非线性系统滚动时域控制的性质研究*

针对非线性系统,对滚动时域控制的一些性质进行了研究.首先提出使系统稳定的充分条件;该条件覆盖了当前保证稳定的若干滚动时域控制策略.在此稳定性框架下,对控制系统的次优性、鲁棒性进行了扩展研究,得到系统次优性的一个上届,以及在外界衰减扰动下的鲁棒稳定性     

连续非线性系统预测控制的次优性分析

针对一般连续非线性系统,研究了有终端约束的稳定预测控制策略相对传统最优控 制的次优性问题.通过分析预测控制的有限时域滚动优化性质,得到了预测控制次优性的上 界,并且将该结果应用于连续线性系统,得到了一个量化的次优性评价指标.     

基于HM非线性模型的滚动时域H_∞控制

基于HM(HeterogeneousModel)非线性系统模型,提出并研究了滚动时域H∞控制器的设计.给出了基于H∞性能指标的最优控制律和其存在的充分性条件,该控制律可以保证系统稳定和干扰衰减增益不超过某一上限.然后,为了减少计算量,设计了有上述相同性能保证的次优控制器.     

基于HM非线性模型的滚动时域H∞控制

基于HM(Heterogeneous Model)非线性系统模型,提出并研究了滚动时域H∞控 制器的设计.给出了基于H∞性能指标的最优控制律和其存在的充分性条件,该控制律可以 保证系统稳定和干扰衰减增益不超过某一上限.然后,为了减少计算量,设计了有上述相同性 能保证的次优控制器.     

离散广义系统的H2次优控制

研究了离散广义系统的H2次优控制问题，进行了离散广义系统H2范数的时域分析，得到了该系统的H2范数界的一个矩阵不等式的充分条件，进一步给出了H2次优控制器设计。     

广义系统的H2次优控制问题的一个LMIs条件

研究具有动态输出反馈的连续广义系统的H2次优控制问题.在H2范数的时域计算 方法的基础上,关于连续广义系统进行了H2次优性能分析,得到了满足H2次优性能的线性矩 阵不等式组的充要条件.其次,利用线性矩阵不等式(LMI)方法设计了H2次优动态输出反馈 控制器.最后,通过数值例子进一步说明了该文的设计方法.     

不确定系统的滚动时域H∞控制设计

针对存在状态矩阵、输入矩阵结构化摄动和外成动输入等不确定性的连续线性时变系统,给出滚动时域Ｈ＾∞控制律及其存在性的充分条件。该控制律使系统闭环稳定,且系统对扰动输入的增益不超过某一人为设定的上界。进一步考虑执行机构非线性特性,推导出上述系统当执行机构存在扇区非线性摄动时的稳定滚动时域Ｈ＾∞控制律及其存在性的充分条件。     

离散Markov跳变系统的滚动时域H_∞跟踪控制

针对离散Markov跳变系统,研究滚动时域H∞跟踪控制问题。为便于工程应用,假定系统当前时刻的状态和模态总是可测的,而系统未来时刻的模态是不可知的。利用庞特里亚金极小值原理,构造哈密尔顿函数,求解min-max优化问题,得到当前采样时刻的最优控制作用以及最严峻的外界扰动。控制器的求解可等效为在一组线性矩阵不等式约束条件下,迭代方程的可解性问题。控制律采用滚动时域结构,每次仅施加当前采样时刻计算得到的控制作用,在下一采样时刻将重新计算控制作用。该控制律保证系统在给定H∞扰动抑制水平的情形下,获得最优线性二次型性能指标以及良好的输出跟踪性能。最后仿真示例验证了该方法的可行性和有效性。     

网联车辆协同巡航系统快速滚动时域状态估计

考虑云平台监控下的网联车辆协同自动巡航控制(CACC)系统,提出一种快速滚动时域估计方法.采用网联车队纵向动力学模型描述网联车辆CACC系统,降低网联车辆CACC系统的状态能观性要求.再应用块概念设计滚动时域估计算法的噪声块结构,压缩滚动时域估计问题的优化变量个数,从而减少其在线计算量.进一步,应用李雅普诺夫稳定性定理证明估计误差系统的渐近稳定性.最后以5车网联车队系统仿真验证所提算法的有效性.     

非线性时滞系统次优控制的逐次逼近法

对状态变量含有时滞的非线性系统的次优控制问题进行了研究，提出了一种次优控制的逐次逼近设计方法．针对由最优控制理论导出的既含有时滞项又含有超前项的非线性两点边值问题，构造了其解序列一致收敛于原问题最优解的非齐次线性两点边值问题序列．从而将两点边值问题解序列的有限次迭代结果作为系统的次优控制律．仿真结果表明了所提出方法的有效性．     

Decentralized receding horizon control for large scale dynamically decoupled systems

We present a detailed study on the design of decentralized receding horizon control (RHC) schemes for decoupled systems. We formulate an optimal control problem for a set of dynamically decoupled systems where the cost function and constraints couple the dynamical behavior of the systems. The coupling is described through a graph where each system is a node, and cost and constraints of the optimization problem associated with each node are only function of its state and the states of its neighbors. The complexity of the problem is addressed by breaking a centralized RHC controller into distinct RHC controllers of smaller sizes. Each RHC controller is associated with a different node and computes the local control inputs based only on the states of the node and of its neighbors. We analyze the properties of the proposed scheme and introduce sufficient stability conditions based on prediction errors. Finally, we focus on linear systems and show how to recast the stability conditions into a set of matrix semi-definiteness tests.     

NONLINEAR OPTIMAL CONTROL: A CONTROL LYAPUNOV FUNCTION AND RECEDING HORIZON PERSPECTIVE

Two well known approaches to nonlinear control involve the use of control Lyapunov functions (CLFs) and receding horizon control (RHC), also known as model predictive control (MPC). The on-line Euler-Lagrange computation of receding horizon control is naturally viewed in terms of optimal control, whereas researchers in CLF methods have emphasized such notions as inverse optimality. We focus on a CLF variation of Sontag's formula, which also results from a special choice of parameters in the so-called pointwise minnorm formulation. Viewed this way, CLF methods have direct connections with the Hamilton-Jacobi-Bellman formulation of optimal control. A single example is used to illustrate the various limitations of each approach. Finally, we contrast the CLF and receding horizon points of view, arguing that their strengths are complementary and suggestive of new ideas and opportunities for control design. The presentation is tutorial, emphasizing concepts and connections over details and technicalities.     

General receding horizon control for linear time-delay systems

A general receding horizon control (RHC), or model predictive control (MPC), for time-delay systems is proposed. The proposed RHC is obtained by minimizing a new cost function that includes two terminal weighting terms, which are closely related to the closed-loop stability. The general solution of the proposed RHC is derived using the generalized Riccati method. Furthermore, an explicit solution is obtained for the case where the horizon length is less than or equal to the delay size. A linear matrix inequality (LMI) condition on the terminal weighting matrices is proposed, under which the optimal cost is guaranteed to be monotonically non-increasing. It is shown that the monotonic condition of the optimal cost guarantees closed-loop stability of the RHC. Simulations demonstrate that the proposed RHC effectively stabilizes time-delay systems.     

High‐precision control of tracked field robots in the presence of unknown traction coefficients

Accurate steering through crop rows that avoids crop damage is one of the most important tasks for agricultural robots utilized in various field operations, such as monitoring, mechanical weeding, or spraying. In practice, varying soil conditions can result in off‐track navigation due to unknown traction coefficients so that it can cause crop damage. To address this problem, this paper presents the development, application, and experimental results of a real‐time receding horizon estimation and control (RHEC) framework applied to a fully autonomous mobile robotic platform to increase its steering accuracy. Recent advances in cheap and fast microprocessors, as well as advances in solution methods for nonlinear optimization problems, have made nonlinear receding horizon control (RHC) and receding horizon estimation (RHE) methods suitable for field robots that require high‐frequency (milliseconds) updates. A real‐time RHEC framework is developed and applied to a fully autonomous mobile robotic platform designed by the authors for in‐field phenotyping applications in sorghum fields. Nonlinear RHE is used to estimate constrained states and parameters, and nonlinear RHC is designed based on an adaptive system model that contains time‐varying parameters. The capabilities of the real‐time RHEC framework are verified experimentally, and the results show an accurate tracking performance on a bumpy and wet soil field. The mean values of the Euclidean error and required computation time of the RHEC framework are equal to 0.0423 m and 0.88 ms, respectively.     

Receding horizon control for multi-UAVs close formation control based on differential evolution

Close formation flight is one of the most complicated problems on multi-uninhabited aerial vehicles (UAVs) coordinated control. Based on the nonlinear model of multi-UAVs close formation, a novel type of control strategy of using hybrid receding horizon control (RHC) and differential evolution algorithm is proposed. The issue of multi-UAVs close formation is transformed into several on-line optimization problems at a series of receding horizons, while the differential evolution algorithm is adopted to optim...     

Input-to-state stability of robust receding horizon control with an expected value cost

This paper is concerned with the stability of a class of receding horizon control (RHC) laws for constrained linear discrete-time systems subject to bounded state disturbances and convex state and input constraints. The paper considers the class of finite horizon feedback control policies parameterized as affine functions of the system state, calculation of which can be shown to be tractable via a convex reparameterization. When minimizing the expected value of a finite horizon quadratic cost, we show that the value function is convex. When solving this optimal control problem at each time step and implementing the result in a receding horizon fashion, we provide sufficient conditions under which the closed-loop system is input-to-state stable (ISS).     

Receding horizon control of an F-16 aircraft: A comparative study

A comparison between receding horizon control (RHC) approaches is presented for the longitudinal axis control of an F-16 aircraft. The results suggest that the flexibility provided by a scheduled RHC scheme based on flight condition-dependent linear prediction models is a necessary requirement for achieving good performance as opposed to a single LTI model-based method. The scheduled scheme offers an attractive alternative to a full nonlinear model-based RHC approach by trading off an acceptable degradation in performance to modest computational complexity and real-time implementability.     

Receding horizon guidance laws for constrained missiles with autopilot lags

In this paper, a new stabilizing receding horizon control (RHC) scheme is proposed for linear continuous time-invariant systems with input and state constraints. The control scheme is based on the minimization of the finite horizon cost with a finite terminal weighting matrix subject to constraints. A new algorithm is suggested to implement the RHC scheme for a constrained receding horizon guidance law (CRHG). The proposed CRHG, which does not use information on the time-to-go, is obtained by using linear matrix inequality (LMI) optimization. Through simulation examples, the performance of the proposed CRHG is illustrated.     

基于DHNN的移动域控制策略及应用

为避免基于Riccati方程求解移动域控制问题时复杂的矩阵求逆运算,提出一种基于离散Hopfield网络(DHNN)的移动域控制策略.对每个离散时刻,通过建立DHNN能量函数与移动域线性二次(LQ)性能指标间的等价关系,在线构建相应时刻的DHNN,理论设计能够保证该网络具有稳定性,而且由其稳态输出可获得移动域控制输入.应用于倒立摆平衡控制的仿真实验说明了论文提出的移动域控制策略的正确性及与滚动优化思想相结合实现无限域闭环最优控制的可行性.