Inverse Optimal Control with Continuous Updating for a Steering Behavior Model with Reference Trajectory

Abstract

Most real control processes continuously evolve in time and a participant may not have all the information about the process at the time of its initiation. For example, a driver only has local information about the curvature of a road or any obstacles that might necessitate a lane change. The continuous updating approach allows us to arrive at models accounting for the limited information available to subjects during the decision making process. Previously, authors have considered many variations and methods for applying the continuous information updating approach: optimality conditions for equilibrium and cooperative strategies were constructed for the linear-quadratic case [18, 20], the Hamilton-Jacobi-Belman equation [29, 30], Pontryagin’s maximum principle [31, 43]. Also an application of the continuous updating approach was introduced for the general inverse optimal control problem with continuous updating in the paper [27], where the continuous updating was used for identifying cost function parameters from measured data and also the value of the information horizon. In this paper, we apply a continuous updating approach to a special and practical case of an inverse optimal control problem of determining the behavior of a driver while driving along a reference trajectory. Here the inverse optimal control problem becomes nonautonomous since the reference trajectory is included in the objective function of the driver as a function of time. The real motion data from the steering wheel driving simulator is used and the conclusion is drawn.