Differential dynamic programming technique for constrained optimal control

摘要

In Part 1, two approaches for constrained optimal control problems (OCP) using the differential dynamic programming (DDP) are presented. In the present paper, three illustrative examples are used to evaluate the approaches: (1) A linear quadratic problem (LQP) with an inequality constraint on the state variable, (2) a single degree of freedom nonlinear impact absorber with an inequality constraint on the state variable, and (3) a linear structural control problem with inequality constraints on the state and control variables. The solutions are compared with the results available in the literature. It is found that the DDP is far more efficient compared to the NLP approach. Also, the continuous-time DDP formulation is superior to the discrete-time formulation. The continuous-time DDP with the multiplier approach is recommended for applications since it is more general compared to the one based on quadratic programming.