Model Predictive Control for Nonlinear Mechanical Systems

9813099文本研究项目涉及使用反馈控制器开发各种全驱动和欠驱动机械系统的路径规划方法，包括机器人和航天器。该方案可以保证在信息不完全的情况下闭环的渐近稳定性。此外，该算法还可以利用内罚函数来处理不等式约束。这种类型的反馈控制律可以看作是一类特殊的模型预测控制（MPC），因为每个时间实例的控制动作是根据未来轨迹确定的。然而，与标准MPC方案需要在每个控制时间间隔内解决一个优化问题相比，只需计算一个牛顿步，涉及固定的计算量。该算法的有效性已经在一些困难的例子中得到了证明，包括轮式车辆的运动学控制、欠驱动六自由度卫星的稳定以及欠驱动机械手的稳定。本文拟开展的研究重点包括：1)建立保证闭环稳定性的算法参数选择规则；Ii)量化向量场由于模型不完善和外部干扰而受到扰动时的稳定性鲁棒裕度；Iii)通过参数自适应增强鲁棒性；Iv)利用梯度算子中的零空间进行奇点规避和约束处理；V)制定控制计算中选择近似基的策略，并分析近似对收敛的影响，vi)应用于涉及非线性机械系统的一些实验。＊＊＊

9813099 Wen This research project deals with the development of path planning methods using a feedback controller for a variety of fully and under-actuated mechanical systems, including robots and spacecrafts. The proposed scheme can guarantee the closed-loop asymptotic stability when information is imperfect. Furthermore, by using interior penalty functions, inequality constraints can also be handled by the algorithm. This type of feedback control law can be considered as a special class of model predictive control (MPC), since the control action at each time instance is determined based on the future trajectory. However, in contrast with the standard MPC schemes where an optimization problem needs to be solved at each control time interval, only one Newton step needs to be computed involving a fixed amount of computation. The efficacy of this algorithm has been demonstrated on a number of difficult examples, including the kinematic control of wheeled vehicles, stabilization of underactuated 6-DOF satellites, and stabilization of underactuated manipulators. The key research thrusts in the proposed research include: i)develop parameter selection rule in the algorithm that will grarantee closed loop stability; ii) quantify the stability robustness margin when the vector field is perturbed due to model imperfection and external disturbances; iii)enhance robustness through parameter adaptation; iv)utilize null space in the gradient operator for singularity avoidance and constraint handling; v)develop stategies for choosing the approximation basis in control computation and analyze the effect of approximation on convergences, and vi) apply to a number of experiments involving nonlinear mechanical systems. ***