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.     

Distributed MPC of polytopic uncertain systems: handling quantised communication and packet dropouts

In this paper, we study the distributed model predictive control (MPC) of polytopic uncertain systems with quantised communication and packet dropouts. The model of the whole plant is divided into a certain number of incomplete subsystems. Due to the nature of the distributed control structure, there is generally a lack of information about the state of the overall system. Each subsystem shares its information with neighbour subsystems via reliable connection. Distributed MPC controllers are designed for each subsystem by solving the linear matrix inequalities optimisation problem. The distributed state feedback laws are quantised and transmitted via communication network. An iterative algorithm is presented to make coordination among distributed state feedback laws. The communication is assumed to be affected by random packet dropouts in a representation of Bernoulli distributed white sequences with known conditional probabilities. A case study is carried out to demonstrate the effectiveness of the proposed distributed MPC technique.     

Deterministic finite automata representation for model predictive control of hybrid systems

As is well known, the computational complexity in the mixed integer programming (MIP) problem is one of the main issues in model predictive control (MPC) of hybrid systems such as mixed logical dynamical systems. Thus several efficient MIP solvers such as multi-parametric MIP solvers have been extensively developed to cope with this problem. On the other hand, as an alternative approach to this issue, this paper addresses how a deterministic finite automaton, which is a part of a hybrid system, should be expressed to efficiently solve the MIP problem to which the MPC problem is reduced. More specifically, a modeling method to represent a deterministic finite automaton in the form of a linear state equation with a smaller set of binary input variables and binary linear inequalities is proposed. After a motivating example is described, a derivation procedure of a linear state equation with linear inequalities representing a deterministic finite automaton is proposed as three steps; modeling via an implicit system, coordinate transformation to a linear state equation, and state feedback binarization. Various significant properties on the proposed modeling are also presented throughout the proofs on the derivation procedure.     

Contractive model predictive control for constrained nonlinearsystems

This paper addresses the development of stabilizing state and output feedback model predictive control (MPC) algorithms for constrained continuous-time nonlinear systems with discrete observations. Moreover, we propose a nonlinear observer structure for this class of systems and derive sufficient conditions under which this observer provides asymptotically convergent estimates. The MPC scheme proposed consists of a basic finite horizon nonlinear MPC technique with the introduction of an additional state constraint, which has been called a contractive constraint. The resulting MPC scheme has been denoted contractive MPC. This is a Lyapunov-based approach in which a Lyapunov function chosen a priori is decreased, not continuously, but discretely; it is allowed to increase at other times. We show in this work that the implementation of this additional constraint into the online optimization makes it possible to prove strong nominal stability properties of the closed-loop system     

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.     

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.     

Design of networked control systems with bounded arbitrary time delays

This paper is mainly concerned with the model predictive control (MPC) of networked control systems (NCSs) with uncertain time delay and data packets disorder. The network-induced time delay is described as bounded and arbitrary process. For the usual state feedback controller, by considering all the possibilities of delays, an augmented state space model of the closed-loop system, which characterizes all the delay cases, is obtained. The stability conditions are given according to the Lyapunov method based on this augmented model. The stability property is inherited in MPC which explicitly considers the physical constraints. A numerical example is given to demonstrate the effectiveness of the proposed MPC.     

Robust MPC for polytopic uncertain systems with time-varying delays

This paper addresses robust model predictive control (MPC) for time-delay systems with polytopic uncertainty. Uncertain time-varying input delay and state delays are considered, and the infinite horizon control moves are parametrised into an augmented state feedback law at each time instant. A receding horizon implementation of this state feedback law renders satisfaction of input/state constraints and closed-loop stability. For time-invariant delays and known delays, simplified results are obtained. A numerical example and a benchmark problem on continuous stirred tank reactor (CSTR) are given to illustrate the effectiveness of the proposed techniques.     

A fast ellipsoidal MPC scheme for discrete-time polytopic linear parameter varying systems

This paper proposes a fast ellipsoidal Model Predictive Control (MPC) strategy to address feedback regulation problems for constrained polytopic Linear Parameter Varying (LPV) systems subject to bounded disturbances. In order to deal with the specific non-convex structure of the state prediction tubes arising in LPV contexts, a new convexification procedure is proposed and, based on the off-line computation of a sequence of inner ellipsoidal approximations of exact one-step controllable sets, a computationally low-demanding MPC algorithm is presented. Comparisons with state-of-the-art MPC control algorithms for LPV systems are reported in a final numerical example where several methods are contrasted in terms of achievable domains of attraction, control performance, numerical burdens and memory requirements.     

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.     

A linear differential operator approach to flatness based tracking for linear and non-linear systems

This contribution presents a flatness based solution to the tracking for linear systems in differential operator representation. Since the differential operator representation is a flat system representation, tracking controllers can easily be designed using dynamic output feedback. Then, the differential operator approach for flatness based tracking of linear systems is extended to non-linear systems. The design of the resulting linear time varying dynamic output feedback controller is based on a linearization about the trajectory, which directly yields the differential operator representation. Different from the non-linear flatness based controller design the new approach uses linear methods, both in stabilizing the tracking and in computing the output feedback controller. The proposed design procedure assures exact tracking in the steady state when no disturbances are present. A simple example demonstrates the design of a dynamic output feedback controller for the tracking of a non-linear system.     

Hybrid Fuzzy Modelling for Model Predictive Control

Model predictive control (MPC) has become an important area of research and is also an approach that has been successfully used in many industrial applications. In order to implement a MPC algorithm, a model of the process we are dealing with is needed. Due to the complex hybrid and nonlinear nature of many industrial processes, obtaining a suitable model is often a difficult task. In this paper a hybrid fuzzy modelling approach with a compact formulation is introduced. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for the hybrid fuzzy modelling purposes is presented. An efficient method for identifying the hybrid fuzzy model is also proposed. A MPC algorithm suitable for systems with discrete inputs is treated. The benefits of the MPC algorithm employing the hybrid fuzzy model are verified on a batch-reactor simulation example: a comparison between the proposed modern intelligent (fuzzy) approach and a classic (linear) approach was made. It was established that the MPC algorithm employing the proposed hybrid fuzzy model clearly outperforms the approach where a hybrid linear model is used, which justifies the usability of the hybrid fuzzy model. The hybrid fuzzy formulation introduces a powerful model that can faithfully represent hybrid and nonlinear dynamics of systems met in industrial practice, therefore, this approach demonstrates a significant advantage for MPC resulting in a better control performance.     

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.     

Stabilization of linear systems over networks with bounded packet loss and its use in model predictive control

This paper considers stabilization of discrete-time linear systems, where network exists for transmitting the sensor and controller information, and arbitrary bounded packet loss occurs in the sensor–controller link and the controller–actuator link. The stabilization of this system is transformed into the robust stabilization of a set of systems. The stability result for this system is specially applied on model predictive control (MPC) that explicitly considers the satisfaction of input and state constraints. Two synthesis approaches of MPC are presented, one parameterizing the infinite horizon control moves into a single state feedback law, the other into a free control move followed by the single state feedback law. Two simulation examples are given to illustrate the effectiveness of the proposed techniques.     

Model predictive control of magnetically actuated mass spring dampers for automotive applications

Mechatronic systems such as those arising in automotive applications are characterized by significant non-linearities, tight performance specifications as well as by state and input constraints which need to be enforced during system operation. This paper takes a view that model predictive control (MPC) and hybrid models can be an attractive and systematic methodology to handle these challenging control problems, even when the underlying process is not hybrid. In addition, the piecewise affine (PWA) explicit form of MPC solutions avoids on-line optimization and can make this approach computationally viable even in situations with rather constrained computational resources. To illustrate the MPC design procedure and the underlying issues, we focus on a specific non-linear process example of a mass spring damper system actuated by an electromagnet. Such a system is one of the most common elements of mechatronic systems in automotive systems, with fuel injectors representing a concrete example. We first consider a linear MPC design for the mechanical part of the system. The approach accounts for all the constraints in the system but one, which is subsequently enforced via a state-dependent saturation element. Second, a hybrid MPC approach for the mechanical subsystem is analysed that can handle all the constraints by design and achieves better performance, at the price of a higher complexity of the controller. Finally, a hybrid MPC design that also takes into account the electrical dynamics of the system is considered.     

具有状态和控制约束的受扰离散线性切换系统的反馈控制

本文的主要贡献是针对一类具有重置函数及由外部不能控事件决定动态的离散时间线性切换系统,给出一些稳定性综合结论. 当系统受到外部有界扰动, 及状态和控制量约束时, 在输入到状态稳定性理论框架下, 研究使得系统镇定的线性状态反馈控制器设计方法. 针对这类混杂系统, 本文引入了受控D不变性的概念, 并给出检测某一混杂区域具有受控D不变性的充要条件. 进而, 提出一种能够使得受扰的线性切换系统镇定, 同时保证状态和控制量满足其约束的反馈矩阵的计算方法. 最后, 通过一个由两个子系统构成的数值例子来说明本文技术的应用性.     

Discrete-time certainty equivalence output feedback: allowing discontinuous control laws including those from model predictive control

We present certainty equivalence output feedback results for discrete-time nonlinear systems that employ possibly discontinuous control laws in the feedback loop. Coupling assumptions of nominal robustness with uniform observability or detectability assumptions, we assert nominally robust stability for output feedback closed loops. We further show that model predictive control (MPC) can be used to generate a feedback control law that is robustly globally asymptotically stabilizing when used in a certainty equivalence output feedback closed loop. Allowing for discontinuous feedback control laws is important for systems employing MPC, since the method can, and sometimes necessarily does, result in discontinuous control laws.