Allocating the value of an open-loop optimal control problem between its state variables

2009 ◽  
Vol 30 (2) ◽  
pp. 209-216
Author(s):  
Axel Pierru ◽  
Damien Gaumont
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Open Loop ◽  
State Variables

scholarly journals Prospects on Solving an Optimal Control Problem with Bounded Uncertainties on Parameters using Interval Arithmetics

2021 ◽  
Author(s):  
Etienne Bertin ◽  
Elliot Brendel ◽  
Bruno Hérissé ◽  
Julien Alexandre dit Sandretto ◽  
Alexandre Chapoutot
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Closed Loop ◽  
Minimum Principle ◽  
Open Loop ◽  
Pontryagin Minimum Principle ◽  
Interval Method ◽  
Bounded Uncertainties ◽  
The Given

An interval method based on the Pontryagin Minimum Principle is proposed to enclose the solutions of an optimal control problem with embedded bounded uncertainties. This method is used to compute an enclosure of all optimal trajectories of the problem, as well as open loop and closed loop enclosures meant to enclose a concrete system using an optimal control regulator with inaccurate knowledge of the parameters. The differences in geometry of these enclosures are exposed, as well as some applications. For instance guaranteeing that the given optimal control problem will yield a satisfactory trajectory for any realization of the uncertainties or on the contrary that the problem is unsuitable and needs to be adjusted.

The Optimal Adaptive Sampled-Data Regulator

1974 ◽  
Vol 96 (3) ◽  
pp. 334-340
Author(s):  
R. A. Schlueter ◽  
A. H. Levis
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Closed Loop ◽  
Open Loop ◽  
Sampled Data ◽  
Threshold Values ◽  
Regulator Problem

The optimal control problem for sampled-data processes in which sampling is not triggered by a timer, but occurs when one or more outputs attain preset threshold values is formulated as an adaptive optimal sampled-data regulator problem. Both open loop and closed loop solutions are determined and a comparison of a system’s performance with adaptive and with periodic sampling is presented.

scholarly journals Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems of Markovian regime switching system

2021 ◽  
Author(s):  
Xin Zhang ◽  
Xun Li ◽  
Jie Xiong
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Regime Switching ◽  
Closed Loop ◽  
Open Loop ◽  
Switching System ◽  
Linear Quadratic ◽  
Markovian Regime Switching ◽  
Markovian Regime

This paper investigates the stochastic linear quadratic (LQ, for short) optimal control problem of Markovian regime switching system. The representation of the cost functional for the stochastic LQ optimal control problem of Markovian regime switching system is derived by the technique of It{\^o}'s formula with jumps. For the stochastic LQ optimal control problem of Markovian regime switching system, we establish the equivalence between the open-loop (closed-loop, resp.) solvability and the existence of an adapted solution to the corresponding forward-backward stochastic differential equation with constraint (the existence of a regular solution to Riccati equations). Also, we analyze the interrelationship between the strongly regular solvability of Riccati equations and the uniform convexity of the cost functional. Finally, we present an example which is open-loop solvable but not closed-loop solvable.

scholarly journals Sparse Optimal Control for Fractional Diffusion

2018 ◽  
Vol 18 (1) ◽  
pp. 95-110 ◽  
Author(s):  
Enrique Otárola ◽  
Abner J. Salgado
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
A Priori ◽  
Control Variable ◽  
Fractional Diffusion ◽  
State Equation ◽  
Solution Technique ◽  
State Variables ◽  
Regularity Results

AbstractWe consider an optimal control problem that entails the minimization of a nondifferentiable cost functional, fractional diffusion as state equation and constraints on the control variable. We provide existence, uniqueness and regularity results together with first-order optimality conditions. In order to propose a solution technique, we realize fractional diffusion as the Dirichlet-to-Neumann map for a nonuniformly elliptic operator and consider an equivalent optimal control problem with a nonuniformly elliptic equation as state equation. The rapid decay of the solution to this problem suggests a truncation that is suitable for numerical approximation. We propose a fully discrete scheme: piecewise constant functions for the control variable and first-degree tensor product finite elements for the state variable. We derive a priori error estimates for the control and state variables.

scholarly journals Finite Element Approximation of Optimal Control Problem with Weighted Extended B-Splines

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 452 ◽  
Author(s):  
Madiha Sana ◽  
Muhammad Mustahsan
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
State Variables ◽  
B Splines ◽  
Regularity Of Solution ◽  
Distinct Aspect

In this research article, an optimal control problem (OCP) with boundary observations is approximated using finite element method (FEM) with weighted extended B-splines (WEB-splines) as basis functions. This type of OCP has a distinct aspect that the boundary observations are outward normal derivatives of state variables, which decrease the regularity of solution. A meshless FEM is proposed using WEB-splines, defined on the usual grid over the domain, R 2 . The weighted extended B-spline method (WEB method) absorbs the regularity problem as the degree of the B-splines is increased. Convergence analysis is also performed by some numerical examples.

A Simple Technique for the Minimum Mass Design of Continuous Structural Members

1977 ◽  
Vol 44 (2) ◽  
pp. 285-290 ◽  
Author(s):  
M. Foley ◽  
S. J. Citron
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimization Problem ◽  
Simple Technique ◽  
Minimum Mass ◽  
Structural Members ◽  
State Variables ◽  
Simply Supported ◽  
Euler Buckling

A technique for determining the minimum mass design of continuous structural members is presented. The method involves formulating the minimum mass design problem as an optimal control problem, transforming the differential equations modeling the member into a penalty function, and then representing the state variables in terms of a Ritz-type expansion and discretizing to reduce the original optimal control problem to a parameter optimization problem. The technique is applied to determine the optimal design of a simply supported beam with fixed fundamental frequency of free vibration and a fixed-free column with specified Euler buckling load.

scholarly journals Solving Optimal Control Linear Systems by Using New Third kind Chebyshev Wavelets Operational Matrix of Derivative

2014 ◽  
Vol 11 (2) ◽  
pp. 229-234
Author(s):  
Baghdad Science Journal
Keyword(s):  
Optimal Control ◽  
Linear System ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Problems ◽  
Operational Matrix ◽  
Control Problems ◽  
State Variables ◽  
Algebraic Equations ◽  
Chebyshev Wavelets

In this paper, a new third kind Chebyshev wavelets operational matrix of derivative is presented, then the operational matrix of derivative is applied for solving optimal control problems using, third kind Chebyshev wavelets expansions. The proposed method consists of reducing the linear system of optimal control problem into a system of algebraic equations, by expanding the state variables, as a series in terms of third kind Chebyshev wavelets with unknown coefficients. Example to illustrate the effectiveness of the method has been presented.

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