基于自适应MPC算法的轨迹跟踪控制研究

为了保证智能车辆在低附着且变速条件下跟踪控制的精确性和稳定性,提出一种基于自适应模型预测控制（MPC）的轨迹跟踪控制算法。针对低附着条件下轨迹跟踪存在行驶稳定性较差的问题,对车辆动力学模型添加侧偏角软约束,分别设计有无添加侧偏角约束的MPC控制器。仿真结果表明,添加侧偏角约束后MPC控制器性能更优,车辆行驶稳定性得到有效提高。在此基础上,又提出了一种自适应的轨迹跟踪控制策略,能够根据车辆速度的变化,实时产生预测时域[(Hp)],分别设计自适应的MPC控制器与4组定值[Hp]的MPC控制器。仿真结果表明,基于自适应模型预测控制的轨迹跟踪控制算法在提高低附着且变速条件下智能车辆轨迹跟踪控制的精度和稳定性方面具有一定的有效性和先进性。     

Distributed robust MPC for nonholonomic robots with obstacle and collision avoidance

Considering that the inevitable disturbances and coupled constraints pose an ongoing challenge to distributed control algorithms, this paper proposes a distributed robust model predictive control (MPC) algorithm for a multi-agent system with additive external disturbances and obstacle and collision avoidance constraints. In particular, all the agents are allowed to solve optimization problems simultaneously at each time step to obtain their control inputs, and the obstacle and collision avoidance are accomplished in the context of full-dimensional controlled objects and obstacles. To achieve the collision avoidance between agents in the distributed framework, an assumed state trajectory is introduced for each agent which is transmitted to its neighbors to construct the polyhedral over-approximations of it. Then the polyhedral over-approximations of the agent and the obstacles are used to smoothly reformulate the original nonconvex obstacle and collision avoidance constraints. And a compatibility constraint is designed to restrict the deviation between the predicted and assumed trajectories. Moreover, recursive feasibility of each local MPC optimization problem with all these constraints derived and input-to-state stability of the closed-loop system can be ensured through a sufficient condition on controller parameters. Finally, simulations with four agents and two obstacles demonstrate the efficiency of the proposed algorithm.     

Emitter location using an angle-only tracking filter with own-ship trajectory estimation

An angle-only tracking algorithm to locate the emitter source position from an overflight vehicle is presented. The algorithm uses an extended Kalman filter with angular data from an onboard direction finder. The dynamic relationship between the emitter and own-ship motion is formulated in modified polar coordinates (MPC), which yields good noise-handling performance. The MPC filter method, however, encounters slow convergence problem under realistic overflight scenarios, where the lateral sightline motion inputs are mild. By using the knowledge on an own-ship estimator and computed pseudo-measurements for range and range-rate over range, the convergence of estimator is greatly accelerated. The combined scheme of this trajectory estimation filter and the MPC filter markedly improves the tracking accuracy as well. Simulation results reveal that the proposed algorithm is superior to that of the MPC filter algorithm.     

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.     

Integrated predictive iterative learning control based on updating reference trajectory for point-to-point tracking

A novel control technique is proposed by combining iterative learning control (ILC) and model predictive control (MPC) with updating-reference trajectory for point-to-point tracking problem of batch process. In this paper, a batch-to-batch updating-reference trajectory, which passes through the desired points, is firstly designed as the tracking trajectory within a batch. The updating control law consists of P-type ILC part and MPC part, in which P-type ILC part can improve the performance by learning from previous executions and MPC part is used to suppress the model perturbations and external disturbances. Convergence properties of the integrated predictive iterative learning control (IPILC) are analyzed theoretically, and the sufficient convergence conditions of output tracking error are also derived for a class of linear systems. Comparing with other point-to-point tracking control algorithms, the proposed algorithm can perform better in robustness. Furthermore, updating-reference relaxes the constraints for system outputs, and it may lead to faster convergence and more extensive range of application than those of fixed-reference control algorithms. Simulation results on typical systems show the effectiveness of the proposed algorithm.     

Consensus seeking via iterative learning for multi‐agent systems with switching topologies and communication time‐delays

This paper deals with the high‐precision consensus seeking problem of multi‐agent systems when they are subject to switching topologies and varying communication time‐delays. By combining the iterative learning control (ILC) approach, a distributed consensus seeking algorithm is presented based on only the relative information between every agent and its local (or nearest) neighbors. All agents can be enabled to achieve consensus exactly on a common output trajectory over a finite time interval. Furthermore, conditions are proposed to guarantee both exponential convergence and monotonic convergence for the resulting ILC processes of multi‐agent consensus systems. In particular, the linear matrix inequality technique is employed to formulate the established convergence conditions, which can directly give formulas for the gain matrix design. An illustrative example is included to validate the effectiveness of the proposed ILC‐motivated consensus seeking algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

初始误差修正的多智能体一致性迭代学习控制

研究了重复运行的分布式多智能体系统在有限时间内的一致性问题。针对具有固定拓扑结构的多智能体系统,在期望轨迹对应的初始状态未知,且系统存在干扰的情况下,引入虚拟领导者技术,提出了一种同时对各智能体的输入和初始状态误差进行迭代修正的分布式学习控制算法。收敛性分析表明,该算法能够消除由于各智能体初始状态和期望轨迹对应的初始状态不同而引起的各智能体输出不能完全跟踪期望轨迹的状况,实现系统在有限时间内的完全跟踪;仿真结果也证明了算法的有效性。     

Robust consensus tracking for a class of high‐order multi‐agent systems

In this paper, we study the robust consensus tracking problem for a class of high‐order multi‐agent systems with unmodelled dynamics and unknown disturbances. A continuous robust state feedback control algorithm is proposed to enable the agents to achieve robust consensus tracking of a desired trajectory. By utilizing Lyapunov analysis methods and an invariance‐like theorem, sufficient conditions for semi‐global asymptotic consensus tracking are established. A robust output feedback control algorithm is designed to obtain a uniformly ultimately bounded consensus tracking result. Numerical simulations are provided to show the effectiveness of the proposed algorithms. Copyright © 2015 John Wiley & Sons, Ltd.     

基于多参数规划的显式模型预测系统设计的可行域扩张算法

基于约束线性优化控制问题的多参数二次规划求解方法, 提出设计显式模型预测控制系统的可行域逐步扩张算法. 首先建立一种求取优化控制问题输出不变集的迭代算法. 以该输出不变集作为多参数规划问题中状态区域约束限制的初始条件, 通过反复求解多参数规划问题和不断改变状态区域约束限制, 能够逐步扩大显式模型预测控制系统的无限时间可行区域, 直到可行域不再继续扩大. 算法收敛时设计得到的显式模型预测控制系统在其所有的状态分区上都是无限时间可行的. 通过数值仿真计算, 验证本文提出算法的有效性.     

V2X环境下基于MPC算法的弯道区域CACC车队轨迹跟踪控制策略

针对CACC(cooperative adaptive cruise control)车队在弯道行驶的安全性和稳定性问题,提出一种V2X(vehicle to everything)环境下基于MPC(model predictive control)算法的弯道区域CACC车队行驶轨迹跟踪策略.首先,分析CACC车队在弯道区域的行驶工况以及纵向平衡问题,并基于牛顿第二定律构建车辆在弯道行驶的车辆动力学模型;其次,CACC车队基于V2X技术实现车车之间状态信息的实时交互,并以基于车辆运动学的MPC算法为基础,引入可变间距的车队安全距离控制模型,提出一种适用于弯道区域的轨迹跟踪模型;最后,通过二次规划进行模型求解.实验分析结果表明:V2X环境下的CACC车队在弯道行驶过程中面对不同的行驶工况能够不同程度地保证车车之间的安全性、稳定性以及驾乘人员的舒适性,有效验证了所提V2X环境下基于MPC算法的弯道区域CACC车队轨迹跟踪策略的可行性.     

Distributed model predictive control of linear systems with persistent disturbances

This article presents a new form of robust distributed model predictive control (MPC) for multiple dynamically decoupled subsystems, in which distributed control agents exchange plans to achieve satisfaction of coupling constraints. The new method offers greater flexibility in communications than existing robust methods, and relaxes restrictions on the order in which distributed computations are performed. The local controllers use the concept of tube MPC – in which an optimisation designs a tube for the system to follow rather than a trajectory – to achieve robust feasibility and stability despite the presence of persistent, bounded disturbances. A methodical exploration of the trades between performance and communication is provided by numerical simulations of an example scenario. It is shown that at low levels of inter-agent communication, distributed MPC can obtain a lower closed-loop cost than that obtained by a centralised implementation. A further example shows that the flexibility in communications means the new algorithm has a relatively low susceptibility to the adverse effects of delays in computation and communication.     

面向自由飞行目标捕获的四旋翼最优轨迹规划

自由飞行目标物捕获作为动态任务，在其被执行的过程中，四旋翼不仅要规划出一条时间最优的追踪轨迹，而且还要根据目标物的位置反馈信息实时对轨迹进行重新规划，以实现在最短的时间内追上目标物.针对这一问题，提出了诱导时间最优MPC （model predictive control）算法用于四旋翼的轨迹规划.该算法通过宽松约束条件下时间最优轨迹的引导，利用MPC的滚动优化策略，可以在每个控制周期内用反馈信息实时求解时间最优的追踪轨迹.为了躲避追踪路径中的障碍物，本文还提出了一种用动态线性约束表示障碍物的方法，以提高障碍物约束下轨迹求解的效率.结合诱导时间最优MPC的算法，可以在线实时地求解出具有障碍物避碰能力的时间最优轨迹.仿真结果表明了本文提出算法的有效性，其高效的计算效率也能满足实际系统对算法实时性的要求.     

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.     

Robust asymptotic model matching and its application to output synchronization of heterogeneous multi-agent systems

Output synchronization of heterogeneous multi-agent systems has been one of the most interesting cooperative control problems. This paper first gives a brief survey of the research on the problem from which we see that the problem can be solved in a two-step manner with the aid of a properly designed local reference for each agent: (i) a controller is designed for each agent to achieve the trajectory regulation of the agent output to its associated reference; (ii) network collaboration is added to achieve consensus among references. In the presence of system uncertainties, the robust trajectory regulation problem in (i) can be solved by an internal model design. In this paper, we formulate a novel robust asymptotic model matching problem which is less conservative than trajectory regulation and can be solved by a static controller not relying on an internal model. Moreover, network collaboration is designed in (ii) within the so-called output communication setting such that consensus among references occurs concurrently with robust asymptotic model matching. As a result, output synchronization of heterogeneous multi-agent systems is achieved with a novel approach.     

非仿射非线性多智能体系统迭代学习一致跟踪

为了解决非仿射非线性多智能体系统在给定时间区间上一致性完全跟踪问题,基于迭代学习控制方法设计一种分布式一致性跟踪控制算法.首先,由引入的虚拟领导者与所有跟随者组成多智能体系统的通信拓扑,其中虚拟领导者的作用是提供期望轨迹.然后,在只有部分跟随者能够获得领导者信息的条件下,利用每个跟随者及其邻居的跟踪误差构造每个跟随者的迭代学习一致性跟踪控制器.同时采用中值定理将非仿射非线性多智能体系统转化仿射形式,并基于压缩映射方法证明所提算法的收敛性,给出算法的收敛条件.理论分析表明,在智能体的非线性函数未知情况下,利用所提算法可以使非仿射非线性多智能体系统在给定时间区间上随迭代次数增加逐次实现一致性完全跟踪.最后,通过仿真算例进一步验证所提算法的有效性.     

Augmented Lagrangian Pattern Search Based Multi‐Agent Model Predictive Control of Rhine‐Meuse Delta

In Large Scale Systems the concept of centrality fails due to the lack of centralized computing capability. The control of such systems has to be performed using multiple control agents. In this case, the matter of interactions among neighboring subsystems needs to be considered. In this paper, a water control system in the Netherlands is studied as a real large scale system. A multi‐agent scheme is applied to control the flow through the system which is decomposed into two interconnected subsystems. Each agent employs a model‐based predictive control (MPC) technique. The model of this large scale system is nonlinear and nonconvex. Therefore, an augmented Lagrangian pattern search optimization algorithm is used to implement multi‐agent MPC for this system. This proposed algorithm is applied by each control agent to solve its own interconnected optimization problem, at each subsystem of whole the water system. Simulation results show the effectiveness of the proposed approach.     

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.     

Periodic event‐triggered control for distributed networked multiagents with asynchronous communication: A predictive control approach

This paper investigates the periodic event‐triggered control problem for distributed networked multiagent systems with interconnected nonlinear dynamics subject to asynchronous communication. A method of state trajectory estimation for the interconnected neighboring agents over each prediction horizon with guaranteed error bounds is addressed to handle the asynchronous communication. Based on it, a distributed robust model predictive control (MPC) is proposed with a distributed periodic event‐triggered scheme for each agent. According to this algorithm, each subsystem generates presumed state trajectories for all its upstream neighbors and computes its own control locally. By checking the designed triggering condition periodically, the optimization problem of MPC will be implemented and solved when the local error of the subsystem exceeds a specified threshold. Then, the optimized control input will be determined and applied until the next time instant when the triggering condition is invoked. Moreover, sufficient condition for ensuring feasibility of the designed algorithm is conducted, along with the analysis of asymptotic stabilization of the closed‐loop system. The illustrative example for a set of coupled Van der Pol oscillators is reported to verify the effectiveness of the proposed approach.     

Conflict-free navigation in unknown urban environments

This paper presents an autonomous exploration method in an unknown environment that uses model predictive control (MPC)-based obstacle avoidance with local map building by onboard sensing. An onboard laser scanner is used to build an online map of obstacles around the vehicle with outstanding accuracy. This local map is combined with a real-time MPC algorithm that generates a safe vehicle path, using a cost function that penalizes the proximity to the nearest obstacle. The adjusted trajectory is then sent to a position tracking layer in the hierarchical unmanned aerial vehicle (UAV) avionics architecture. In a series of experiments using a Berkeley UAV, the proposed approach successfully guided the vehicle safely through the urban canyon.     

Distributed adaptive output consensus control of second-order systems containing unknown non-linear control gains

In this paper, we address the output consensus problem of tracking a desired trajectory for a group of second-order agents on a directed graph with a fixed topology. Each agent is modelled by a second-order non-linear system with unknown non-linear dynamics and unknown non-linear control gains. Only a subset of the agents is given access to the desired trajectory information directly. A distributed adaptive consensus protocol driving all agents to track the desired trajectory is presented using the backstepping technique and approximation technique of Fourier series (FSs). The FS structure is taken not only for tracking the non-linear dynamics but also the unknown portion in the controller design procedure, which can avoid virtual controllers containing the uncertain terms. Stability analysis and parameter convergence of the proposed algorithm are conducted based on the Lyapunov theory and the algebraic graph theory. It is also demonstrated that arbitrary small tracking errors can be achieved by appropriately choosing design parameters. Though the proposed work is applicable for second-order non-linear systems containing unknown non-linear control gains, the proposed controller design can be easily extended to higher-order non-linear systems containing unknown non-linear control gains. Simulation results show the effectiveness of the proposed schemes.