Model Predictive Control for Nonlinear Mechanical Systems

9813099 Wen本研究项目涉及使用反馈控制器为各种全驱动和欠驱动机械系统（包括机器人和航天器）开发路径规划方法。 当信息不完全时，该方案能保证闭环系统的渐近稳定性。此外，通过使用内部罚函数，该算法还可以处理不等式约束。 这种类型的反馈控制律可以被认为是一类特殊的模型预测控制（MPC），因为在每个时刻的控制动作是基于未来的轨迹来确定的。 然而，与需要在每个控制时间间隔处求解优化问题的标准MPC方案相比，仅需要计算一个牛顿步长，涉及固定的计算量。 该算法的有效性已被证明在一些困难的例子，包括轮式车辆的运动控制，欠驱动6自由度卫星的稳定，欠驱动机械手的稳定。本文的主要研究内容包括：（1）提出了保证闭环系统稳定性的参数选择规则;（2）量化了系统在模型不完善和外部扰动下的稳定鲁棒裕度;（3）通过参数自适应提高系统的鲁棒性;（4）在梯度算子中利用零空间来避免奇异性和约束处理;（5）在非线性系统中利用零空间来提高系统的鲁棒性。v）发展了在控制计算中选择逼近基的策略，并分析了逼近对收敛的影响，vi）应用于一些涉及非线性力学系统的实验。 ***

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. ***