Optimal Control of Dynamical Systems Governed by Partial Differential Equations: A Perspective from Real-life Applications ⋆
نویسنده
چکیده
This survey article summarizes some ideas of the two principle procedures for solving optimal control problems governed by partial differential (algebraic) equations: the indirect method or first-optimize-then-discretize approach based on first-order necessary conditions, and the direct method or first-discretize-then-optimize approach based on non-linear programming software. The focus of this paper is to discuss some pros and cons when applications come from real-life problems. It also glances at the main method which currently may have the best chance for online applications in PDE constrained optimization. The demonstrator example deals with the optimal control of a certain type of high temperature fuel cell system.
منابع مشابه
Optimal control of switched systems by a modified pseudo spectral method
In the present paper, we develop a modified pseudospectral scheme for solving an optimal control problem which is governed by a switched dynamical system. Many real-world processes such as chemical processes, automotive systems and manufacturing processes can be modeled as such systems. For this purpose, we replace the problem with an alternative optimal control problem in which the switching t...
متن کاملA New Computational Method for Optimal Control of a Class of Constrained Systems Governed by Partial Differential Equations
A computationally efficient technique for the numerical solution of constrained optimal control problems governed by one-dimensional partial differential equations is considered in this paper. This technique utilizes inversion to map the optimal control problem to a lower dimensional space. Results are presented using the Nonlinear Trajectory Generation software package (NTG) showing that real-...
متن کاملFractional dynamical systems: A fresh view on the local qualitative theorems
The aim of this work is to describe the qualitative behavior of the solution set of a given system of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. In order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. This is done by the extension of...
متن کاملSystematic Discretization of Input/Output Maps and Control of Partial Differential Equations
We present a framework for the direct discretization of the input/output map of dynamical systems governed by linear partial differential equations with distributed inputs and outputs. The approximation consists of two steps. First, the input and output signals are discretized in space and time, resulting in finite dimensional spaces for the input and output signals. These are then used to appr...
متن کاملApplication of the linear Differential Equations on the Plane and Elements of Nonlinear Systems, In Economics
In recent years, it has become increasingly important to incorporate explicit dynamics in economic analysis. These two tools that mathematicians have developed, differential equations and optimal control theory, are probably the most basic for economists to analyze dynamic problems. In this paper I will consider the linear differential equations on the plane (phase diagram) and elements of nonl...
متن کامل