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 Firstly, a trigger condition is designed to judge if parameters of the predictive model are out of date and differ a lot from their current true values so that there is no feasible solution to regulate the state within the given bound without predictive model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.     

Model predictive control of constrained LPV systems

This article considers robust model predictive control (MPC) schemes for linear parameter varying (LPV) systems in which the time-varying parameter is assumed to be measured online and exploited for feedback. A closed-loop MPC with a parameter-dependent control law is proposed first. The parameter-dependent control law reduces conservativeness of the existing results with a static control law at the cost of higher computational burden. Furthermore, an MPC scheme with prediction horizon ‘1’ is proposed to deal with the case of asymmetric constraints. Both approaches guarantee recursive feasibility and closed-loop stability if the considered optimisation problem is feasible at the initial time instant.     

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.     

Predictive control of switched nonlinear systems with scheduled mode transitions

In this work, a predictive control framework is proposed for the constrained stabilization of switched nonlinear systems that transit between their constituent modes at prescribed switching times. The main idea is to design a Lyapunov-based predictive controller for each constituent mode in which the switched system operates and incorporate constraints in the predictive controller design which upon satisfaction ensure that the prescribed transitions between the modes occur in a way that guarantees stability of the switched closed-loop system. This is achieved as follows: For each constituent mode, a Lyapunov-based model predictive controller (MPC) is designed, and an analytic bounded controller, using the same Lyapunov function, is used to explicitly characterize a set of initial conditions for which the MPC, irrespective of the controller parameters, is guaranteed to be feasible, and hence stabilizing. Then, constraints are incorporated in the MPC design which, upon satisfaction, ensure that: 1) the state of the closed-loop system, at the time of the transition, resides in the stability region of the mode that the system is switched into, and 2) the Lyapunov function for each mode is nonincreasing wherever the mode is reactivated, thereby guaranteeing stability. The proposed control method is demonstrated through application to a chemical process example.     

On real-time robust model predictive control

High-speed applications impose a hard real-time constraint on the solution of a model predictive control (MPC) problem, which generally prevents the computation of the optimal control input. As a result, in most MPC implementations guarantees on feasibility and stability are sacrificed in order to achieve a real-time setting. In this paper we develop a real-time MPC approach for linear systems that provides these guarantees for arbitrary time constraints, allowing one to trade off computation time vs. performance. Stability is guaranteed by means of a constraint, enforcing that the resulting suboptimal MPC cost is a Lyapunov function. The key is then to guarantee feasibility in real-time, which is achieved by the proposed algorithm through a warm-starting technique in combination with robust MPC design. We address both regulation and tracking of piecewise constant references. As a main contribution of this paper, a new warm-start procedure together with a Lyapunov function for real-time tracking is presented. In addition to providing strong theoretical guarantees, the proposed method can be implemented at high sampling rates. Simulation examples demonstrate the effectiveness of the real-time scheme and show that computation times in the millisecond range can be achieved.     

Periodic optimal control of nonlinear constrained systems using economic model predictive control

In this paper, we consider the problem of periodic optimal control of nonlinear systems subject to online changing and periodically time-varying economic performance measures using model predictive control (MPC). The proposed economic MPC scheme uses an online optimized artificial periodic orbit to ensure recursive feasibility and constraint satisfaction despite unpredictable changes in the economic performance index. We demonstrate that the direct extension of existing methods to periodic orbits does not necessarily yield the desirable closed-loop economic performance. Instead, we carefully revise the constraints on the artificial trajectory, which ensures that the closed-loop average performance is no worse than a locally optimal periodic orbit. In the special case that the prediction horizon is set to zero, the proposed scheme is a modified version of recent publications using periodicity constraints, with the important difference that the resulting closed loop has more degrees of freedom which are vital to ensure convergence to an optimal periodic orbit. In addition, we detail a tailored offline computation of suitable terminal ingredients, which are both theoretically and practically beneficial for closed-loop performance improvement. Finally, we demonstrate the practicality and performance improvements of the proposed approach on benchmark examples.     

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.     

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     

Event-triggered model predictive control of switched systems with denial-of-service attacks

Observer-based model predictive control (MPC) for the discrete-time switched systems suffered by event-triggered mechanism and denial-of-service (DoS) attacks is discussed in this paper. We assume that the switch is slow enough and the attacker's energy is limited. To save network resources, an event-triggered mechanism is designed based on dwell time and triggered error. Under the coupled influence of attack and trigger, a complex mismatch of system mode and controller mode occurs, which brings difficulties to the transformation of MPC optimization problem. To address this problem, a new performance index coefficient is designed by using the increasing/decreasing law of Lyapunov function. On this basis, the transformation of the optimization problem is realized. Then, the controller gain and observer gain for the attack-free case are designed to guarantee the exponential convergence of the closed-loop system. In the presence of attacks, we obtain the upper bound of attack duty cycle, below which the exponential convergence of the system can still be archived. An example is illustrated at last to verify the validity of the main results.     

基于扩展BP神经网络的一类非线性系统自适应控制设计

针对单输入单输出非线性系统的不确定性问题,提出了一种新型的基于扩展反向传播（BP）神经网络的自适应控制方法。首先,采用离线数据来训练BP神经网络的权值向量;然后,通过在线调节伸缩因子和逼近精度估计值的更新律,从而来达到控制整个系统的目的。在控制器的设计过程中,利用李亚普诺夫稳定性分析原理,保证了闭环系统的所有状态一致终极有界（UUB）。相比传统的BP神经网络自适应控制,所提方法能有效地减少在线调节的参数数目、减轻计算负担。仿真结果表明,该方法能够使闭环系统的所有状态都趋于零,即系统达到稳定状态。     

约束非线性系统构造性模型预测控制

研究了连续时间约束非线性系统模型预测控制设计.利用控制Lyapunov函数离线构造单变量可调预测控制器,再根据性能指标在线优化可调参数,其中该参数近似于闭环系统的"衰减率".同时,控制Lyapunov函数保证了算法的可行性和闭环系统的稳定性.最后通过数值仿真验证了该算法的有效性.     

A stabilizing model predictive control for networked control system with data packet dropout

A constrained model predictive control （MPC） algorithm for networked control system with data packet dropout is proposed in this paper. A buffer is designed to store the predicted control sequence between controller and actuator. It is shown that if the control horizon of MPC is not less than the number of data packets lost continuously, feasibility of MPC at initial time implies asymptotical stability of the closed-loop system. A simulation example illustrates the effectiveness of the proposed approach.     

自适应神经网络四旋翼无人机有限时间轨迹跟踪控制

针对带有模型不确定性和未知外部干扰的四旋翼无人机轨迹跟踪控制问题,提出一种基于径向基(radial basis function, RBF)神经网络的自适应全局快速终端滑模控制方法,确保系统对期望轨迹的有限时间跟踪。该方法考虑到全局快速终端滑模控制在实际应用中的适应性和抖振问题,利用RBF神经网络替代等效控制量,以神经网络的在线学习能力补偿系统内部的不确定性和未知的外部干扰,有效地降低了系统的抖振;根据Lyapunov方法导出的自适应律在线调整神经网络权值,以保证闭环系统的稳定性。通过一系列仿真算例和飞行实验验证了该方法的有效性与可行性,结果表明:该控制方法相对于滑模控制的抖振更小,具有更好的收敛性和抗干扰能力,同时对模型的参数摄动具有更强的鲁棒性。     

考虑输入受限的航天器安全接近姿轨耦合控制

针对存在外部扰动和输入受限的航天器安全接近的问题,当扰动上界未知时,基于积分滑模控制理论设计了抗饱和的有限时间自适应姿轨耦合控制器.控制器的设计过程中采用了新型的避碰函数限制追踪航天器运动区域进而保证接近过程中航天器的安全性,同时通过辅助系统和自适应算法分别处理了输入受限和扰动上界未知.借助李雅普诺夫理论证明了在控制器的作用下系统状态在有限时间内收敛,且能够保证追踪航天器在实现航天器接近的过程中不与目标航天器发生碰撞.最后通过数字仿真进一步验证了所设计控制器的有效性.     

Robust adaptive path-following control of underactuated marine vessel with off-track error constraint

In this paper, a new robust adaptive controller is investigated to force an underactuated surface marine vessel to follow a predefined parameterised path at a desired speed, despite actuator saturation and the presence of model uncertainties as well as environmental disturbances induced by waves, wind and sea-currents. To ensure robustness of the path-following controller, time-varying constraint on the off-track error (i.e. the maximal distance from the ship to the reference path) is considered. To address the off-track error constraint the tan-barrier Lyapunov function is incorporated with the control scheme, where the idea of auxiliary design system introduced in Chen, Sam, and Ren (2011) is adopted and its states are used in combination with backstepping and Lyapunov synthesis to adaptive tracking control design with guaranteed stability. Furthermore, the command filters are adopted to implement physical constraints on the virtual control laws so that analytic differentiation of the virtual control laws is avoided. We show that the proposed robust adaptive control law is able to guarantee semi-global uniform ultimate bounded stability of the closed-loop system. Numerical simulations and experimental results are carried out to demonstrate the effectiveness of the proposed algorithm.     

机械臂鲁棒自适应运动控制

针对具有不确定性的机械臂系统,文中阐述了一种基于势函数和Lyapunov稳定性理论的鲁棒自适应控制方法．它是通过合理选择与控制目标相关的势函数,并根据模型中不确定性的实时变化,在控制器中引入可在线可调参数,使得控制器机械臂能够跟踪给定的有界参考信号,跟踪误差收敛到包含零点的很小的邻域内．同时该闭环系统的所有状态半全局最终一致有界（SGUUB）．仿真研究表明该方法的有效性．     

A receding horizon control approach to sampled-data implementation of continuous-time controllers

We propose a novel way for sampled-data implementation (with the zero order hold assumption) of continuous-time controllers for general nonlinear systems. We assume that a continuous-time controller has been designed so that the continuous-time closed-loop satisfies all performance requirements. Then, we use this control law indirectly to compute numerically a sampled-data controller. Our approach exploits a model predictive control (MPC) strategy that minimizes the mismatch between the solutions of the sampled-data model and the continuous-time closed-loop model. We propose a control law and present conditions under which stability and sub-optimality of the closed loop can be proved. We only consider the case of unconstrained MPC. We show that the recent results in [G. Grimm, M.J. Messina, A.R. Teel, S. Tuna, Model predictive control: for want of a local control Lyapunov function, all is not lost, IEEE Trans. Automat. Control 2004, to appear] can be directly used for analysis of stability of our closed-loop system.     

Online adaptive optimal control for continuous-time nonlinear systems with completely unknown dynamics

An online adaptive optimal control is proposed for continuous-time nonlinear systems with completely unknown dynamics, which is achieved by developing a novel identifier-critic-based approximate dynamic programming algorithm with a dual neural network (NN) approximation structure. First, an adaptive NN identifier is designed to obviate the requirement of complete knowledge of system dynamics, and a critic NN is employed to approximate the optimal value function. Then, the optimal control law is computed based on the information from the identifier NN and the critic NN, so that the actor NN is not needed. In particular, a novel adaptive law design method with the parameter estimation error is proposed to online update the weights of both identifier NN and critic NN simultaneously, which converge to small neighbourhoods around their ideal values. The closed-loop system stability and the convergence to small vicinity around the optimal solution are all proved by means of the Lyapunov theory. The proposed adaptation algorithm is also improved to achieve finite-time convergence of the NN weights. Finally, simulation results are provided to exemplify the efficacy of the proposed methods.     

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.     

A stable block model predictive control with variable implementation horizon

In this paper, we present a stable model predictive control method for discrete-time nonlinear systems. The standard MPC scheme is modified to incorporate (1) a block implementation scheme where a sub-string of the optimized input sequence is applied instead of a single value; (2) an additional constraint which guarantees that a Lyapunov function will decrease over time; (3) a variable implementation window that facilitates the stability constraint enforcement. Stability of the closed-loop system with the proposed algorithm is established. Examples are given to illustrate the effectiveness of the control scheme. The impacts of several key design parameters on the overall performance are also analyzed and discussed.