(A) study on the state dependent riccati equation based optimal controller

Abstract

The State-Dependent Riccati Equation(SDRE) is a technique that has been recently proposed as a nonlinear optimal control. Despite the benefits arising from its flexibility, the SDRE method places a high demand on the computational load of real-time applications, which is one of its most significant drawbacks. We discuss a new nonlinear feedback, which eventually converges to a conventional SDRE-based optimal controller. The proposed controller is derived by direct forward integration of a proposed SDRE. This enables a fast computation time, and so is applicable to real-time applications. For a state-dependent system, the proposed controller may be an alternative candidate to a conventional SDRE-based optimal controller if the system is slow-varying to different states. To cope with a fast-varying system, we have introduced a deviation index, which indicates the extent of deviation of the proposed controller from the solution of a conventional SDRE-based optimal controller. Whenever the index exceeds a designated bound, the controller is initialized to the conventional SDRE optimal value. Using the deviation index, a designer can achieve a compromise between fast computation time and enhanced optimality. However, since the computation load instantaneously increases at the switching action point, we proposed the varying system matrix, which is one of the benefits of the conventional SDRE. The appropriate choice of the system matrix enables the proposed controller to be more close to the true optimal solution. We have applied the proposed controller to a numerical nonlinear system, a nonlinear benchmark problem (Langson and Alleyne 1999) and a numerical model of an AUV called ODIN (Choi et al. 1995) to evaluate the feasibility of the given strategy.