Robust MPC for Linear Systems with Structured Time‐Varying Uncertainties and Saturating Actuator

In this paper, a synthesis of model predictive control (MPC) algorithm is presented for uncertain systems subject to structured time‐varying uncertainties and actuator saturation. The system matrices are not exactly known, but are affine functions of a time varying parameter vector. To deal with the nonlinear actuator saturation, a saturated linear feedback control law is expressed into a convex hull of a group of auxiliary linear feedback laws. At each time instant, a state feedback law is designed to ensure the robust stability of the closed‐loop system. The robust MPC controller design problem is formulated into solving a minimization problem of a worst‐case performance index with respect to model uncertainties. The design of controller is then cast into solving a feasibility of linear matrix inequality (LMI) optimization problem. Then, the result is further extended to saturation dependent robust MPC approach by introducing additional variables. A saturation dependent quadratic function is used to reduce the conservatism of controller design. To show the effectiveness, the proposed robust MPC algorithms are applied to a continuous‐time stirred tank reactor (CSTR) process.     

Stochastic model predictive control for probabilistically constrained Markovian jump linear systems with additive disturbance

Model predictive control (MPC) for Markovian jump linear systems with probabilistic constraints has received much attention in recent years. However, in existing results, the disturbance is usually assumed with infinite support, which is not considered reasonable in real applications. Thus, by considering random additive disturbance with finite support, this paper is devoted to a systematic approach to stochastic MPC for Markovian jump linear systems with probabilistic constraints. The adopted MPC law is parameterized by a mode‐dependent feedback control law superimposed with a perturbation generated by a dynamic controller. Probabilistic constraints can be guaranteed by confining the augmented system state to a maximal admissible set. Then, the MPC algorithm is given in the form of linearly constrained quadratic programming problems by optimizing the infinite sum of derivation of the stage cost from its steady‐state value. The proposed algorithm is proved to be recursively feasible and to guarantee constraints satisfaction, and the closed‐loop long‐run average cost is not more than that of the unconstrained closed‐loop system with static feedback. Finally, when adopting the optimal feedback gains in the predictive control law, the resulting MPC algorithm has been proved to converge in the mean square sense to the optimal control. A numerical example is given to verify the efficiency of the proposed results.     

Model predictive control design for polytopic uncertain systems by synthesising multi-step prediction scenarios

A common objective of model predictive control (MPC) design is the large initial feasible region, low online computational burden as well as satisfactory control performance of the resulting algorithm. It is well known that interpolation-based MPC can achieve a favourable trade-off among these different aspects. However, the existing results are usually based on fixed prediction scenarios, which inevitably limits the performance of the obtained algorithms. So by replacing the fixed prediction scenarios with the time-varying multi-step prediction scenarios, this paper provides a new insight into improvement of the existing MPC designs. The adopted control law is a combination of predetermined multi-step feedback control laws, based on which two MPC algorithms with guaranteed recursive feasibility and asymptotic stability are presented. The efficacy of the proposed algorithms is illustrated by a numerical example.     

Robust model predictive control under redundant channel transmission with applications in networked DC motor systems

In networked systems, intermittent failures in data transmission are usually inevitable due to the limited bandwidth of the communication channel, and an effective countermeasure is to add redundance so as to improve the reliability of the communication service. This paper is concerned with the model predictive control (MPC) problem by using static output feedback for a class of polytopic uncertain systems with redundant channels under both input and output constraints. By utilizing the min–max control approach combined with stochastic analysis, sufficient conditions are established to guarantee the feasibility of the designed MPC scheme that ensures the robust stability of the closed‐loop system. In terms of the solution to an auxiliary optimization problem, an easy‐to‐implement MPC algorithm is proposed to obtain the desired sub‐optimal control sequence as well as the upper bound of the quadratic cost function. Finally, to illustrate its effectiveness, the proposed design method is applied to control a networked direct current motor system. Copyright © 2016 John Wiley & Sons, Ltd.     

Fault detection model‐based controller for process systems

This paper develops a model‐based control system for fault detection and controller reconfiguration using stochastic model predictive control (MPC). The system can determine online the optimal control actions, detect faults quickly, and reconfigure the controller accordingly. Such a system can perform its function correctly in the presence of internal faults. A fault detection model based (FDMB) controller consists of two main parts: the first is fault detection and diagnosis (FDD) and the second is controller reconfiguration (CR). Systems subject to such abrupt failures are modeled as stochastic hybrid systems with variable‐structure. This paper deals with three challenging issues: design of the fault‐model set; estimation of hybrid multiple models; and stochastic MPC of hybrid multiple models. For the first issue, we propose a simple scheme for designing a fault model set based on random variables. For the second issue, we consider and select a fast and reliable FDD system applied to the above model set. Finally, we develop a stochastic MPC scheme for multiple model CR with soft switching signals based on the weighted probabilities of the outputs of different models. Simulations for the proposed FDMB controller are illustrated and analyzed. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Feedback min–max model predictive control using robust one-step sets

A solution to the infinite-horizon min–max model predictive control (MPC) problem of constrained polytopic systems has recently been defined in terms of a sequence of free control moves over a fixed horizon and a state feedback law in the terminal region using a time-varying terminal cost. The advantage of this formulation is the enlargement of the admissible set of initial states without sacrificing local optimality, but this comes at the expense of higher computational complexity. This article, by means of a counterexample, shows that the robust feasibility and stability properties of such algorithms are not, in general, guaranteed when more than one control move is adopted. For this reason, this work presents a novel formulation of min–max MPC based on the concept of within-horizon feedback and robust contractive set theory that ensures robust stability for any choice of the control horizon. A parameter-dependent feedback extension is also proposed and analysed. The effectiveness of the algorithms is demonstrated with two numerical examples.     

Stochastic model predictive control with active uncertainty learning: A Survey on dual control

This paper provides a review of model predictive control (MPC) methods with active uncertainty learning. System uncertainty poses a key theoretical and practical challenge in MPC, which can be aggravated when system uncertainty increases due to the time-varying nature of system dynamics. For uncertain systems with stochastic uncertainty, this paper presents the stochastic MPC (SMPC) problem in the dual control paradigm, where the control inputs to an uncertain system have a probing effect for active uncertainty learning and a directing effect for controlling the system dynamics. The complexity of the SMPC problem with dual control effect is described in connection to stochastic dynamic programming as well as Bayesian estimation for its output feedback implementation. Further, implicit and explicit dual control methods for approximating the receding-horizon control problem with dual control effect are surveyed and analyzed with the intent to discuss the key challenges and opportunities in SMPC with dual control effect.     

Dynamic Output Feedback Robust MPC With one Free Control Move for LPV Model With Bounded Disturbance

For a linear parameter‐varying (LPV) model which is a convex combination of several linear time invariant sub‐models, this paper considers the case when the combining coefficients are unknown (except being nonnegative and their sum being one). For this model with norm‐bounded unknown disturbance, an output feedback robust model predictive control (MPC) is proposed by parameterizing the infinite horizon control moves and estimated states into one free control move, one free estimated state (i.e., one control move and one estimated state as degrees of freedom for optimization) and a dynamic output feedback law. This is the first endeavour to apply the free control move and free estimated state in the output feedback MPC for this model. The algorithm is shown to be recursively feasible and the system state is guaranteed to converge to the neighborhood of the equilibrium point. A numerical example verifies the effectiveness of the proposed algorithm.     

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.     

Computation delay compensation for real time implementation of robust model predictive control

The implementation of model predictive control (MPC) requires to solve an optimization problem online. The computation time, often not negligible especially for nonlinear MPC (NMPC), introduces a delay in the feedback loop. Moreover, it impedes fast sampling rate setting for the controller to react to uncertainties quickly. In this paper, a dual time scale control scheme is proposed for linear/nonlinear systems with external disturbances. A pre-compensator works at fast sampling rate to suppress uncertainty, while the outer MPC controller updates the open loop input sequence at a slower rate. The computation delay is explicitly considered and compensated in the MPC design. Four robust MPC algorithms for linear/nonlinear systems in the literature are adopted and tailored for the proposed control scheme. The recursive feasibility and stability are rigorously analysed. Three simulation examples are provided to validate the proposed approaches.     

基于反馈线性化的永磁同步电机模型预测控制

提出一种基于反馈线性化和模型预测控制(MPC)策略的永磁同步电机(PMSM)控制方案.运用微分几何理论讨论了非线性PMSM模型可进行反馈线性化的充分必要条件,并将其转换为新坐标空间中的线性模型;分析了MPC原理和对系统约束条件的处理方法.针对获得的PMSM线性模型,分别采用MPC和状态反馈极点配置方法设计了控制器.在有...     

Output feedback model predictive control of uncertain norm‐bounded linear systems

A constrained output feedback model predictive control (MPC) scheme for uncertain Norm‐Bounded discrete‐time linear systems is presented. This scheme extends recent results achieved by the authors under full‐state availability to the more interesting case of incomplete and noisy state information. The design procedure consists of an off‐line step where a state feedback and an asymptotic observer (dynamic primal controller) are designed via bilinear matrix inequalities and used to robustly stabilize a suitably augmented state plant. The on‐line moving horizon procedure adds N free control moves to the action of the primal controller which are computed by solving a linear matrix inequality optimization problem whose numerical complexity grows up only linearly with the control horizon N. The effectiveness of the proposed MPC strategy is illustrated by a numerical example. Copyright © 2010 John Wiley & Sons, Ltd.     

Stochastic model predictive control with joint chance constraints

ABSTRACT

This article investigates model predictive control (MPC) of linear systems subject to arbitrary (possibly unbounded) stochastic disturbances. An MPC approach is presented to account for hard input constraints and joint state chance constraints in the presence of unbounded additive disturbances. The Cantelli–Chebyshev inequality is used in combination with risk allocation to obtain computationally tractable but accurate surrogates for the joint state chance constraints when only the mean and variance of the arbitrary disturbance distributions are known. An algorithm is presented for determining the optimal feedback gain and optimal risk allocation by iteratively solving a series of convex programs. The proposed stochastic MPC approach is demonstrated on a continuous acetone–butanol–ethanol fermentation process, which is used in the production of biofuels.     

Tube-based robust sampled-data MPC for linear continuous-time systems

This note extends to the continuous-time case the “tube-based” approach for the design of discrete-time robust model predictive control (MPC) algorithms developed in Mayne, Seron, and Rakovi? (2005). This extension is of interest in view of the simplicity and popularity of the method as well as of the industrial relevance of continuous-time implementations of MPC. The proposed robust control law is composed of two terms: (1) a sampled-data MPC control law and (2) a continuous-time state feedback term.     

Multi‐primary‐color LCD: Its characteristics and extended applications

Abstract— The development of multi‐primary‐color (MPC) display systems is one of the big paradigm shifts in recent display technologies and induces new potentials of display devices. The development of MPC display systems for different goals is briefly reviewed. Especially, by employing MPC systems, it is possible to reproduce the real material colors faithfully and efficiently. For signal processing, MPC systems have a big advantage in the so‐called color‐reproduction redundancy. A number of applications can be derived from this characteristic, such as improving the viewing‐angle dependency issue and power savings. On the other hand, MPC systems have a typical trade‐off versus RGB‐standardized input signals, especially for reproducing bright green. New algorithms to moderate this trade‐off on MPC systems by employing color‐reproduction redundancy are proposed. The goal of our algorithms is to maintain the compatibility with RGB‐based input signals though the initial display design so that the characteristics of MPC systems are not changed or lost. These algorithms indicate that MPC display systems are applicable not only for a specifically limited objective but also for other applications, e.g., TV broadcasting.     

A general dissipativity constraint for feedback system design,with emphasis on MPC

A “general dissipativity constraint” (GDC) is introduced to facilitate the design of stable feedback systems. A primary application is to MPC controllers when it is preferred to avoid the use of “stabilising ingredients” such as terminal constraint sets or long prediction horizons. Some very general convergence results are proved under mild conditions. The use of quadratic functions, replacing GDC by “quadratic dissipativity constraint” (QDC), is introduced to allow implementation using linear matrix inequalities. The use of QDC is illustrated for several scenarios: state feedback for a linear time‐invariant system, MPC of a linear system, MPC of an input‐affine system, and MPC with persistent disturbances. The stability that is guaranteed by GDC is weaker than Lyapunov stability, being “Lagrange stability plus convergence.” Input‐to‐state stability is obtained if the control law is continuous in the state. An example involving an open‐loop unstable helicopter illustrates the efficacy of the approach in practice.     

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.     

不确定系统的鲁棒与随机模型预测控制算法比较研究

近几十年来,不确定系统模型预测控制的理论和应用得到了飞速发展.本文简要地回顾了不确定系统中鲁棒模型预测控制和随机模型预测控制的发展历史,总结了它们的相关应用,并较为细致地分析了线性不确定系统模型预测控制的各种主要算法.通过总结各种算法的通用模型、运作方式、问题规模,以及它们保证递归可行性、稳定性的方法,分析了部分算法可行域间的关系,揭示了各种算法的主要特点、适用场合和未来可发展方向,并通过仿真实例直观地分析了各种算法的性能和可靠性.     

Global Output‐Feedback Stabilization for Stochastic Nonlinear Systems with Function Control Coefficients

This paper investigates the global output‐feedback stabilization for a class of stochastic nonlinear systems with function control coefficients. Notably, the systems in question possess control coefficients that are functions of output, rather than constants; hence, they are different from the existing literature on stochastic stabilization. To solve the control problem, an appropriate reduced‐order observer is introduced to reconstruct the unmeasured system states before a smooth output‐feedback controller is designed using the backstepping method, which guarantees that the closed‐loop system is globally asymptotically stable in probability. This paper combines the related results in the deterministic and stochastic setting and gives the first treatment on the global output‐feedback stabilization for the stochastic nonlinear systems with function control coefficients. A simulation example is given also to illustrate the effectiveness of the proposed approach.