An Extension of Interior Point Differential Dynamic Programming for Optimal Control Problems with Second-Order Conic Constraints

초록

This paper presents the second-order conic IPDDP (SOC-IPDDP) that modifies interior point differential dynamic programming (IPDDP) to explicitly handle second-order conic constraints. Differential dynamic programming (DDP) has been widely used to solve nonlinear optimal control problems in control and robotics. However, DDP has a big drawback that it cannot handle hard constraints and constraints are usually encoded softly as parts of the cost functions. To overcome this constraint-handling limitation of DDP, interior point differential dynamic programming (IPDDP) is proposed to deal with hard constraints using the interior point method. In this paper, we extend IPDDP to efficiently take care of second-order conic constraints by exploiting their algebraic structures. For demonstration, the performances of SOC-IPDDP are compared with IPDDP in the planar rocket landing optimal control problem. It is shown that the proposed SOC-IPDDP has a comparable convergence rate to the existing IPDDP and is less sensitive to the changes in the parameters of the cost function. Copyright © The Korean Institute of Electrical Engineers.

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