PID控制器参数调整的滚动优化算法

A novel supervised receding horizon optimal scheme is presented for discrete time systems in the process control. In the employing level, PID controller is used, while the receding horizon approach is applied to the optimized level. The considered problem is to optimize the employing level PID controller parameters through minimizing a generalized predictive control criterion. Compared with a fixed parameters PID controller, the proposed algorithm provides well performance over a range of operating condition.     

Robust one-step receding horizon control of discrete-time Markovian jump uncertain systems

This paper proposes a receding horizon control scheme for a set of uncertain discrete-time linear systems with randomly jumping parameters described by a finite-state Markov process whose jumping transition probabilities are assumed to belong to some convex sets. The control scheme for the underlying systems is based on the minimization of the worst-case one-step finite horizon cost with a finite terminal weighting matrix at each time instant. This robust receding horizon control scheme has a more general structure than the existing robust receding horizon control for the underlying systems under the same design parameters. The proposed controller is obtained using semidefinite programming.     

Robust one-step receding horizon control for constrained systems

This paper proposes a robust receding horizon control scheme for discrete-time uncertain linear systems with input and state constraints. The control scheme is based on the minimization of the worst-case one-step finite horizon cost with a finite terminal weighting matrix. It is shown that the proposed receding horizon control robustly asymptotically stabilizes uncertain constrained systems under some matrix inequality conditions on the terminal weighting matrices. This robust receding horizon control scheme has a larger feasible initial-state set and a more general structure than existing robust receding horizon controls for uncertain constrained systems under the same design parameters. The proposed controller is obtained using semidefinite programming. Copyright © 1999 John Wiley & Sons, Ltd.     

Receding horizon H∞ control problems for sampled-data systems§

In this article, the receding horizon H_∞ control problems for sampled-data systems are considered. Since sampled-data systems can be rewritten as equivalent jump systems, the receding horizon H_∞ control problems for time-varying jump systems are considered first and the design methods of a state feedback receding horizon H_∞ controller and an output feedback receding horizon H_∞ controller are given. Then the obtained results are applied to sampled-data systems and the design methods of a state feedback receding horizon H_∞ controller and an output feedback receding horizon H_∞ controller are given. Two numerical examples are given to illustrate the theory.     

Robust receding horizon control of constrained nonlinear systems

We present a method for the construction of a robust dual-mode, receding horizon controller which can be employed for a wide class of nonlinear systems with state and control constraints and model error. The controller is dual-mode. In a neighborhood of the origin, the control action is generated by a linear feedback controller designed for the linearized system. Outside this neighborhood, receding horizon control is employed. Existing receding horizon controllers for nonlinear, continuous time systems, which are guaranteed to stabilize the nonlinear system to which they are applied, require the exact solution, at every instant, of an optimal control problem with terminal equality constraints. These requirements are considerably relaxed in the dual-mode receding horizon controller presented in this paper. Stability is achieved by imposing a terminal inequality, rather than an equality, constraint. Only approximate minimization is required. A variable time horizon is permitted. Robustness is achieved by employing conservative state and stability constraint sets, thereby permitting a margin of error. The resultant dual-mode controller requires considerably less online computation than existing receding horizon controllers for nonlinear, constrained systems     

Numerical optimization method for HJI equations derived from robust receding horizon control schemes and controller design

This paper addresses how to numerically solve the Hamilton-Jacobin-Isaac(HJI)equations derived from the robust receding horizon control schemes.The developed numerical method,the finite dierence scheme with sigmoidal transformation,is a stable and convergent algorithm for HJI equations.A boundary value iteration procedure is developed to increase the calculation accuracy with less time consumption.The obtained value function can be applied to the robust receding horizon controller design of some kind of uncertain nonlinear systems.In the controller design,the finite time horizon is extended into the infinite time horizon and the controller can be implemented in real time.It can avoid the on-line repeated optimization and the dependence on the feasibility of the initial state which are encountered in the traditional robust receding horizon control schemes.     

基于终端不变集的 Markov 跳变系统约束预测控制

针对离散 Markov 跳变系统, 研究带输入输出约束的有限时域预测控制问题. 对于给定预测时域内的每条模态轨迹, 设计控制输入序列, 驱动系统状态到达相应的终端不变集内, 在预测时域外, 则寻求一个虚拟的状态反馈控制器以保证系统的随机稳定性, 在此基础上, 分别给出了以线性矩阵不等式 (LMI) 描述的带输入、输出约束预测控制器的设计方法.     

Stabilization of sampled-data nonlinear systems by receding horizon control via discrete-time approximations

Results on stabilizing receding horizon control of sampled-data nonlinear systems via their approximate discrete-time models are presented. The proposed receding horizon control is based on the solution of Bolza-type optimal control problems for the parametrized family of approximate discrete-time models. This paper investigates both situations when the sampling period T is fixed and the integration parameter h used in obtaining approximate model can be chosen arbitrarily small, and when these two parameters coincide but they can be adjusted arbitrary. Sufficient conditions are established which guarantee that the controller that renders the origin to be asymptotically stable for the approximate model also stabilizes the exact discrete-time model for sufficiently small integration and/or sampling parameters.     

A new approach to stability analysis for constrained finitereceding horizon control without end constraints

We present a new approach to the stability analysis of finite receding horizon control applied to constrained linear systems. By relating the final predicted state to the current state through a bound on the terminal cost, it is shown that knowledge of upper and lower bounds for the finite horizon costs is sufficient to determine the stability of a receding horizon controller. This analysis is valid for receding horizon schemes with arbitrary positive-definite terminal weights and does not rely on the use of stabilizing constraints. The result is a computable test for stability, and two simple examples are used to illustrate its application     

增广非最小状态空间法的稳定平台预测控制研究

针对传统的模型预测控制器鲁棒性较差及模糊PID控制系统比较复杂的问题,提出了利用增广非最小状态空间模型与模型预测控制相结合的稳定平台预测控制。建立了稳定平台广义被控对象的数学模型,以增广形式的非最小状态空间模型为基础,结合滚动时域控制原则和线性二次型最优控制,通过对稳定平台离散模型的非最小状态空间形式进行增广变换,给出了基于Laguerre函数的状态反馈增益矩阵算法,设计了增广非最小状态模型下的预测控制器,实现了对导向钻井稳定平台控制系统的仿真研究。仿真结果表明稳定平台预测控制系统可以很好地满足钻井工程对控制精度和动态特性的要求,而且对有时变性的盘阀摩擦干扰力矩及模型参数摄动具有较强的鲁棒性。     

The stability of constrained receding horizon control

An infinite horizon controller that allows incorporation of input and state constraints in a receding horizon feedback strategy is developed. For both stable and unstable linear plants, feasibility of the contraints guarantees nominal closed-loop stability for all choices of the tuning parameters in the control law. The constraints' feasibility can be checked efficiently with a linear program. It is always possible to remove state constraints in the early portion of the infinite horizon to make them feasible. The controller's implementation requires only the solution of finite-dimensional quadratic programs     

Nonlinear stochastic receding horizon control: stability,robustness and Monte Carlo methods for control approximation

This work considers the stability of nonlinear stochastic receding horizon control when the optimal controller is only computed approximately. A number of general classes of controller approximation error are analysed including deterministic and probabilistic errors and even controller sample and hold errors. In each case, it is shown that the controller approximation errors do not accumulate (even over an infinite time frame) and the process converges exponentially fast to a small neighbourhood of the origin. In addition to this analysis, an approximation method for receding horizon optimal control is proposed based on Monte Carlo simulation. This method is derived via the Feynman–Kac formula which gives a stochastic interpretation for the solution of a Hamilton–Jacobi–Bellman equation associated with the true optimal controller. It is shown, and it is a prime motivation for this study, that this particular controller approximation method practically stabilises the underlying nonlinear process.     

A hardware implementable receding horizon controller forconstrained nonlinear systems

We present a two-phase parallel computing method for obtaining an implementable receding horizon control solution for constrained nonlinear systems. The phase 1 method solves a feasibility problem to find an approximate open-loop admissible control and horizon pair. The phase 2 method successively improves the admissible control to obtain an implementable open-loop receding horizon control solution. We briefly sketch an approach to realizing this two-phase method using VLSI array processors. Solution times for simulation examples estimated on the basis of current VLSI technology confirm that our controller is well suited to the stabilization of real-time processing, fast, constrained nonlinear systems     

LTL receding horizon control for finite deterministic systems

This paper considers receding horizon control of finite deterministic systems, which must satisfy a high level, rich specification expressed as a linear temporal logic formula. Under the assumption that time-varying rewards are associated with states of the system and these rewards can be observed in real-time, the control objective is to maximize the collected reward while satisfying the high level task specification. In order to properly react to the changing rewards, a controller synthesis framework inspired by model predictive control is proposed, where the rewards are locally optimized at each time-step over a finite horizon, and the optimal control computed for the current time-step is applied. By enforcing appropriate constraints, the infinite trajectory produced by the controller is guaranteed to satisfy the desired temporal logic formula. Simulation results demonstrate the effectiveness of the approach.     

鲁棒后退时域控制中HJI方程的数值解法及控制器设计

本文讨论了由不确定非线性系统鲁棒后退时域控制(robust receding horizon control,RRHC)策略导出的Hamilton-Jacobin-Isaac(HJI)方程的求解,提出了一种新的带反曲变换的有限差分算法计算值函数,所提出算法对HJI方程的求解是一种稳定且收敛的算法.同时提出基于边界值迭代的加速过程,加速优化问题的求解,在花费更少计算时间的前提下,提高计算精度.所求得的值函数可直接应用于一类不确定非线性系统鲁棒后退时域控制器的设计,在控制器设计中,传统鲁棒后退时域控制策略中的有限时域被扩展到无限时域,求得的控制器可实时实现,避免对初始点可解性的依赖以及反复在线优化问题.     

Predictive control for networked systems affected by correlated packet loss

In this paper, we consider the predictive control problem of designing receding horizon controllers for networked linear systems subject to random packet loss in the controller to actuator link. The packet dropouts are temporarily correlated in the sense that they obey a Markovian transition model. Our design task is to solve the optimal controller that minimizes a given receding horizon cost function, using the available packet loss history. Due to the correlated nature of the packet loss, standard linear quadratic regulator methods do not apply. We first present the optimal control law by considering the correlations. This controller turns out to depend on the packet loss history and would typically require a large lookup table for implementation when the Markovian order is high. To address this issue, we present and compare several suboptimal design approaches to reduce the number of control laws.     

Q-PSO: Fast Quaternion-Based Pose Estimation from RGB-D Images

This paper investigates the leader–follower formation control problem for a group of networked nonholonomic mobile robots that are subject to bounded time-varying communication delays and an asynchronous clock. First we convert the formation control problem into a trajectory tracking problem, and then a fully distributed unified control framework based on the receding horizon control is implemented to converge the tracking errors. By adding an auxiliary acceleration term into the receding horizon controller, the framework is able to solve the impractical velocity jump problem. Considering the time-varying delays, the timing and order features of the messages are utilized to guarantee their logical correctness. To compensate for the delay effect, an improved control framework that exploits the predictability of the receding horizon controller is proposed. The asynchronous clock problem, which makes the communication delay unmeasurable, is studied. We give a definition of the syn point that is inspired from investigation of the property that messages are received out of order in a bounded time-varying delayed network. A novel method that detects the occurrence of syn points is integrated into the control framework to solve the asynchronous clock problem. Finally the effectiveness of the proposed approaches is demonstrated in the Player/Stage simulation environment.     

线性时序逻辑约束下的滚动时域控制路径规划

针对有限确定性系统中的路径规划问题,本文提出了一种线性时序逻辑约束下的在线实时求解滚动时域控制的新方法。该方法将滚动时域控制方法和满足线性时序逻辑公式的策略相结合,控制目标是在满足高级别任务规范的同时,使收集的累积回报值最大化。其中,在有限时域内的每个时间步长上局部优化回报值,并应用当前时刻计算获得的最优控制序列。通过执行适当的约束,保证控制器产生的无限轨迹满足期望的时序逻辑公式。而且,由于地势影响因子的引入,所建议的方案更接近于真实情况。仿真实验结果验证了文中提出方法的可行性和有效性。     

Stabilization of unknown nonlinear systems using neural networks

This paper deals with stabilization of unknown nonlinear systems using a nonlinear controller made with a backpropagation neural network. Control strategies based on an inverse state neural model built from an off-line learning step are proposed. The proposed strategies can be implemented following two approaches. The first one consists on computing control horizon based on actual state vector and desired one at a future instant. The second approach applies control action in the sense of a receding horizon. Adaptive control has been considered where the updating of the neural controller is accomplished to optimize different control objectives.     

Unconstrained receding-horizon control of nonlinear systems

It is well known that unconstrained infinite-horizon optimal control may be used to construct a stabilizing controller for a nonlinear system. We show that similar stabilization results may be achieved using unconstrained finite horizon optimal control. The key idea is to approximate the tail of the infinite horizon cost-to-go using, as terminal cost, an appropriate control Lyapunov function. Roughly speaking, the terminal control Lyapunov function (CLF) should provide an (incremental) upper bound on the cost. In this fashion, important stability characteristics may be retained without the use of terminal constraints such as those employed by a number of other researchers. The absence of constraints allows a significant speedup in computation. Furthermore, it is shown that in order to guarantee stability, it suffices to satisfy an improvement property, thereby relaxing the requirement that truly optimal trajectories be found. We provide a complete analysis of the stability and region of attraction/operation properties of receding horizon control strategies that utilize finite horizon approximations in the proposed class. It is shown that the guaranteed region of operation contains that of the CLF controller and may be made as large as desired by increasing the optimization horizon (restricted, of course, to the infinite horizon domain). Moreover, it is easily seen that both CLF and infinite-horizon optimal control approaches are limiting cases of our receding horizon strategy. The key results are illustrated using a familiar example, the inverted pendulum, where significant improvements in guaranteed region of operation and cost are noted