具有不确定性的非线性切换系统的约束预测控制

针对一类具有不确定性和变量约束的非线性切换系统, 提出了一种基于Lyapunov函数的预测控制方法, 其中状态约束分为两种情况: 1)要求状态变量在所有时刻都满足约束(称为硬约束); 2)允许状态在某些时刻超出约束(称为软约束). 主要思想是: 对切换系统的每一个子系统, 在输入和状态均受约束的情况下, 设计基于Lyapunov函数的有界控制器和预测控制器, 在两者之间适当切换, 得到初始稳定区域的描述并使得子闭环系统保持稳定. 对整个切换系统, 设计适当的切换律以保证: 1)在切换时刻, 闭环系统的状态处在切入系统的稳定区域内; 2)切入模块的Lyapunov函数是非增的, 从而可保证稳定性. 在状态变量的约束是软约束时, 对每一子模块首先设计一个控制策略, 尽快将状态控制到初始稳定区域, 然后再利用稳定区域内的控制律使系统稳定.     

Constrained control Lyapunov function based model predictive control design

This work considers linear systems with input constraints with the objective of designing a controller that guarantees stability from all initial conditions in the null‐controllable region (the set of initial conditions from where the system can be stabilized). To this end, a recently developed procedure for construction of constrained control Lyapunov functions is utilized within a Lyapunov‐based model predictive controller coupled with an auxiliary control design to achieve stabilization from all initial conditions in the null‐controllable region. Illustrative simulation results as well as an application to a nonlinear chemical process example is presented to demonstrate the efficacy of the results.Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

Lyapunov-based model predictive control of stochastic nonlinear systems

In this work, we design a Lyapunov-based model predictive controller (LMPC) for nonlinear systems subject to stochastic uncertainty. The LMPC design provides an explicitly characterized region from where stability can be probabilistically obtained. The key idea is to use stochastic Lyapunov-based feedback controllers, with well characterized stabilization in probability, to design constraints in the LMPC that allow the inheritance of the stability properties by the LMPC. The application of the proposed LMPC method is illustrated using a nonlinear chemical process system example.     

Uniting bounded control and MPC for stabilization of constrained linear systems

In this work, a hybrid control scheme, uniting bounded control with model predictive control (MPC), is proposed for the stabilization of linear time-invariant systems with input constraints. The scheme is predicated upon the idea of switching between a model predictive controller, that minimizes a given performance objective subject to constraints, and a bounded controller, for which the region of constrained closed-loop stability is explicitly characterized. Switching laws, implemented by a logic-based supervisor that constantly monitors the plant, are derived to orchestrate the transition between the two controllers in a way that safeguards against any possible instability or infeasibility under MPC, reconciles the stability and optimality properties of both controllers, and guarantees asymptotic closed-loop stability for all initial conditions within the stability region of the bounded controller. The hybrid control scheme is shown to provide, irrespective of the chosen MPC formulation, a safety net for the practical implementation of MPC, for open-loop unstable plants, by providing a priori knowledge, through off-line computations, of a large set of initial conditions for which closed-loop stability is guaranteed. The implementation of the proposed approach is illustrated, through numerical simulations, for an exponentially unstable linear system.     

Decentralized tube‐based model predictive control of uncertain nonlinear multiagent systems

This paper addresses the problem of decentralized tube‐based nonlinear model predictive control (NMPC) for a general class of uncertain nonlinear continuous‐time multiagent systems with additive and bounded disturbance. In particular, the problem of robust navigation of a multiagent system to predefined states of the workspace while using only local information is addressed under certain distance and control input constraints. We propose a decentralized feedback control protocol that consists of two terms: a nominal control input, which is computed online and is the outcome of a decentralized finite horizon optimal control problem that each agent solves at every sampling time, for its nominal system dynamics; and an additive state‐feedback law which is computed offline and guarantees that the real trajectories of each agent will belong to a hypertube centered along the nominal trajectory, for all times. The volume of the hypertube depends on the upper bound of the disturbances as well as the bounds of the derivatives of the dynamics. In addition, by introducing certain distance constraints, the proposed scheme guarantees that the initially connected agents remain connected for all times. Under standard assumptions that arise in nominal NMPC schemes, controllability assumptions, communication capabilities between the agents, it is guaranteed that the multiagent system is input‐to‐state stable with respect to the disturbances, for all initial conditions satisfying the state constraints. Simulation results verify the correctness of the proposed framework.     

基于多层概率集的随机预测控制算法设计

考虑具有乘型不确定性的离散随机系统约束控制问题, 设计了一种基于多层概率集的随机预测控制算法. 多层概率集描述了状态在多步反馈控制律下的一系列不同概率的分布区域, 因此能够同时保证多个不同概率要求的软约束. 通过动态优化多步反馈律, 算法具有较大的可行范围. 之后设计的简化算法在降低计算负担的同时保证了算法的可行范围.     

Fuzzy robust constrained model predictive control for nonlinear systems

This paper addresses robust constrained model predictive control (MPC) for a class of nonlinear systems with structured time‐varying uncertainties. First, the Takagi‐Sugeno (T‐S) fuzzy model is employed to represent a nonlinear system. Then, we develop some techniques for designing fuzzy control which guarantees the system stabilization subject to input and output constraints. Both parallel and nonparallel distributed compensation control laws (PDC and non‐PDC) are considered. Sufficient conditions for the solvability of the controller design problem are given in the form of linear matrix inequalities. A simulation example is presented to illustrate the design procedures and performances of the proposed methods. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

滑动变量受限情况下的二阶滑模控制设计

在实际系统中状态受限普遍存在,因此考虑状态受限下的控制设计问题具有重要的理论意义和工程价值.本文考虑了滑动变量受限情况下的二阶滑模控制设计问题.首先,在不考虑滑动变量受限的情况下,基于Lyapunov方法,给出了一种新的二阶滑模控制器构造方法,并严格证明了在该控制器的作用下滑动变量将在有限时间内稳定到平衡点.其次,考虑滑动变量受限情况,证明了在受限区域内存在一个与控制参数相关的吸引域,使得当初始状态在该吸引域内时其相轨迹不会逃离它.最后,状态受限情况下倒立摆系统的控制设计验证了该算法的有效性.     

Model predictive control of axial dispersion chemical reactor

This paper discusses the development of model predictive control algorithm which accounts for the input and state constraints applied to the parabolic partial differential equations (PDEs) system describing the axial dispersion chemical reactor. Spatially varying terms arising from the nonlinear PDEs model are accounted for in model development. Finite-dimensional modal representation capturing the dominant dynamics of the PDEs system is derived for controller design through Galerkin's method and modal decomposition technique. Tustin's discretization and Cayley transform are used to obtain infinite-dimensional discrete-time dynamic modal representations which are used in subsequent constrained controller design. The proposed discrete-time constrained model predictive control synthesis is constructed in a way that the objective function is only based on the low-order modal representation of the PDEs system, while higher-order modes are utilized only in the constraints of the PDEs state. Finally, the MPC formulations are successfully applied, via simulation results, to the PDEs system with input and state constraints.     

Backstepping control integrated with Lyapunov-based model predictive control

In this study, backstepping control integrated with Lyapunov-based model predictive control (BS-MPC) is proposed for nonlinear systems in a strict-feedback form. The virtual input of the first step is designed by solving the finite-horizon optimal control problem (FHOCP), and the real input is designed by the backstepping method. BS-MPC guarantees (semiglobal) ultimate boundedness of the closed-loop system when the control is implemented in a zero-order hold manner. When the robustness of BS-MPC is analyzed for uniformly bounded disturbances, the ultimate boundedness of the solution of perturbed system is guaranteed. BS-MPC can provide a better desired value of the virtual input of the first step by solving the FHOCP, resulting in a faster stabilization of the system compared with the backstepping control. In addition, BS-MPC requires less computational load compared with MPC because the dimension of the states considered in the on-line optimization problem of BS-MPC is lower than that of MPC.     

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.     

Coherent quantum LQG control

Based on a recently developed notion of physical realizability for quantum linear stochastic systems, we formulate a quantum LQG optimal control problem for quantum linear stochastic systems where the controller itself may also be a quantum system and the plant output signal can be fully quantum. Such a control scheme is often referred to in the quantum control literature as “coherent feedback control”. It distinguishes the present work from previous works on the quantum LQG problem where measurement is performed on the plant and the measurement signals are used as the input to a fully classical controller with no quantum degrees of freedom. The difference in our formulation is the presence of additional non-linear and linear constraints on the coefficients of the sought after controller, rendering the problem as a type of constrained controller design problem. Due to the presence of these constraints, our problem is inherently computationally hard and this also distinguishes it in an important way from the standard LQG problem. We propose a numerical procedure for solving this problem based on an alternating projections algorithm and, as an initial demonstration of the feasibility of this approach, we provide fully quantum controller design examples in which numerical solutions to the problem were successfully obtained. For comparison, we also consider the case of classical linear controllers that use direct or indirect measurements, and show that there exists a fully quantum linear controller which offers an improvement in performance over the classical ones.     

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.     

Stabilization of linear systems over networks with bounded packet loss and its use in model predictive control

This paper considers stabilization of discrete-time linear systems, where network exists for transmitting the sensor and controller information, and arbitrary bounded packet loss occurs in the sensor–controller link and the controller–actuator link. The stabilization of this system is transformed into the robust stabilization of a set of systems. The stability result for this system is specially applied on model predictive control (MPC) that explicitly considers the satisfaction of input and state constraints. Two synthesis approaches of MPC are presented, one parameterizing the infinite horizon control moves into a single state feedback law, the other into a free control move followed by the single state feedback law. Two simulation examples are given to illustrate the effectiveness of the proposed techniques.     

高超声速飞行器的调度离线预测控制

本文将调度预测控制的思想应用于离线鲁棒预测控制,设计了高超声速飞行器计算有效的调度离线预测控制器.首先在不同的平衡点离线设计一系列控制规则,实际实施时只需要在不同的控制器之间进行切换,避免进行在线优化,大幅度减少了在线计算时间.通过估计局部控制器的稳定域,保证了切换控制器的稳定性.另外在确保良好控制品质的同时,还能够保证所有输入和状态均在给定约束范围.仿真试验表明,提出的方法能实现速度和高度较大范围的指令跟踪,所有输入和状态均在给定约束范围内;相比于在线鲁棒预测控制方法,仿真运行时间减少,可以实现高超声速飞行器的实时控制.     

Virtual control with hard constraints

Practical control problems are always subject to plant state and/or input constraints, which make designing an effective controller a challenging task. This paper introduces a novel virtual control approach to handling the presence of hard constraints in control systems by utilizing virtual mechanisms in the form of nonlinear springs and dampers. The augmented virtual mechanisms are to assist in better shaping the closed‐loop responses, especially when operating near the constrained boundary. A linear quadratic regulator based model predictive control method is utilized to develop stabilizing controllers that not only achieve desired system performance, but also meet the imposed hard constraints. The basic idea is to dramatically increase control penalty by way of tuning the spring and damper effect when the constrained state/input response is close to its hard constraint. The proposed method is applied to a balancing ball problem to demonstrate its applicability and effectiveness, and the simulation results validate the proposed concept.