分段状态约束非线性预测控制数值算法研究

Research on numerical algorithms for nonlinear predictive control problems based on segmented state constraints

针对含分段状态约束的非线性预测控制问题,在状态约束隐式法基础上提出了一种改进的快速数值算法。通过平滑处理将分段状态约束转化为与目标函数相同的正则形式,转化后的状态约束连续可微,从而可以由相同Hamiltonian方法计算目标函数和状态约束函数对控制参数的一阶导数。仿真结果表明,状态转换法能够求解双足机器人非线性预测控制问题。与惩罚函数法相比,状态转换法寻优时间短,数值最优解是所有约束范围的内点,从而证明了该方法的有效性。

To solve nonlinear model predictive control（NMPC） problems based on segmented state constraints, an improved quick numerical method is proposed. Through smoothing process, the segmented state constraints are transformed into the same canonical form as the cost function, which is continuous and differential. Thus the first order derivative of both the cost function and state constraints with respect to control parameters can be computed by same Hamiltonian method. Simulation results show that the state transformation method could tackle the NMPC problem of biped robots. Compared with the penalty function method, the state transformation method needs less computational time, and the computed optimal solution is the inner point of restricted regions, thus verifying the effectiveness of this method.