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.     

Constrained output feedback model predictive control for nonlinear systems

A constrained output feedback model predictive control approach for nonlinear systems is presented in this paper. The state variables are observed using an unscented Kalman filter, which offers some advantages over an extended Kalman filter. A nonlinear dynamic model of the system, considered in this investigation, is developed considering all possible effective elements. The model is then adaptively linearized along the prediction horizon using a state-dependent state space representation. In order to improve the performance of the control system as many linearized models as the number of prediction horizons are obtained at each sample time. The optimum results of the previous sample time are utilized for linearization at the current sample time. Subsequently, a linear quadratic objective function with constraints is formulated using the developed governing equations of the plant. The performance and effectiveness of the proposed control approach is validated both in simulation and through real-time experimentation using a constrained highly nonlinear aerodynamic test rig, a twin rotor MIMO system (TRMS).     

六自由度机械臂约束预测控制系统的设计

本文提出了一种基于约束预测控制的机械臂实时运动控制方法.该控制方法分为两层,分别设计了约束预测控制器和跟踪控制器.其中,约束预测控制器在考虑系统物理约束的条件下,在线为跟踪控制器生成参考轨迹;跟踪控制器采用最优反馈控制律,使机械臂沿参考轨迹运动.为了简化控制器的设计和在线求解,本文采用输入输出线性化的方式简化机械臂动力学模型.同时,为了克服扰动,在约束预测控制器中引入前馈策略,提出了带前馈一反馈控制结构的预测控制设计.因此,本文设计的控制器可以使机械臂在满足物理约束的条件下快速稳定地跟踪到目标位置.通过在PUMA560机理模型上进行仿真实验,验证了预测控制算法的可行性和有效性.     

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.     

An improved structure for model predictive control using non-minimal state space realisation

This paper describes a new method for the design of model predictive control (MPC) using non-minimal state space models, in which the state variables are chosen as the set of measured input and output variables and their past values. It shows that the proposed design approach avoids the use of an observer to access the state information and, as a result, the disturbance rejection, particularly the system input disturbance rejection, is significantly improved when constraints become activated. In addition, when there is no model/plant mismatch, the paper shows that the system output constraints can be realised in the proposed approach. Furthermore, closed-form transfer function representation of the model predictive control system enables the application of frequency response analysis tools to the nominal performance of the system.     

Economic MPC of nonlinear systems with nonmonotonic Lyapunov functions and its application to HVAC control

This paper proposes a Lyapunov‐based economic model predictive control (MPC) scheme for nonlinear systems with nonmonotonic Lyapunov functions. Relaxed Lyapunov‐based constraints are used in the MPC formulation to improve the economic performance. These constraints will enforce a Lyapunov decrease after every few steps. Recursive feasibility and asymptotical convergence to the steady state can be achieved using Lyapunov‐like stability analysis. The proposed economic MPC can be applied to minimize energy consumption in heating ventilation and air conditioning control of commercial buildings. The Lyapunov‐based constraints in the online MPC problem enable the tracking of the desired set‐point temperature. The performance is demonstrated by a virtual building composed of 2 adjacent zones.     

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.     

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.     

Model predictive control using reduced order models: Guaranteed stability for constrained linear systems

The problem of controlling a high-dimensional linear system subject to hard input and state constraints using model predictive control is considered. Applying model predictive control to high-dimensional systems typically leads to a prohibitive computational complexity. Therefore, reduced order models are employed in many applications. This introduces an approximation error which may deteriorate the closed loop behavior and may even lead to instability. We propose a novel model predictive control scheme using a reduced order model for prediction in combination with an error bounding system. We employ the explicit time and input dependent bound on the model order reduction error to achieve design conditions for constraint fulfillment, recursive feasibility and asymptotic stability for the closed loop of the model predictive controller when applied to the high-dimensional system. Moreover, for a special choice of design parameters, we establish local optimality of the proposed model predictive control scheme. The proposed MPC approach is assessed via examples demonstrating that a good trade-off between computational efficiency and conservatism can be achieved while guaranteeing constraint satisfaction and asymptotic stability.     

约束非线性系统理想点多目标安全预测控制

考虑具有状态和控制约束的仿射非线性系统多目标安全控制问题,本文提出一种保证安全和稳定的多目标安全模型预测控制(MOSMPC)策略.首先通过理想点逼近方法解决多个控制目标的冲突问题.其次,利用控制李雅普诺夫障碍函数(CLBF)参数化局部控制律,并确定系统不安全域.在此基础上,构造非线性系统的参数化双模控制器,减少在线求解模型预测控制(MPC)优化问题的计算量.进一步,应用双模控制原理和CLBF约束,建立MOSMPC策略的递推可行性和闭环系统的渐近稳定性,并保证闭环系统状态避开不安全域.最后,以加热系统的多目标控制为例,验证了本文策略的有效性.     

Predictive metamorphic control

In spite of its easy implementation, ability to handle constraints and nonlinearities, etc., model predictive control (MPC) does have drawbacks including tuning difficulties. In this paper, we propose a refinement to the basic MPC strategy by incorporating a tuning parameter such that one can move smoothly from an existing controller to a new MPC strategy. Each change of this tuning parameter leads to a new stabilising control law, therefore, allowing one to gradually move from an existing control law to a new and better one. For the infinite horizon case without constraints and for the general case with state and input constraints, stability results are established. We also examine the practical applicability of the proposed approach by employing it in the nominal prediction model of the tube-based output feedback robust MPC method. The merits of the proposed method are illustrated by examples.     

Robust constrained predictive control using comparison model

This paper proposes a quadratic programming (QP) approach to robust model predictive control (MPC) for constrained linear systems having both model uncertainties and bounded disturbances. To this end, we construct an additional comparison model for worst-case analysis based on a robust control Lyapunov function (RCLF) for the unconstrained system (not necessarily an RCLF in the presence of constraints). This comparison model enables us to transform the given robust MPC problem into a nominal one without uncertain terms. Based on a terminal constraint obtained from the comparison model, we derive a condition for initial states under which the ultimate boundedness of the closed loop is guaranteed without violating state and control constraints. Since this terminal condition is described by linear constraints, the control optimization can be reduced to a QP problem.     

A control matching model predictive control approach to string stable vehicle platooning

A predictive control strategy for vehicle platoons is presented in this paper, accommodating both string stability and constraints (e.g., physical and safety) satisfaction. In the proposed design procedure, the two objectives are achieved by matching a model predictive controller (MPC), enforcing constraints satisfaction, with a linear controller designed to guarantee string stability. The proposed approach neatly combines the straightforward design of a string stable controller in the frequency domain, where a considerable number of approaches have been proposed in literature, with the capability of an MPC-based controller enforcing state and input constraints.A controller obtained with the proposed design procedure is validated both in simulations and in the field test, showing how string stability and constraints satisfaction can be simultaneously achieved with a single controller. The operating region that the MPC controller is string stable is characterized by the interior of feasible set of the MPC controller.     

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.     

一种基于H∞理论的鲁棒预测控制方法

融合H∞控制的鲁棒概念和预测控制的滚动优化原理,提出了一种全新的约束动态对 策预测控制方法.对有状态和控制约束的不确定线性系统,证明了闭环系统的鲁棒稳定性并给 出了鲁棒性条件.该方法同时具有H∞控制和预测控制的优点:鲁棒性和显式处理约束的能力.     

Output-feedback predictive control of constrained linear systems via set-membership state estimation

This paper combines model predictive control (MPC) and set-membership (SM) state estimation techniques for controlling systems subject to hard input and state constraints. Linear systems with unknown but bounded disturbances and partial state information are considered. The adopted approach guarantees that the constraints are satisfied for all the states which are compatible with the available information and for all the disturbances within given bounds. Properties of the proposed MPC-SM algorithm and simulation studies are reported.     

On the finite time performance of model predictive control

This paper addresses the finite time performance of model predictive control (MPC) for linear-time-invariant (LTI) systems without constraints. The performance of MPC is compared with that of finite horizon optimal control to find out how well model predictive control can perform relative to the optimal performance with the same or different horizons. By exploring the properties of the Riccati difference equation (RDE), an upper and a lower bound of the ratio between the finite time performance of MPC and finite horizon optimal cost are obtained. It is possible to extend the obtained results to more complicated systems such as nonlinear dynamic systems with constraints with appropriate generalizations. Simulation example supports our results.     

Design of explicit model predictive control for constrained linear systems with disturbances

On-line model predictive control approaches require the online solution of an optimization problem. In contrast, the explicit model predictive control moves major part of computation offline. Therefore, eMPC enables one to implement a MPC in real time for wide range of fast systems. The eMPC approach requires the exact system model and results a piecewise affine control law defined on a polyhedral partition in the state space. As an important limitation, disturbances may reduce performance of the explicit model predictive control. This paper presents efficient approach for handling the problem of using eMPC for constrained systems with disturbances. It proposes an approach to improve performance of the closed loop system by designing a suitable state and disturbance estimator. Conditions for observability of the disturbances are considered and it is depicted that applying the disturbance’s estimation leads to rejection of the response error. It is also shown that the proposed approach prevents the reduction of feasible space. Simulation results illustrate the advantages of this approach.     

Economic Lyapunov-based model predictive control with event-triggered parametric identification

This article focuses on the design of model predictive control (MPC) for nonlinear systems with slow time-dynamic change. To avoid frequent updates of the predictive model and guarantee the state always stays inside of a given feasible region, an event-triggered parametric estimation mechanism is designed. Firstly, a trigger condition is designed to judge if parameters of the predictive model are out of date and differ a lot from their current true values so that there is no feasible solution to regulate the state within the given bound without predictive model parameter update. This condition also depends on the current state and is deduced from a designed Lyapunov constraint, inputs constraints, and the mismatched predictive model. Then the EMPC is designed based on this condition. If the trigger condition is met, the MPC recursively updates the parameters and imposes the Lyapunov constraint. The Lyapunov constraint is based on the mismatched model and the real state does not need to be convergence. Else, the MPC only optimizes the cost function to derive a good profit. We proved that the proposed EMPC promises that the closed-loop system state is maintained within a predefined stable region when the model mismatch bound can be estimated accurately. A simulation of a chemical process demonstrates the effectiveness of the proposed method.     

A multivariate statistical controller for on-line quality improvement

Producing good quality products is an important process control objective. However, achieving this objective can be very difficult in a continuous process, especially when quality measurements are not available on-line or they have long time delays. In this paper, a control approach using multivariate statistical models is presented to achieve this objective. The goal of the control approach is to decrease variations in product quality without real time quality measurements. A PCA model which incorporates time lagged variables is used, and the control objective is expressed in the score space of this PCA model. A controller is designed in the model predictive control (MPC) framework, and it is used to control the equivalent score space representation of the process. The score predictive model for the MPC algorithm is built using partial least squares (PLS). The proposed controller can be developed from and implemented on top of existing PID control systems, and it is demonstrated in two case studies, which involve a binary distillation column and the Tennessee Eastman process.