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Numerical Solution to optimal feedback control by Dynamic Programming Approach:A Local Approximation Algorithm

Journal of Systems Science & Complexity 2017年第4期30卷 782-802页

作者： GUO Bao-Zhu WU Tao-Tao Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences

This paper considers optimal feedback control for a general continuous time finite-dimensional deterministic system with finite horizon cost functional. A practically feasible algorithm to calculate the numerical solution of the optimal feedback control by dynamic programming approach is developed. The highlights of this algorithm are: a) It is based on a convergent constructive algorithm for optimal feedback control law which was proposed by the authors before through an approximation for the viscosity solution of the time-space discretization scheme developed by dynamic programming method; b) The computation complexity is significantly reduced since only values of viscosity solution on some local cones around the optimal trajectory are calculated. Two numerical experiments are presented to illustrate the effectiveness and fastness of the algorithm.

关键词： Curse of dimensionality Hamilton-Jacobi-Bellman equation optimal feedback control upwind finite difference viscosity solutions

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Modeling and optimal feedback control of High Throughput Screening System with Dioid

Modeling and Optimal Feedback Control of High Throughput Scr...

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第30届中国控制与决策会议

作者： Ping Wei Minkai Li School of Electrical and Electronic Engineering Shanghai Institute of Technology

High throughput screening systems（HTS） is a new class of discrete event systems. Max-plus algebra models is extended to dioid models to describe the systems efficiently in both time-domain and event-domain with the help of two-variables series. For efficient control and analysis, this paper models the high throughput screening system with a framework of dioid from time-domain and event-domain at the same time. Then, desired behavior of this model as a control requirement is discussed under the output feedback control structure. While, according to residuation theory,the choice of the desired behavior should meet some certain forms. Pre-controller is designed to solve the special requirement, and the output feedback control structure becomes an optimal feedback control in this paper. Finally, an example is given to demonstrate the efficiency of the model and the control method of applying the aforementioned control structure.

关键词： High Throughput System Dioid Desired Behavior Pre-controller optimal feedback control

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A New Algorithm for Finding Numerical Solutions of optimal feedback control Law

A New Algorithm for Finding Numerical Solutions of Optimal F...

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第25届中国控制会议

作者： Guo Baozhu, Sun Bing Institute of Systems Science, Academy of Mathematics and Systems Science Chinese Academy of Sciences, Beijing 100080 School of Computational and Applied Mathematics, University of the Witwatersrand Private Bag 3, Wits 2050, Johannesburg, South Africa

＜正＞A new algorithm for finding numerical solutions of optimal feedback control of a class of general finite dimensional systems with multi-input is developed. The algorithm is based on the fact that the value function of the optimal control problem is the viscosity solution of its associated Hamilton-Jacobi-Bellman equation. An example that the closed form solutions of optimal feedback control-trajectory pairs are available is validated. It is shown that the numerical solutions completely tally with the analytical solutions.

关键词： optimal feedback control Viscosity Solution Dynamic Programming Numerical Solutionl

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