水面船舶航迹稳定性的最优控制研究

Research on Optimal Control for Trajectory Stability of Surface Vessels

不具备侧向推进器的水面船舶是一类典型的欠驱动系统,对这类船舶稳定性的研究是其能够在水面安全行驶的基础。针对欠驱动船舶的航迹稳定性控制问题,提出一种Gauss伪谱法与遗传算法相结合的混合优化策略。首先,在船舶水平面运动的运动学和动力学模型的基础上,对欠驱动船舶系统的最优控制问题进行描述。然后,利用Gauss伪谱法将最优控制问题离散为非线性规划问题,采用遗传算法求解在较少离散节点时状态变量和控制变量对应的可行解。最后,在更多的离散节点处离散这些设计变量,作为序列二次规划算法的初值,进而求解欠驱动船舶系统的优化航行轨迹和最优控制输入。通过数值仿真,系统优化航行轨迹光滑平稳,最优控制输入也能很好地满足约束条件,仿真结果验证了上述混合优化策略的有效性。

A surface vessel equipped with no side thruster is a typical underaetuated system, and its stability is the basis for safe sailing on the water. A hybrid optimization strategy based on Gauss pseudospectral method （ GPM ） and genetic algorithm （GA） was presented for the stability control of an underactuated surface vessel. First, the optimal control problem was formulated based on the kinematic and dynamic equations of the system. Then, the optimal control problem was transformed into a nonlinear programming problem based on GPM. By using fewer discrete points, GA was employed to calculate the feasible solution of the states and controls. Finally, these variables were discretized at more discrete points and used as the initial values of sequential quadratic programming （SQP） algorithm, the optimal trajectory and the optimal control inputs of the system were obtained. Through numerical simulation, the optimal trajectory of the system is stable with no detours, and the control inputs satisfy the constraints well. The results demonstrate the effectiveness of the hybrid optimization strategy.