Initialization of the Shooting Method via the Hamilton-Jacobi-Bellman Approach
نویسندگان
چکیده
The aim of this paper is to investigate from the numerical point of view the coupling of the Hamilton-Jacobi-Bellman (HJB) equation and the Pontryagin minimum principle (PMP) to solve some control problems. A rough approximation of the value function computed by the HJB method is used to obtain an initial guess for the PMP method. The advantage of our approach over other initialization techniques (such as continuation or direct methods) is to provide an initial guess close to the global minimum. Numerical tests involving multiple minima, discontinuous control, singular arcs and state constraints are considered.
منابع مشابه
A New Near Optimal High Gain Controller For The Non-Minimum Phase Affine Nonlinear Systems
In this paper, a new analytical method to find a near-optimal high gain controller for the non-minimum phase affine nonlinear systems is introduced. This controller is derived based on the closed form solution of the Hamilton-Jacobi-Bellman (HJB) equation associated with the cheap control problem. This methodology employs an algebraic equation with parametric coefficients for the systems with s...
متن کاملCoupling MPC and HJB for the Computation of POD-based Feedback Laws
In this paper we use a reference trajectory computed by a model predictive method to shrink the computational domain where we set the Hamilton-Jacobi Bellman (HJB) equation. Via a reduced-order approach based on proper orthogonal decomposition(POD), this procedure allows for an efficient computation of feedback laws for systems driven by parabolic equations. Some numerical examples illustrate t...
متن کاملAn Optimal Control Approach to Robust Control of Nonlinear Spacecraft Rendezvous System with Θ-d Technique
In this paper, a new optimal robust control design approach is proposed for the task of spacecraft rendezvous such that both the stabilization and optimal performance are achieved. An approximate closed-form solution to the nonlinear optimal control problem is obtained by employing the θ-D technique, which is derived based on an approximate solution to the Hamilton-Jacobi-Bellman equation obtai...
متن کاملApproximations to Optimal Feedback Control Using a Successive Wavelet Collocation Algorithm
Wavelets, which have many good properties such as time/freqency localization and compact support, are considered for solving the Hamilton-Jacobi-Bellman (HJB) equation as appears in optimal control problems. Specifically, we propose a Successive Wavelet Collocation Algorithm (SWCA) that uses interpolating wavelets in a collocation scheme to iteratively solve the Generalized-Hamilton-Jacobi-Bell...
متن کاملMultitime linear-quadratic regulator problem based on curvilinear integral
This paper interrelates the performance criteria involving path independent curvilinear integrals, the multitime maximum principle, the multitime Hamilton-Jacobi-Bellman PDEs and the multitime dynamic programming, to study the linear-quadratic regulator problems and to characterize the optimal control by means of multitime variant of the Riccati PDE that may be viewed as a feedback law. Section...
متن کامل