一类输入受限不确定时滞系统的准Min-Max模型预测控制

针对一类输入受限离散不确定时滞系统,提出一种基于准Ｍｉｎ-Ｍａｘ的模型预测控制器设计方法．定义了时滞系统的鲁棒性能指标,给出了系统稳定的充分条件,通过求解ＬＭＩ凸优化获得控制器．准Ｍｉｎ-Ｍａｘ预测控制将当前控制量作为独立优化变量,与其他作为反馈控制的时域控制序列分开处理,有效地降低了算法的保守性,提高了可行性．仿真算例验证了所提出控制方法的有效性．     

An improved approach for constrained robust model predictive control

In this paper, we present a new technique to address constrained robust model predictive control. The main advantage of this new approach with respect to other well-known techniques is the reduced conservativeness. Specifically, the technique described in this paper can be applied to polytopic uncertain systems and is based on the use of several Lyapunov functions each one corresponding to a different vertex of the uncertainty's polytope.     

Stability analysis of a multi-model predictive control algorithm with application to control of chemical reactors

We study a stabilizing multi-model predictive control strategy for controlling nonlinear process at different operating conditions. The control algorithm is a receding horizon scheme with a quasi-infinite horizon objective function that has finite and infinite horizon cost components. The finite horizon cost consists of free input variables that direct the system towards a terminal region which contains the desired operating point. The infinite horizon cost has an upper bound and steers the system to the desired operating point. The system is represented by a sequence of piecewise linear models. Based on the condition of the system states, the sequence of piecewise linear models is updated and the controller’s objective function switches form quasi-infinite to infinite horizon objective function. This results in a hybrid control structure. A recent approach in the analysis of hybrid systems that uses multiple Lyapunov functions is employed in the stability analysis of the closed-loop system. The stabilizing hybrid control strategy is illustrated on two examples and their closed-loop stability properties are studied.     

A framework for design of scheduled output feedback model predictive control

We present a stabilizing scheduled output feedback Model Predictive Control (MPC) algorithm for constrained nonlinear systems with large operating regions. We design a set of local output feedback predictive controllers with their estimated regions of stability covering the desired operating region, and implement them as a single scheduled output feedback MPC which on-line switches between the set of local controllers and achieves nonlinear transitions with guaranteed stability. This algorithm provides a general framework for scheduled output feedback MPC design.     

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.     

A new approach to control design with overlapping information structure constraints

In this paper, a new strategy is proposed for decentralized state feedback design with overlapping information structure constraints. The method combines linear matrix inequalities and the inclusion principle in a way that eliminates controllability problems that are inherent to standard decentralized control design in the expanded space. This approach can be extended to include an important class of uncertain nonlinearities, and its validity is demonstrated through applications to strings of moving vehicles.     

Estimating the region of attraction for large-scale systems with uncertainties

In this paper, a new approach is proposed for estimating regions of attraction for large-scale dynamic systems. In designing control laws for such systems, it is essential to incorporate the underlying information structure constraints while keeping the number of optimization variables at a minimum. The proposed method successfully accomplishes both of these objectives. It is computationally efficient, and can produce decentralized control laws without imposing structural constraints on the Lyapunov function (a feature that can considerably improve the quality of the estimate). The design algorithm is based on linear matrix inequalities and can easily accommodate various types of uncertainties in the system model. An example with 300 states is provided to demonstrate the suitability of this approach for large, sparse systems.     

Improved robust model predictive control with structured uncertainty

In this paper, a dilation of the LMI characterization is presented to address constrained robust model predictive control (MPC) for a class of uncertain linear systems with structured time-varying uncertainties. The uncertainty is described in linear fractional transformation (LFT) form. By introducing slack variables and using parameter dependent Lyapunov functions, the design conservativeness is reduced compared with other existing MPC approaches. The proposed approach is applied to an industrial CSTR benchmark system to demonstrate the merits of our proposed solution.     

A robust distributed model predictive control algorithm

Although distributed model predictive control (DMPC) has received significant attention in the literature, the robustness of DMPC with respect to model errors has not been explicitly addressed. In this paper, a novel online algorithm that deals explicitly with model errors for DMPC is proposed. The algorithm requires decomposing the entire system into N subsystems and solving N convex optimization problems to minimize an upper bound on a robust performance objective by using a time-varying state-feedback controller for each subsystem. Simulations examples were considered to illustrate the application of the proposed method.     

具有执行器饱和特性的不确定系统预测控制器设计

针对具有执行器饱和特征的不确定系统,提出了一种带有状态观测器的新型预测控制器设计方法.该方法在滚动优化的每一步,采用带有饱和特性的反馈控制结构得到一个最优控制律.使无穷时域性能指标最小.考虑在状态不完全已知的情况下,设计了带有状态观测器的预测控制器,并通过观测器参数调整使闭环系统渐近稳定.通过仿真实验验证了所设计控制器的有效性.     

A scheduling quasi–min-max model predictive control algorithm for nonlinear systems

In this paper, a model predictive control algorithm is designed for nonlinear systems. Combination of a linear model with a linear parameter varying model approximates the nonlinear behavior. The linear model is used to express the current nonlinear dynamics, and the linear parameter varying model is used to cover the future nonlinear behavior. In the algorithm, a “quasi-worst-case” value of an infinite horizon objective function is minimized. Closed-loop stability is guaranteed when the algorithm is implemented in a receding horizon fashion by including a Lyapunov constraint in the formulation. The proposed approach is applied to control a jacketed styrene polymerization reactor.     

一类不确定非线性时变时滞系统的鲁棒H∞ 滤波器设计

研究一类不确定非线性时变时滞系统的鲁棒H∞滤波问题,其中假定非线性项满足全局Lipschitz条件,利用S-procedure方法处理非线性项.避免了在Lyapunov-Krasovskii泛函导数中对非线性项和其他交叉项的界定.所提出方法具有更低的保守性,仿真实例证明了该方法的有效性.     

-like control for nonlinear stochastic systems

In this paper we develop a H_∞-type theory, from the dissipation point of view, for a large class of time-continuous stochastic nonlinear systems. In particular, we introduce the notion of stochastic dissipative systems analogously to the familiar notion of dissipation associated with deterministic systems and utilize it as a basis for the development of our theory. Having discussed certain properties of stochastic dissipative systems, we consider time-varying nonlinear systems for which we establish a connection between what is called the L₂-gain property and the solution to a certain Hamilton–Jacobi inequality (HJI), that may be viewed as a bounded real lemma for stochastic nonlinear systems. The time-invariant case with infinite horizon is also considered, where for this case we synthesize a worst case-based stabilizing controller. Stability in this case is taken to be in the mean-square sense. In the stationary case, the problem of robust state feedback control is considered in the case of norm-bounded uncertainties. A solution is then derived in terms of linear matrix inequalities.     

一类非线性时滞互联系统模糊分散输出反馈控制

对于一类状态不可测非线性互联时滞系统,给出一种基于观测器的模糊分散输出反馈控制方法.首先采用模糊T-S模型对非线性互联时滞系统进行模糊建模,在此基础上给出了模糊分散观测器和基于观测器的模糊分散输出控制器的设计.应用李亚普诺夫函数法和线性矩阵不等式方法给出了模糊分散控制系统稳定的充分条件.仿真结果进一步验证了所提出的模糊分散控制方法的有效性.     

Adaptive output control of uncertain nonlinear systems with non-symmetric dead-zone input

This paper deals with the adaptive output feedback control problem of a class of uncertain nonlinear systems with an unknown non-symmetric dead-zone nonlinearity. The nonlinear system considered here is dominated by a triangular system without zero dynamics satisfying polynomial growth in the unmeasurable states. An adaptive control scheme is developed without constructing the dead-zone inverse. The proposed adaptive control scheme requires only the information of bounds of the slopes and the breakpoint of dead-zone nonlinearity. The novelty of this paper is that a universal-type adaptive output feedback controller is numerically constructed by using a sum of squares (SOS) optimization algorithm, which ensures the boundedness of all the signals in the adaptive closed-loop without knowing the growth rate of the uncertainties. An example is presented to show the effectiveness of the proposed approach.     

不确定广义系统的输出反馈鲁棒预测控制

针对一类具有范数有界不确定性的广义系统,当系统状态不可测时,提出了一种基于输出反馈的鲁棒预测控制器综合算法．采用ＬＭＩ方法以及变量变换思想,将无限时域“最小最大”优化问题转化为线性规划问题．确定出一组分段连续的输出反馈控制序列,给出了输出反馈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可以保证广义闭环系统是渐近稳定且正则无脉冲的．仿真实例验证了所提出方法的有效性．