A Direct Shooting Method is Equivalent to an Indirect Method

Analytical Initialization of a Continuation-Based Indirect Method for Optimal Control of Endo-Atmospheric Launch Vehicle Systems

In this paper, we propose a strategy to solve endo-atmospheric launch vehicle optimal control problems using indirect methods. More specifically, we combine shooting methods with an adequate continuation algorithm, taking advantage of the knowledge of an analytical solution of a simpler problem. This procedure is resumed in two main steps. We first simplify the physical dynamics to obtain an analytical guidance law which is used as initial guess for a shooting method. Then, a continuation procedure makes the problem converge to the complete dynamics leading to the optimal solution of the origi…

Solving nonlinear optimal control problems with state and control delays by shooting methods combined with numerical continuation on the delays

In this paper we introduce a new procedure to solve nonlinear optimal control problems with delays which exploits indirect methods combined with numerical homotopy procedures. It is known that solving this kind of problems via indirect methods (which arise from the Pontrya-gin Maximum Principle) is complex and computationally demanding because their implementation is faced to two main difficulties: the extremal equations involve forward and backward terms, and besides, the related shooting method has to be carefully initialized. Here, starting from the solution of the non-delayed version of th…

粗糙随机庞特里亚金最大值原理及一种间接打靶法

Rough Stochastic Pontryagin Maximum Principle and an Indirect Shooting Method

该研究推导了高斯粗糙路径驱动RDE系统的随机庞特里亚金最大值原理，提出首个非线性随机最优控制间接打靶法，收敛速度较直接法快10倍。

Numerical solution of optimal control of atherosclerosis using direct and indirect methods with shooting/collocation approach

We present a direct numerical method for the solution of an optimal control problem controlling the growth of LDL, HDL and plaque. The optimal control problem is constrained with a system of coupled nonlinear free and mixed boundary partial differential equations consisting of three parabolics one elliptic and one ordinary differential equations. In the first step, the original problem is transformed from a free boundary problem into a fixed one and from the mixed boundary condition to a Neumann one. Then, employing a fixed point-collocation method, we solve the optimal control problem. In eac…

On Direct vs Indirect Data-Driven Predictive Control

In this work, we compare the direct and indirect approaches to data-driven predictive control of stochastic linear time-invariant systems. The distinction between the two approaches lies in the fact that the indirect approach involves identifying a lower dimensional model from data which is then used in a certainty-equivalent control design, while the direct approach avoids this intermediate step altogether. Working within an optimization-based framework, we find that the suboptimality gap measuring the control performance w.r.t. the optimal model-based control design vanishes with the size of…

关于直接和间接数据驱动LQR控制的Tikhonov正则化

On Tikhonov Regularization for Direct and Indirect Data-Driven LQR Control

本文提出了一种基于正则化协方差参数化的新型正则化方法，用于直接数据驱动LQR控制，有效处理病态问题，并扩展到非线性系统控制。