Efficient Solution for the State Avoidance Control Problem on Concurrent Systems Using a Disjunctive Architecture

2006 ◽  
Author(s):  
B. Gaudin
Keyword(s):  
Control Problem ◽  
Efficient Solution ◽  
Concurrent Systems ◽  
The State ◽  
Avoidance Control

Guaranteed Avoidance Control and Holding Control

1982 ◽  
Vol 104 (2) ◽  
pp. 166-172 ◽  
Author(s):  
W. E. Schmitendorf ◽  
B. R. Barmish ◽  
B. S. Elenbogen
Keyword(s):  
Control Problem ◽  
State Space ◽  
The State ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Avoidance Control ◽  
Avoidance Problem

This paper considers the problem of steering the state of a system, in the presence of disturbances, so that it avoids a specified subset of the state space. This subset is called the avoidance set and the problem is called the avoidance control problem. An avoidance control is a control which guarantees that the system does not enter the avoidance set regardless of the disturbance. A necessary condition and a sufficient condition for the existence of an avoidance control are given when the disturbance is subject to magnitude constraints. Closely related to the avoidance problem is the holding problem which is concerned with guaranteeing that the state of the system remains within a specified set. We also reinterpret our conditions for the existence of an avoidance control within the context of the holding problem.

scholarly journals Ana posteriorierror analysis for an optimal control problem with point sources

2018 ◽  
Vol 52 (5) ◽  
pp. 1617-1650 ◽  
Author(s):  
Alejandro Allendes ◽  
Enrique Otárola ◽  
Richard Rankin ◽  
Abner J. Salgado
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Weighted Sobolev Spaces ◽  
Control Variable ◽  
The State ◽  
Point Sources ◽  
Adjoint Equations ◽  
Error Estimator ◽  
A Posteriori

We propose and analyze a reliable and efficienta posteriorierror estimator for a control-constrained linear-quadratic optimal control problem involving Dirac measures; the control variable corresponds to the amplitude of forces modeled as point sources. The proposeda posteriorierror estimator is defined as the sum of two contributions, which are associated with the state and adjoint equations. The estimator associated with the state equation is based on Muckenhoupt weighted Sobolev spaces, while the one associated with the adjoint is in the maximum norm and allows for unbounded right hand sides. The analysis is valid for two and three-dimensional domains. On the basis of the deviseda posteriorierror estimator, we design a simple adaptive strategy that yields optimal rates of convergence for the numerical examples that we perform.

STERILIZATION OF CANNED VISCOUS FOODS: AN OPTIMAL CONTROL APPROACH

2004 ◽  
Vol 14 (03) ◽  
pp. 355-374 ◽  
Author(s):  
L. J. ALVAREZ-VAZQUEZ ◽  
M. MARTA ◽  
A. MARTINEZ
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Nutrient Retention ◽  
Reaction Diffusion ◽  
The State ◽  
Reaction Diffusion Equations ◽  
Boussinesq System ◽  
Temperature Dependent Viscosity ◽  
Control Approach ◽  
Dependent Viscosity

In this paper, we study an optimal control problem with pointwise constraints on state and control, related to sterilization processes involving heat transfer by natural convection. We introduce the mathematical model for the state system, which couples the Boussinesq system for temperature-dependent viscosity and the convection-reaction-diffusion equations, and we set the whole problem as a control problem, assuring the micro-organism reduction, the nutrient retention and the energy saving. The existence and the regularity of the state are studied. Finally, we obtain existence results for the optimal solutions and a first-order optimality condition for their characterization.

scholarly journals Điều khiển thích nghi vị trí trên cơ sở kỹ thuật vi xử lý Phần I: Hệ thống điều chỉnh vị trí nhờ quan sát và phản hồi trạng thái

2018 ◽  
Vol 5 (4) ◽  
pp. 10-16
Author(s):  
Pham Huy Thoa
Keyword(s):  
Control System ◽  
Feedback Control ◽  
Control Problem ◽  
Control Algorithm ◽  
Position Control ◽  
The State ◽  
Control Algorithms ◽  
State Variable ◽  
Load Characteristics ◽  
Positional Control

  In order to investigate different position control algorithms for numerical controlled machines and robots, a positional control system was built on the base of  a microcomputer. In part I, the paper presents the  observer algorithm for  state variable estimation and the state variable feedback control algorithm applied to the position control of a  particular machine-table. With the hardware and software structure of the microcomputer based digital system described in this paper different control algorithms can be  realized flexibly. The position control problem for the plant with variations or  uncertainties of  parameters and load characteristics will be reported in part II.

scholarly journals A problem in control of elastodynamics with piezoelectric effects

2019 ◽  
Vol 40 (4) ◽  
pp. 2839-2870
Author(s):  
Harbir Antil ◽  
Thomas S Brown ◽  
Francisco-Javier Sayas
Keyword(s):  
Control Problem ◽  
Control Variable ◽  
Sufficient Conditions ◽  
The State ◽  
Adjoint Equations ◽  
Elastic Displacement ◽  
Complete Analysis ◽  
Well Posedness ◽  
State Equations ◽  
Piezoelectric Effects

Abstract We consider an optimal control problem where the state equations are a coupled hyperbolic–elliptic system. This system arises in elastodynamics with piezoelectric effects—the elastic stress tensor is a function of elastic displacement and electric potential. The electric flux acts as the control variable and bound constraints on the control are considered. We develop a complete analysis for the state equations and the control problem. The requisite regularity on the control, to show the well-posedness of the state equations, is enforced using the cost functional. We rigorously derive the first-order necessary and sufficient conditions using adjoint equations and further study their well-posedness. For spatially discrete (time-continuous) problems, we show the convergence of our numerical scheme. Three-dimensional numerical experiments are provided showing convergence properties of a fully discrete method and the practical applicability of our approach.

Optimal impulsive control for advertising strategy problems based on a gradient-based PSO algorithm

2018 ◽  
Vol 41 (8) ◽  
pp. 2280-2292 ◽  
Author(s):  
Xiang Wu ◽  
Jinxing Lin ◽  
Kanjian Zhang ◽  
Ming Cheng
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Inequality Constraints ◽  
Pso Algorithm ◽  
The State ◽  
Optimization Techniques ◽  
Advertising Strategy ◽  
Gradient Based ◽  
State Inequality Constraints

This paper considers an optimal advertising strategy problem. This is an important problem in marketing investment for new products in a free market. The main contributions of this paper are as follows. First, the problem is formulated as an optimal control problem of switched impulsive systems with the state inequality constraints, which is different from the existing nonlinear system models. As the complexity of such constraints and the switching instants are unknown, it is difficult to solve this problem by using conventional optimization techniques. To overcome this difficulty, by applying the penalty function, all the state inequality constraints are first written as non-differentiable penalty terms and imposed into the cost function. Then, the penalty terms are smoothed by using a novel smooth function, leading to a smooth optimal control problem with no state inequality constraints, and an improved gradient-based particle swarm optimization (PSO) algorithm is proposed for solving this problem. Error analysis results show that if the adjustable parameter is sufficiently small, the solution of the smooth optimal control problem is approximately equal to the original problem. Finally, a switched impulsive system for beer sales is established to illustrate the effectiveness of the developed algorithm.

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