On an Optimal Control Problem With Two-Sided Inequality Constraints Whose Number Exceeds That of the Control Variables

1963 ◽  
Vol 30 (1) ◽  
pp. 146-147
Author(s):  
George Leitmann
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Inequality Constraints ◽  
Control Variables

scholarly journals Prevention of Leptospirosis Infected Vector and Human Population by Multiple Control Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Saeed Islam ◽  
Sher Afzal Khan ◽  
Ilyas Khan ◽  
Sharidan Shafie ◽  
...  
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Human Population ◽  
Cost Effective ◽  
Farm Animals ◽  
Effective Control ◽  
Multiple Control ◽  
Control Variables ◽  
Control Functions

Leptospirosis is an infectious disease that damages the liver and kidneys, found mainly in dogs and farm animals and caused by bacteria. In this paper, we present the optimal control problem applied to a dynamical leptospirosis infected vector and human population by using multiple control variables. First, we show the existence of the control problem and then use analytical and numerical techniques to investigate the existence cost effective control efforts for prevention of indirect and direct transmission of this disease. In order to do this, we consider three control functions two for human and one for vector population. We completely characterize the optimal control problem and compute the numerical solution of the optimality system using an iterative method.

scholarly journals Robust Multi-Objective Singular Optimal Control Ofpenicillin Fermentation Process

2020 ◽  
pp. 23-30
Author(s):  
Gustavo B. Libotte ◽  
Fran S. Lobato ◽  
Gustavo M. Platt ◽  
Francisco D. Moura Neto
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Fermentation Process ◽  
Singular Problem ◽  
Fed Batch ◽  
Control Variables ◽  
Singular Optimal Control ◽  
Multi Objective ◽  
Singular Optimal Control Problem

The determination of optimal feeding profile of fed-batch fermentation requires the solution of a singular optimal control problem. The complexity in obtaining the solution to this singular problem is due to the nonlinear dynamics of the system model, the presence of control variables in linear form and the existence of constraints in both the state and control variables. Traditionally, during the optimization process, uncertainties associated with design variables, control parameters and mathematical model are not considered. In this contribution, a systematic methodology to evaluate uncertainties during the resolution of a singular optimal control problem is proposed. This approach consists of the Multi-objective Optimization Differential Evolution algorithm associated with Effective Mean Concept. The proposed methodology is applied to determine the feed substrate concentration in fed-batch penicillin fermentation process. The robust multi- objective singular optimal control problem consists of maximizing the productivity and minimizing the operation total time.

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.

scholarly journals Optimal Control of a Nonlinear Time-Delay System in Batch Fermentation Process

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yongsheng Yu
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Batch Process ◽  
Delay System ◽  
High Yield ◽  
Time Delay System ◽  
Control Variables ◽  
Terminal Time

The main control goal in batch process is to get a high yield of products. In this paper, to maximize the yield of 1,3-propanediol (1,3-PD) in bioconversion of glycerol to 1,3-PD, we consider an optimal control problem involving a nonlinear time-delay system. The control variables in this problem include the initial concentrations of biomass and glycerol and the terminal time of the batch process. By a time-scaling transformation, we transcribe the optimal control problem into a new one with fixed terminal time, which yields a new nonlinear system with variable time-delay. The gradients of the cost and constraint functionals with respect to the control variables are derived using the costate method. Then, a gradient-based optimization method is developed to solve the optimal control problem. Numerical results show that the yield of 1,3-PD at the terminal time is increased considerably compared with the experimental data.

scholarly journals AN EFFICIENT COMPUTATIONAL APPROACH TO A CLASS OF MINMAX OPTIMAL CONTROL PROBLEMS WITH APPLICATIONS

2009 ◽  
Vol 51 (2) ◽  
pp. 162-177 ◽  
Author(s):  
B. LI ◽  
K. L. TEO ◽  
G. H. ZHAO ◽  
G. R. DUAN
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Problems ◽  
Inequality Constraints ◽  
Necessary Condition ◽  
Computation Method ◽  
Control Problems ◽  
Continuous State ◽  
State Inequality Constraints

AbstractIn this paper, an efficient computation method is developed for solving a general class of minmax optimal control problems, where the minimum deviation from the violation of the continuous state inequality constraints is maximized. The constraint transcription method is used to construct a smooth approximate function for each of the continuous state inequality constraints. We then obtain an approximate optimal control problem with the integral of the summation of these smooth approximate functions as its cost function. A necessary condition and a sufficient condition are derived showing the relationship between the original problem and the smooth approximate problem. We then construct a violation function from the solution of the smooth approximate optimal control problem and the original continuous state inequality constraints in such a way that the optimal control of the minmax problem is equivalent to the largest root of the violation function, and hence can be solved by the bisection search method. The control parametrization and a time scaling transform are applied to these optimal control problems. We then consider two practical problems: the obstacle avoidance optimal control problem and the abort landing of an aircraft in a windshear downburst.

scholarly journals A Simple Exact Penalty Function Method for Optimal Control Problem with Continuous Inequality Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Xiangyu Gao ◽  
Xian Zhang ◽  
Yantao Wang
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Function Method ◽  
Optimal Control Problems ◽  
Optimal Parameter ◽  
Inequality Constraints ◽  
Terminal State ◽  
Control Problems ◽  
Penalty Function Method

We consider an optimal control problem subject to the terminal state equality constraint and continuous inequality constraints on the control and the state. By using the control parametrization method used in conjunction with a time scaling transform, the constrained optimal control problem is approximated by an optimal parameter selection problem with the terminal state equality constraint and continuous inequality constraints on the control and the state. On this basis, a simple exact penalty function method is used to transform the constrained optimal parameter selection problem into a sequence of approximate unconstrained optimal control problems. It is shown that, if the penalty parameter is sufficiently large, the locally optimal solutions of these approximate unconstrained optimal control problems converge to the solution of the original optimal control problem. Finally, numerical simulations on two examples demonstrate the effectiveness of the proposed method.

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