Robust output feedback model predictive control of constrained linear systems

This paper provides a solution to the problem of robust output feedback model predictive control of constrained, linear, discrete-time systems in the presence of bounded state and output disturbances. The proposed output feedback controller consists of a simple, stable Luenberger state estimator and a recently developed, robustly stabilizing, tube-based, model predictive controller. The state estimation error is bounded by an invariant set. The tube-based controller ensures that all possible realizations of the state trajectory lie in a simple uncertainty tube the ‘center’ of which is the solution of a nominal (disturbance-free) system and the ‘cross-section’ of which is also invariant. Satisfaction of the state and input constraints for the original system is guaranteed by employing tighter constraint sets for the nominal system. The complexity of the resultant controller is similar to that required for nominal model predictive control.     

Tube-based robust economic model predictive control

In this paper, we develop a tube-based economic MPC framework for nonlinear systems subject to unknown but bounded disturbances. Instead of simply transferring the design procedure of tube-based stabilizing MPC to an economic MPC framework, we rather propose to consider the influence of the disturbance explicitly within the design of the MPC controller, which can lead to an improved closed-loop average performance. This will be done by using a specifically defined integral stage cost, which is the key feature of our proposed robust economic MPC algorithm. Furthermore, we show that the algorithm enjoys similar properties as a nominal economic MPC algorithm (i.e., without disturbances), in particular with respect to bounds on the asymptotic average performance of the resulting closed-loop system, as well as stability and optimal steady-state operation.     

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.     

基于高阶观测器和干扰补偿控制的模型预测控制方法

针对状态不可测、外部干扰未知, 并且状态和输入受限的离散时间线性系统, 将高阶观测器、干扰补偿控制与标准模型预测控制(Model predictive control, MPC)相结合, 提出了一种新的MPC方法. 首先利用高阶观测器同步观测未知状态和干扰, 使得观测误差一致有界收敛;然后基于该干扰估计值设计新的干扰补偿控制方法, 并将该方法与基于状态估计的标准MPC相结合, 实现上述系统的优化控制. 所提出的MPC方法克服了利用现有MPC方法求解具有外部干扰和状态约束的优化控制问题时存在无可行解的局限, 能够保证系统状态在每一时刻都满足约束条件, 并且使系统的输出响应接近采用标准MPC方法控制线性标称系统时得到的输出响应. 最后, 将所提控制方法应用到船舶航向控制系统中, 仿真结果表明了所提方法的有效性和优越性.     

Robust tube-based predictive control for mobile robots in off-road conditions

This paper focuses on the design of a tube-based Model Predictive Control law for the control of constrained mobile robots in off-road conditions with longitudinal slip while ensuring robustness and stability. A time-varying trajectory tracking error model is used, where uncertainties are assumed to be bounded and additive. The robust tube-based MPC is compared with other motion control techniques through simulation and physical experiments. These tests show the satisfactory behavior of the presented control strategy.     

Robust economic model predictive control based on a periodicity constraint

This paper proposes robust economic model predictive control based on a periodicity constraint for linear systems subject to unknown‐but‐bounded additive disturbances. In this economic MPC design, a periodic steady‐state trajectory is not required and thus assumed unknown, which precludes the use of enforcing terminal state constraints as in other standard economic formulations. Instead, based on the desired periodicity of system operation, we optimize the economic performance over a set of periodic trajectories that include the current state. To achieve robust constraint satisfaction, we use a tube‐based technique in the economic MPC formulation. The mismatches between the nominal model and the closed‐loop system with perturbations are limited using a local control law. With the proposed robust tube‐based strategy, recursive feasibility is guaranteed. Moreover, under a convexity assumption, the closed‐loop convergence of the closed‐loop system is analyzed, and an optimality certificate is provided to check if the closed‐loop trajectory reaches a neighborhood of the optimal nominal periodic steady trajectory using Karush‐Kuhn‐Tucker optimality conditions. Finally, through numerical examples, we show the effectiveness of the proposed approach.     

Finite-time control of mobile robot systems with unmeasurable angular and linear velocities via bioinspired neurodynamics approach

This paper addresses the stability analysis and adaptive robust finite-time bioinspired neurodynamics control for a class of mobile robot systems with unmeasurable angular and linear velocities, and time-varying bounded disturbance. The error system of the mobile robot is decomposed into two subsystems based on the system model. The state feedback control laws with observers are designed for the two subsystems, and the adaptive robust finite-time bioinspired neurodynamics controller (ARFBNC) is designed based on the state feedback control laws and two subsystems. The stability conditions in the form of linear matrix inequalities (LMIs) are derived by introducing the Lyapunov–Krasovskii functional. The unmeasurable angular and linear velocities, and time-varying bounded disturbance are estimated effectively by employing the state feedback control laws with observers. The smooth bounded outputs are obtained and the sharp jumps of initial values for the state variables are reduced. The closed-loop system is asymptotically stable and the state errors converge to an adjustable bounded region by introducing the Lyapunov–Krasovskii functional. The simulations are performed to show the effectiveness of the proposed methods.     

An integrated robust probing motion planning and control scheme: A tube-based MPC approach

‘This paper introduces the integration of a probing scheme into a robust MPC-based robot motion planning and control algorithm. The proposed solution tackles the output-feedback tube-based MPC problem using the partially-closed loop strategy to incorporate future measurements in a computationally efficient manner. This combination will provide not only a robust controller but also avoids overly conservative planning which is a drawback of the original implementation of the output-feedback tube-based MPC. The proposed solution is composed of two controllers: (i) a nominal MPC controller with probing feature to plan a globally convergent trajectory in conjunction with active localization, and (ii) an ancillary MPC controller to stabilize the robot motion around the planned trajectory. The performance and real-time implementation of the proposed planning and control algorithms have been verified through both extensive numerical simulations and experiments with a mobile robot.     

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.     

基于鲁棒一步集的Tube不变集鲁棒模型预测控制

针对一类干扰有界的输入和状态受约束线性离散系统,提出了一种基于鲁棒一步集的Tube不 变集鲁棒模型预测控制方法.首先采用多面体不变集离线设计方法得到基于多面体不变集序列的扩 展终端约束集;然后为了扩大鲁棒模型预测控制的初始状态允许区域,并提高系统的鲁棒性,在扩展终端约束集的基础上,通过引入鲁棒一步集并借助Tube不变集控制策略,设计了基于鲁棒一步集的鲁棒模型预测控制方法,并给出了算法的存在性和稳定性证明. 该方法不仅极大地扩大了初始状态允许区域,而且对有界干扰具有有效的抑制作用,使得受扰系统收敛到以原点为中心的最小鲁棒正不变集内.最后仿真验证了算法的有效性.     

Robust backstepping output tracking control for SISO uncertain nonlinear systems with unknown virtual control coefficients

The output tracking controller design problem is dealt with for a class of nonlinear strict-feedback form systems in the presence of nonlinear uncertainties, external disturbance, unmodelled dynamics and unknown time-varying virtual control coefficients. A new method based on signal compensation is proposed to design a linear time-invariant robust controller, which consists of a nominal controller and a robust compensator. It is shown that the closed-loop control system with a controller designed by the proposed method has robust asymptotical practical tracking property for any bounded initial conditions and robust tracking transient property if all initial states are zero.     

一类干扰有界约束非线性系统的鲁棒模型预测控制

针对一类干扰有界约束非线性系统设计了基于控制不变集切换策略的鲁棒模型预测控制算法.针对非线性系统线性化之后的结果,给出了平衡点的非线性标称系统控制不变集的计算方法.然后在考虑线性化误差和加性有界干扰影响的基础上,构造了平衡点附近最小鲁棒正不变集.结合不变集切换策略和Tube不变集控制方法,提出了干扰有界约束非线性系统的不变集切换策略.最后将该算法应用到一类典型的非线性化工过程连续搅拌反应釜(CSTR)中,仿真结果验证了算法的有效性.     

Robust output-feedback model predictive control for systems with unstructured uncertainty

In this paper, we present novel results that parameterize a broad class of robust output-feedback model predictive control (MPC) policies for discrete-time systems with constraints and unstructured model uncertainty. The MPC policies we consider employ: (i) a linear state estimator, (ii) a pre-determined feedback gain (iii) a set of “tighter constraints” and (iv) a quadratic cost function in the degrees of freedom and the estimated state. Contained within the class, we find both well-known control policies and policies with novel features. The unifying aspect is that all MPC policies within the class satisfy a robust stability test. The robust stability test is suited to synthesis and incorporates a novel linear matrix inequality (LMI) condition which involves the parameters of the cost function. The LMI is shown to always be feasible under an appropriate small-gain condition on the pre-determined feedback gain and the state estimator. Moreover, we show, by means of both theoretical and numerical results, that choosing the cost function parameters subject to the proposed condition often leads to good nominal performance whilst at the same time guaranteeing robust stability.     

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.     

Robust model predictive control with time-varying tubes

This paper focuses on the problem of robustly stabilizing uncertain discrete-time systems subject to bounded disturbances. The proposed tube-based model predictive controller ensures that all possible realizations of the state trajectory lie in the time-varying tubes so robust stability and satisfaction of the state and input constraints are guaranteed. The time-varying tubes are computed off-line so the on-line computational time is tractable. At each sampling time, the precomputed time-varying tubes are included in the optimal control problem as the constraints in the prediction horizon and only a quadratic programming problem is solved. In comparison to the algorithm that calculates the time-varying tubes on-line, the proposed algorithm can achieve the same level of control performance while the on-line computational time is greatly reduced.     

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.     

Output feedback robust MPC with one free control move for the linear polytopic uncertain system with bounded disturbance

In this paper a previous approach, for the robust model predictive control (MPC) for a linear polytopic uncertain system, is extended to the case with bounded disturbance and unmeasurable state. The controller on-line optimizes a free control move followed by an output feedback control law based on the pre-specified state estimator. A key technique for this controller is an appropriate formulation of the estimation error bound which accounts for recursive feasibility of the optimization problem. The quadratic boundedness (QB) of the augmented state is guaranteed by the proposed approach. A numerical example is given to illustrate the effectiveness of the proposed controller.     

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.     

An integrated robust iterative learning control strategy for batch processes based on 2D system

This paper studies the problem of integrated control in the 2-dimensional (2D) system with parameter uncertainties for batch processes. An integrated iterative learning control (ILC) strategy based on quadratic performance for batch processes is proposed. It realizes comprehensive control by combining robust ILC in batch-axis with model predictive control (MPC) in time-axis. The design of quadratic-criterion-based ILC for the system can be converted into a min-max problem. Then a model predictive controller with time-varying prediction horizon is designed based on a quadratic cost function. For an uncertain model, a novel integrated robust ILC scheme based on a nominal model is further proposed. As a result, the control law of the 2D system can be regulated during one batch, which leads to good tracking performance and strong robustness against the disturbance and the uncertainties. Moreover, the analyses of the convergence and tracking performance are given. The proposed methods are applied to batch reactor, and results demonstrate that the system has good robustness and convergence. This paper provides a new way for batch processes control.