to a NO_x decomposition process illustrates the effectiveness of the modeling and robust MPC approaches proposed in this paper.     

Robust MPC for systems with output feedback and input saturation

In this work, it is proposed an MPC control algorithm with proved robust stability for systems with model uncertainty and output feedback. It is assumed that the operating strategy is such that system inputs may become saturated at transient or steady state. The developed strategy aims at the case in which the controller performs in the output-tracking scheme following an optimal set point that is provided by an upper optimization layer of the plant control structure. In this case, the optimal operating point usually lies at the boundary of the region where the input is defined. Assuming that the system remains stabilizable in the presence of input saturation, the design of the robust controller is performed off-line and an on-line implementation strategy is proposed. At each sampling step, a sub optimal control law is obtained by combining control configurations that correspond to particular subsets of available manipulated inputs. Stability of the closed-loop system is forced by considering in the off-line step of the controller design, a state contracting restriction for the closed-loop system. To produce an offset free controller and to attend the case of unknown steady state, the method is developed for a state-space model in the incremental form. The method is illustrated with simulation examples extracted from the process industry.     

Superposition in efficient robust constrained predictive control

A stabilizing control method, which does not require on-line optimizations, is developed for linear systems with polytopic model uncertainties and hard input constraints. This work is motivated by the constrained robust MPC (CRMPC) approach (IEEE Trans. Automat. Control 45 (2000a) 1765) which adopts the dual mode prediction strategy (i.e. free control moves and invariant set) and minimizes a worst case performance criterion. Based on the observation that, a feasible control sequence for a particular state can be found as a linear combination of feasible sequences for other states, we suggest a stabilizing control algorithm providing sub-optimal and feasible control sequences using pre-computed optimal sequences for some canonical states. The on-line computation of the proposed method reduces to simple matrix multiplication.     

基于终端凸集约束的新MPC 控制器

针对一类离散系统,研究了带有终端约束凸集的MPC控制问题.通过离线设计一组椭圆不变集,并将其组合成一个终端约束凸集,其中凸集参数作为在线优化变量.在线运算时,根据实际的终端状态即时地选择合适的终端不变集,从而有效地扩大了系统的可行域.分别给出了设计MPC控制器的离线和在线算法,仿真实例说明了该方法的有效性.     

基于容许集的变终端约束MPC控制

针对一类输入和状态受约束的离散线性系统,提出一种基于Ⅳ步容许集的变终端约束集模型预测控制方法.首先给出多面体不变集序列作为终端约束集的离线模型预测控制算法,扩大了终端约束集.为进一步扩大初始状态可镇定区域,引入N步容许集,设计了基于容许集的变终端约束集模型预测控制方法.该算法采用离线设计、在线优化方法,实现了系统渐近稳定,不仅降低了在线运算量,而且扩大了初始状态可镇定区域.仿真结果表明了算法的有效性.     

基于标称性能指标的离线鲁棒预测控制器综合

离线鲁棒预测控制综合算法离线确定一个控制律序列,对应一组吸引域,在线根据当前状态的位置选择相应的控制律,该类控制器在线计算量非常小,而可行性和最优性与其它综合算法相比或多或少要差一些,为此,采用标称性能指标而不是“最坏情况”性能指标来改进离线综合算法的可行性和最优性,改进的控制器保持了原有控制器的稳定性以及控制律关于系统状态的连续性.仿真结果说明了采用标称性能指标的优越性。     

基于多面体不变集的变终端约束集RMPC

针对一类状态和输入受约束的多胞不确定线性时变系统,提出了一种基于多面体不变集的变终端约束集鲁棒模型预测控制算法.首先采用基于状态反馈增益的多面体不变集计算方法,给出了一种新的控制不变集序列构造方法,然后以控制不变集序列的并集作为终端约束集,结合在线优化和增益切换,实施变终端约束集双模鲁棒预测控制.该算法不仅有效地扩大了...     

Enlarging the domain of attraction of MPC controllers

This paper presents a method for enlarging the domain of attraction of nonlinear model predictive control (MPC). The usual way of guaranteeing stability of nonlinear MPC is to add a terminal constraint and a terminal cost to the optimization problem such that the terminal region is a positively invariant set for the system and the terminal cost is an associated Lyapunov function. The domain of attraction of the controller depends on the size of the terminal region and the control horizon. By increasing the control horizon, the domain of attraction is enlarged but at the expense of a greater computational burden, while increasing the terminal region produces an enlargement without an extra cost.In this paper, the MPC formulation with terminal cost and constraint is modified, replacing the terminal constraint by a contractive terminal constraint. This constraint is given by a sequence of sets computed off-line that is based on the positively invariant set. Each set of this sequence does not need to be an invariant set and can be computed by a procedure which provides an inner approximation to the one-step set. This property allows us to use one-step approximations with a trade off between accuracy and computational burden for the computation of the sequence. This strategy guarantees closed loop-stability ensuring the enlargement of the domain of attraction and the local optimality of the controller. Moreover, this idea can be directly translated to robust MPC.     

在线优化线性反馈增益的非线性鲁棒预测控制方法

以鲁棒控制不变集作为预测控制的终端约束集,设计了一种新的鲁棒预测控制算法.将预测控制在不同采样点的待优化控制律考虑为线性反馈控制律,并通过在线优化求解线性反馈增益.从理论上证明了若采用所设计的鲁棒预测控制器,则系统是输入状态稳定的.最后通过计算机仿真验证了所提出设计方法的可行性.     

Robust omnidirectional mobile robot topological navigation system using omnidirectional vision

Robust topological navigation strategy for omnidirectional mobile robot using an omnidirectional camera is described. The navigation system is composed of on-line and off-line stages. During the off-line learning stage, the robot performs paths based on motion model about omnidirectional motion structure and records a set of ordered key images from omnidirectional camera. From this sequence a topological map is built based on the probabilistic technique and the loop closure detection algorithm, which can deal with the perceptual aliasing problem in mapping process. Each topological node provides a set of omnidirectional images characterized by geometrical affine and scale invariant keypoints combined with GPU implementation. Given a topological node as a target, the robot navigation mission is a concatenation of topological node subsets. In the on-line navigation stage, the robot hierarchical localizes itself to the most likely node through the robust probability distribution global localization algorithm, and estimates the relative robot pose in topological node with an effective solution to the classical five-point relative pose estimation algorithm. Then the robot is controlled by a vision based control law adapted to omnidirectional cameras to follow the visual path. Experiment results carried out with a real robot in an indoor environment show the performance of the proposed method.     

A tool to analyze robust stability for constrained nonlinear MPC

A sufficient condition for robust asymptotic stability of nonlinear constrained model predictive control (MPC) is derived with respect to plant/model mismatch. This work is an extension of a previous study on the unconstrained nonlinear MPC problem, and is based on nonlinear programming sensitivity concepts. It addresses the discrete time state feedback problem with all states measured. A strategy to estimate bounds on the plant/model mismatch is proposed that can be used off-line as a tool to assess the extent of model mismatch that can be tolerated to guarantee robust stability.