Quasi-min-max output-feedback model predictive control for LPV systems with input saturation

In the research field of model predictive control (MPC), an output-feedback-type MPC method is consistently required for controlling a wide range of constrained systems. In this paper, we propose a two-stage control strategy for polytopic linear parameter varying (LPV) systems subject to input constraints. This strategy consists of a modified quasi-min-max output-feedback MPC method and a novel terminal output-feedback robust control technique. The proposed control mechanism involves the system states to be first controlled via the MPC method to be driven into a prescribed neighborhood of the origin, and then, the terminal output-feedback robust control method guaranteeing the input constraints is applied to make such states converge to the origin. It is also verified that our control method guarantees the closed-loop stability and feasibility in the presence of model uncertainties and input constraints. Finally, a numerical example is given to demonstrate its effectiveness.     

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.     

终端滑模约束的时滞系统模型预测控制

终端约束区域和终端代价项在模型预测控制中起着关键的作用,针对输入受限的时滞系统,提出了终端滑模约束的模型预测控制．将满足输入约束的滑模面作为终端约束区域,使得终端约束区域扩大,有效缩短预测时域,减少计算量,有利于在线应用．最后通过仿真验证了所提方法的有效性．     

Adaptive receding horizon predictive control for constrained discrete-time linear systems with parameter uncertainties

This paper proposes a discrete-time model predictive control (MPC) scheme combined with an adaptive mechanism. To this end, first, an adaptive parameter estimation algorithm suitable for MPC is proposed, which uses the available input and output signals to estimate the unknown system parameters. It enables the prediction of a monotonically decreasing worst-case estimation error bound over the prediction horizon of MPC. These distinctive features allow for future model improvement to be explicitly considered in MPC. Thus, a less conservative adaptive-type MPC controller can be developed based on the proposed estimation method. Second, we show how the discrete-time adaptive-type state-feedback MPC controller is constructed by combining the on-line parameter estimation scheme with a modified robust MPC method based on the comparison model. The developed MPC controller guarantees feasibility and stability of the closed-loop system theoretically in the presence of input and state constraints. A numerical example is given to demonstrate its effectiveness.     

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.     

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.     

Reference trajectory tuning of model predictive control

An approach to minimize tuning effort of nominal Model Predictive Control algorithms is proposed. The algorithm dynamically calculates output set points to accommodate user-defined output importance, which is more intuitive than selecting values for the MPC weighing matrices. Instead of tuning the weights on the outputs deviations from their set points, weights on the input values and input increments, which are the usual tuning parameters of MPC, the desired output control performance of the MPC can be specified by performance factors. The proposed method extends the existing methods that consider a reference trajectory for the output tracking to the case of zone control and input targets. The proposed method also assumes that, as in most commercial MPC packages, the controller has two layers: a static layer and an extended dynamic layer. The method is illustrated by three case studies, contemplating both SISO and MIMO systems. It is observed that: the output set point tracking performance can be changed without modifying the MPC tuning weights, the approach is capable of achieving similar performance to conventional MPC tuned by multiobjective optimization techniques from the literature, with a fraction of computer effort, and it can be integrated with Real Time Optimization algorithms to control complex systems, always respecting output constraints.     

Model Predictive Control Tuning by Controller Matching

The effectiveness of model predictive control (MPC) in dealing with input and state constraints during transient operations is well known. However, in contrast with several linear control techniques, closed-loop frequency-domain properties such as sensitivities and robustness to small perturbations are usually not taken into account in the MPC design. This technical note considers the problem of tuning an MPC controller that behaves as a given linear controller when the constraints are not active (e.g., for perturbations around the equilibrium that remain within the given input and state bounds), therefore inheriting the small-signal properties of the linear control design, and that still optimally deals with constraints during transients. We provide two methods for selecting the MPC weight matrices so that the resulting MPC controller behaves as the given linear controller, therefore solving the posed inverse problem of controller matching, and is globally asymptotically stable.      

Robust nonlinear MPC without terminal constraint for tracking changing setpoints in the presence of non-additive unknown disturbance

This paper develops a novel robust tracking model predictive control (MPC) without terminal constraint for discrete-time nonlinear systems capable to deal with changing setpoints and unknown non-additive bounded disturbances. The MPC scheme without terminal constraint avoids difficult computations for the terminal region and is thus simpler to design and implement. However, the existence of disturbances and/or sudden changes in a setpoint may lead to feasibility and stability issues in this method. In contrast to previous works that considered changing setpoints and/or additive slowly varying disturbance, the proposed method is able to deal with changing setpoints and non-additive non-slowly varying disturbance. The key idea is the addition of tightened input and state (tracking error) constraints as new constraints to the tracking MPC scheme without terminal constraints based on artificial references. In the proposed method, the optimal tracking error converges asymptotically to the invariant set for tracking, and the perturbed system tracking error remains in a variable size tube around the optimal tracking error. Closed-loop input-to-state stability and recursive feasibility of the optimization problem for any piece-wise constant setpoint and non-additive disturbance are guaranteed by tightening input and state constraints as well as weighting the terminal cost function by an appropriate stabilizing weighting factor. The simulation results of the satellite attitude control system are provided to demonstrate the efficiency of the proposed predictive controller.     

Novel MPC‐Based Fault Tolerant Tracking Control Against Sensor Faults

The problem of active fault‐tolerant tracking control with control input and system output constraints is studied for a class of discrete‐time systems subject to sensor faults. A time‐varying fault‐tolerant observer is first developed to estimate the real system state from the faulty sensor output and control input signals. Then by using the estimated state at each time step, a model predictive control (MPC)‐based fault‐tolerant tracking control scheme is presented to guarantee the desired tracking performance and the given input and output constraints on the faulty system. In comparison with many existing fault‐tolerant MPC methods, its main contribution is that the proposed state estimator is designed by the simple and online numerical computation to tolerate the possible sensor faults, so that the regular MPC algorithm without fault information can be adopted for the online calculation of fault‐tolerant control signal. The potential recursive infeasibility and computational complexity due to the faults are avoided in the scheme. Additionally, the closed‐loop stability of the post‐fault system is discussed. Simulative results of an electric throttle control system verify the effectiveness of the proposed method.     

Input-to-state stable finite horizon MPC for neutrally stable linear discrete-time systems with input constraints

MPC or model predictive control is representative of control methods which are able to handle inequality constraints. Closed-loop stability can therefore be ensured only locally in the presence of constraints of this type. However, if the system is neutrally stable, and if the constraints are imposed only on the input, global asymptotic stability can be obtained; until recently, use of infinite horizons was thought to be inevitable in this case. A globally stabilizing finite-horizon MPC has lately been suggested for neutrally stable continuous-time systems using a non-quadratic terminal cost which consists of cubic as well as quadratic functions of the state. The idea originates from the so-called small gain control, where the global stability is proven using a non-quadratic Lyapunov function. The newly developed finite-horizon MPC employs the same form of Lyapunov function as the terminal cost, thereby leading to global asymptotic stability. A discrete-time version of this finite-horizon MPC is presented here. Furthermore, it is proved that the closed-loop system resulting from the proposed MPC is ISS (Input-to-State Stable), provided that the external disturbance is sufficiently small. The proposed MPC algorithm is also coded using an SQP (Sequential Quadratic Programming) algorithm, and simulation results are given to show the effectiveness of the method.     

一类离散不确定系统的Tube不变集离线鲁棒模型预测控制

针对一类输入和状态受限的离散线性不确定系统,提出了一种基于Tube不变集的离线鲁棒模型预测控制方法.首先针对输入和状态约束线性时不变标准系统,设计了改进的基于多面体不变集的离线模型预测控制算法,并证明了稳定性.其次对于存在未知有界干扰的实际不确定系统,引入了Tube不变集策略,通过设计对应标准模型的最优控制序列和状态轨迹,给出了实际不确定系统的离线Tube不变集控制策略,保证系统状态鲁棒渐近稳定,并收敛于终端干扰不变集.仿真结果验证了该控制方法的有效性.     

A fixed-point iteration scheme for real-time model predictive control

A simple model predictive control (MPC) concept for nonlinear systems under input constraints is considered. The presented algorithm takes advantage of an MPC formulation without terminal constraints in order to solve the optimality conditions by a fixed-point iteration scheme that is easy to implement and of algorithmic simplicity. Sufficient conditions for the contraction of the fixed-point iterations are derived. To allow for a real-time implementation within an MPC scheme, a constant number of fixed-point iterations is used in each sampling step and sufficient conditions for asymptotic stability and incremental reduction of the suboptimality are presented.     

An improved design of aggregation-based model predictive control

Linear aggregation in the input is an effective method to reduce the online computational burden of model predictive control (MPC) but at the cost of degradations in the closed-loop performance. In this paper, an improved aggregation-based MPC algorithm is developed to reduce these degradations. In this algorithm, a time-varying base vector is utilized in conjunction with the quasi-equivalent aggregation strategy. Furthermore, by relaxing the constraints with a sequence of reachable sets, a switching strategy is adopted to enlarge the attractive region of the resulting aggregation-based MPC.     

基于容许集的变终端约束MPC控制

针对一类输入和状态受约束的离散线性系统,提出一种基于Ⅳ步容许集的变终端约束集模型预测控制方法.首先给出多面体不变集序列作为终端约束集的离线模型预测控制算法,扩大了终端约束集.为进一步扩大初始状态可镇定区域,引入N步容许集,设计了基于容许集的变终端约束集模型预测控制方法.该算法采用离线设计、在线优化方法,实现了系统渐近稳定,不仅降低了在线运算量,而且扩大了初始状态可镇定区域.仿真结果表明了算法的有效性.     

Reconfigurable predictive control for redundantly actuated systems with parameterised input constraints

A method is proposed for on-line reconfiguration of the terminal constraint used to provide theoretical nominal stability guarantees in linear model predictive control (MPC). By parameterising the terminal constraint, its complete reconstruction is avoided when input constraints are modified to accommodate faults. To enlarge the region of feasibility of the terminal control law for a certain class of input faults with redundantly actuated plants, the linear terminal controller is defined in terms of virtual commands. A suitable terminal cost weighting for the reconfigurable MPC is obtained by means of an upper bound on the cost for all feasible realisations of the virtual commands from the terminal controller. Conditions are proposed that guarantee feasibility recovery for a defined subset of faults. The proposed method is demonstrated by means of a numerical example.     

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.     

Optimal MPC for tracking of constrained linear systems

Model predictive control (MPC) is one of the few techniques which is able to handle constraints on both state and input of the plant. The admissible evolution and asymptotic convergence of the closed-loop system is ensured by means of suitable choice of the terminal cost and terminal constraint. However, most of the existing results on MPC are designed for a regulation problem. If the desired steady-state changes, the MPC controller must be redesigned to guarantee the feasibility of the optimisation problem, the admissible evolution as well as the asymptotic stability. Recently, a novel MPC has been proposed to ensure the feasibility of the optimisation problem, constraints satisfaction and asymptotic evolution of the system to any admissible target steady-state. A drawback of this controller is the loss of a desirable property of the MPC controllers: the local optimality property. In this article, a novel formulation of the MPC for tracking is proposed aimed to recover the optimality property maintaining all the properties of the original formulation.     

Multivariable predictive control for vibrating structures: An application

This paper proposes the use of Model Predictive Control (MPC) to control a fast mechanical system. In particular an MPC strategy is applied to a laboratory flexible arm to perform a fast positioning of the end-effector with limited oscillations during the maneuver. The on-line implementation of a fast MPC is obtained with an ad hoc platform based on C++ and MATLAB while the MPC tuning is based on a non-linear model identified and validated with experimental data. The effectiveness of the proposed method is highlighted with some suitable experiments performed on the plant. In particular the comparison with a Linear Quadratic Regulator stresses the advantage of the MPC capability to explicitly handle input and state constraints.This feature guarantees smaller displacements that imply a structure stress reduction.     

Model Predictive Control oriented experiment design for system identification: A graph theoretical approach

We present a new approach to Model Predictive Control (MPC) oriented experiment design for the identification of systems operating in closed-loop. The method considers the design of an experiment by minimizing the experimental cost, subject to probabilistic bounds on the input and output signals due to physical limitations of actuators, and quality constraints on the identified model. The excitation is done by intentionally adding a disturbance to the loop. We then design the external excitation to achieve the minimum experimental effort while we are also taking care of the tracking performance of MPC. The stability of the closed-loop system is guaranteed by employing robust MPC during the experiment. The problem is then defined as an optimization problem. However, the aforementioned constraints result in a non-convex optimization which is relaxed by using results from graph theory. The proposed technique is evaluated through a numerical example showing that it is an attractive alternative for closed-loop experiment design.