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

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.