Robust model predictive control for constrained continuous-time nonlinear systems

In this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.     

Robust distributed model predictive control of linear systems with structured time-varying uncertainties

In this work, synthesis of robust distributed model predictive control (MPC) is presented for a class of linear systems subject to structured time-varying uncertainties. By decomposing a global system into smaller dimensional subsystems, a set of distributed MPC controllers, instead of a centralised controller, are designed. To ensure the robust stability of the closed-loop system with respect to model uncertainties, distributed state feedback laws are obtained by solving a min–max optimisation problem. The design of robust distributed MPC is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints. An iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance. The simulation results show the effectiveness of the proposed robust distributed MPC algorithm.     

Model predictive control of distributed networked control systems with quantization and switching topology

This work is concerned with the robust model predictive control (MPC) for a class of distributed networked control systems (NCSs), in which the input quantization and switching topology are both considered. By utilizing the sector bound approach, the NCSs with quantization are converted into the linear systems with sector bound uncertainties. The topology switching is governed by a switching signal and the dynamic behavior is modeled as a switched control system. A new robust MPC design technique is derived to minimize the upper bound of a weighted quadratic performance index. Moreover, the conditions of both the recursive feasibility of the MPC design and the stability of the resulting closed‐loop system are developed. Finally, simulation results are presented to verify the effectiveness of the proposed MPC design.     

Periodic event‐triggered control for distributed networked multiagents with asynchronous communication: A predictive control approach

This paper investigates the periodic event‐triggered control problem for distributed networked multiagent systems with interconnected nonlinear dynamics subject to asynchronous communication. A method of state trajectory estimation for the interconnected neighboring agents over each prediction horizon with guaranteed error bounds is addressed to handle the asynchronous communication. Based on it, a distributed robust model predictive control (MPC) is proposed with a distributed periodic event‐triggered scheme for each agent. According to this algorithm, each subsystem generates presumed state trajectories for all its upstream neighbors and computes its own control locally. By checking the designed triggering condition periodically, the optimization problem of MPC will be implemented and solved when the local error of the subsystem exceeds a specified threshold. Then, the optimized control input will be determined and applied until the next time instant when the triggering condition is invoked. Moreover, sufficient condition for ensuring feasibility of the designed algorithm is conducted, along with the analysis of asymptotic stabilization of the closed‐loop system. The illustrative example for a set of coupled Van der Pol oscillators is reported to verify the effectiveness of the proposed approach.     

Energy-aware robust model predictive control based on noisy wireless sensors

Wireless sensor networks (WSNs) are becoming fundamental components of modern control systems due to their flexibility, ease of deployment and low cost. However, the energy-constrained nature of WSNs poses new issues in control design; in particular the discharge of batteries of sensor nodes, which is mainly due to radio communications, must be taken into account. In this paper we present a novel transmission strategy for communication between controller and sensors which is intended to minimize the data exchange over the wireless channel. Moreover, we propose an energy-aware control technique for constrained linear systems based on explicit model predictive control (MPC), providing closed-loop stability in the presence of disturbances. The presented control schemes are compared to traditional MPC techniques. The results show the effectiveness of the proposed energy-aware approach, which achieves a profitable trade-off between energy savings and closed-loop performance.     

提高分布式多预测控制器协调及稳定性的鲁棒区域控制

大型复杂化工程过程控制中,常规的集中式控制方式不利于实时性、灵活性和容错控制。而采用多预测控制器协调的分布式控制是解决这一问题的有效方法:。针对子系统间的动态耦合行为严重影响多预测控制器协调以及稳定性的问题,提出一种鲁棒区域控制策略。即在每个子系统的目标函数中加入松弛因子增加控制器间协调时的余量来达到分布式预测控制的稳定性。通过以反应器-存储器分馏器组成的过程为事例,仿真结果:表明该方法:的可行性和有效性。     

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.     

Networked model predictive control based on neighbourhood optimization for serially connected large-scale processes

In this paper, two novel networked model predictive control schemes based on neighbourhood optimization are presented for on-line optimization and control of a class of serially connected processes (known as the cascade processes in some references), in which the on-line optimization of the whole system is decomposed into that of several small-scale subsystems in distributed structures. Under network environment, the connectivity of the communication network is assumed to be sufficient for each subsystem to exchange information with its neighbour subsystems. An iterative algorithm for networked MPC and a networked MPC algorithm with one-step delay communication are developed according to different network capacities. The optimality of the iteration based networked MPC algorithm is analyzed and the nominal stability is derived for unconstrained distributed control systems. The nominal stability with one-step delay communication is employed for distributed control systems without the inequality constraints. Finally, an illustrative example and the simulation study of the fuel feed flow control for the walking beam reheating furnace are provided to test the effectiveness and practicality of the proposed networked MPC algorithms.     

Handling uncertainty in economic nonlinear model predictive control: A comparative case study

In the last years, the use of an economic cost function for model predictive control (MPC) has been widely discussed in the literature. The main motivation for this choice is that often the real goal of control is to maximize the profit or the efficiency of a certain system, rather than tracking a predefined set-point as done in the typical MPC approaches, which can be even counter-productive. Since the economic optimal operation of a system resulting from the application of an economic model predictive control approach drives the system to the constraints, the explicit consideration of the uncertainties becomes crucial in order to avoid constraint violations. Although robust MPC has been studied during the past years, little attention has yet been devoted to this topic in the context of economic nonlinear model predictive control, especially when analyzing the performance of the different MPC approaches. In this work, we present the use of multi-stage scenario-based nonlinear model predictive control as a promising strategy to deal with uncertainties in the context of economic NMPC. We make a comparison based on simulations of the advantages of the proposed approach with an open-loop NMPC controller in which no feedback is introduced in the prediction and with an NMPC controller which optimizes over affine control policies. The approach is efficiently implemented using CasADi, which makes it possible to achieve real-time computations for an industrial batch polymerization reactor model provided by BASF SE. Finally, a novel algorithm inspired by tube-based MPC is proposed in order to achieve a trade-off between the variability of the controlled system and the economic performance under uncertainty. Simulations results show that a closed-loop approach for robust NMPC increases the performance and that enforcing low variability under uncertainty of the controlled system might result in a big performance loss.     

Robust adaptive tracking control of distributed delay systems with actuator and communication failures

This paper is concerned with the robust adaptive fault‐tolerant tracking control problem for a class of distributed delay systems against faulted and perturbed actuators and communications. As all the faults on actuators and communications, network delays in control and communication channels, and perturbations in communications and exogenous disturbances are unknown, some adaptation schemes are developed to adjust controller parameters in real‐time for constructing a class of distributed compensation controllers based on the delayed signals. Then, according to the information from the adaptive mechanism, the effect of each actuator and communication fault, network delay, channel perturbation and exogenous disturbance can be eliminated completely by using the proposed distributed adaptive‐state feedback controllers. Furthermore, asymptotic tracking results of the distributed closed‐loop systems can be achieved based on Lyapunov stability theory. An example is provided to further illustrate the effectiveness of the proposed direct adaptive design technique. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

基于多步控制集的鲁棒预测控制器设计

针对有约束多胞不确定系统, 本文提出多步控制集的概念, 并将其作为终端集进而设计鲁棒预测控制器. 由于设计了一系列可变的反馈律, 鲁棒预测控制器可以得到更好的控制性能和更大的初始可行域. 另外, 利用多步控制集的特性, 本文提出了一种将预测控制器的在线计算量转移到离线完成的算法. 通过该算法, 可以有效地平衡鲁棒预测控制器的控制性能、在线计算量和初始可行域. 仿真算例验证了这些算法的有效性.     

Handling communication disruptions in distributed model predictive control

In this work, we study distributed model predictive control (DMPC) of nonlinear systems subject to communication disruptions - communication channel noise and data losses - between distributed controllers. Specifically, we focus on a DMPC architecture in which one of the distributed controllers is responsible for ensuring closed-loop stability while the rest of the distributed controllers communicate and cooperate with the stabilizing controller to further improve the closed-loop performance. To handle communication disruptions, feasibility problems are incorporated in the DMPC architecture to determine if the data transmitted through the communication channel is reliable or not. Based on the results of the feasibility problems, the transmitted information is accepted or rejected by the stabilizing MPC. In order to ensure the stability of the closed-loop system under communication disruptions, each model predictive controller utilizes a stability constraint which is based on a suitable Lyapunov-based controller. The theoretical results are demonstrated through a nonlinear chemical process example.     

Nash-based robust distributed model predictive control for large-scale systems

In this paper, a new robust distributed model predictive control (RDMPC) is proposed for large-scale systems with polytopic uncertainties. The time-varying system is first decomposed into several interconnected subsystems. Interactions between subsystems are obtained by a distributed Kalman filter, in which unknown parameters of the system are estimated using local measurements and measurements of neighboring subsystems that are available via a network. Quadratic boundedness is used to guarantee the stability of the closed-loop system. In the MPC algorithm, an output feedback-interaction feedforward control input is computed by an LMI-based optimization problem that minimizes an upper bound on the worst case value of an infinite-horizon objective function. Then, an iterative Nash-based algorithm is presented to achieve the overall optimal solution of the whole system in partially distributed fashion. Finally, the proposed distributed MPC approach is applied to a load frequency control (LFC) problem of a multi-area power network to study the efficiency and applicability of the algorithm in comparison with the centralized, distributed and decentralized MPC schemes.     

Robust hybrid predictive control of nonlinear systems

In this work, we consider nonlinear systems with input constraints and uncertain variables, and develop a robust hybrid predictive control structure that provides a safety net for the implementation of any model predictive control (MPC) formulation, designed with or without taking uncertainty into account. The key idea is to use a Lyapunov-based bounded robust controller, for which an explicit characterization of the region of robust closed-loop stability can be obtained, to provide a stability region within which any available MPC formulation can be implemented. This is achieved by devising a set of switching laws that orchestrate switching between MPC and the bounded robust controller in a way that exploits the performance of MPC whenever possible, while using the bounded controller as a fall-back controller that can be switched in at any time to maintain robust closed-loop stability in the event that the predictive controller fails to yield a control move (due, e.g., to computational difficulties in the optimization or infeasibility) or leads to instability (due, e.g., to inappropriate penalties and/or horizon length in the objective function). The implementation and efficacy of the robust hybrid predictive control structure are demonstrated through simulations using a chemical process example.     

Distributed model predictive control of constrained weakly coupled nonlinear systems

This paper proposes a distributed model predictive control (MPC) strategy for a large-scale system that consists of several dynamically coupled nonlinear systems with decoupled control constraints and disturbances. In the proposed strategy, all subsystems compute their control signals by solving local optimizations constrained by their nominal decoupled dynamics. The dynamic couplings and the disturbances are accommodated through new robustness constraints in the local optimizations. The paper derives relationships among, and designs procedures for, the parameters involved in the proposed distributed MPC strategy based on the analysis of the recursive feasibility and the robust stability of the overall system. The paper shows that, for a given bound on the disturbances, the recursive feasibility is guaranteed if the sampling interval is properly chosen. Moreover, it establishes sufficient conditions for the overall system state to converge to a robust positively invariant set. The paper illustrates the effectiveness of the proposed distributed MPC strategy by applying it to three coupled cart-(nonlinear) spring–damper subsystems.     

A framework for multiple robust explicit MPC controllers for linear systems

This article presents a multi-mode explicit controller for constrained linear systems with bounded disturbances using a switching strategy based on Model Predictive Control (MPC). In the proposed approach, the system switches among several MPC controllers having different performance levels. The switching is done so as to achieve increasing levels of performance as time evolves, reaching the desired controller in finite time steps. The conditions needed for switching and robust convergence of the multi-mode MPC controllers are provided. Compared with standard robust explicit MPC implementations, the proposed approach has the flexibility of having a large domain of attraction, a good asymptotic behaviour and a small number of partitions.     

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.     

Aperiodic event-triggered robust model predictive control for linear parameter-varying system with round-robin protocol

This article investigates the robust model predictive control (MPC) problem for networked control systems represented by the linear parameter-varying model, in which an event-triggered strategy and the round-robin (RR) protocol scheduling locate at the sensor-to-controller and controller-to-actuator channels, respectively. By considering the problems of system state immeasurable and communication burden in engineering application, an output feedback controller that combines the aperiodic event-triggered strategy is applied, where the triggering condition is designed in a time-varying fashion. In addition, in order to avoid unexpected data collisions, the RR protocol is utilized to schedule a shared network and guarantee the efficiency of the control system. The controller parameters are obtained by solving an online convex robust MPC optimization problem, and the feasibility of the optimization problem and closed-loop stability are also addressed. The effectiveness of the proposed theoretical results is illustrated by a numerical simulation example.