Optimal control of a new mechanochemical model with state constraint

2021 ◽  
Author(s):  
Changchun Liu ◽  
Xiaoli Zhang
Keyword(s):  
Optimal Control ◽  
State Constraint ◽  
Mechanochemical Model

scholarly journals On geometric duality for state-constrained control problems

1979 ◽  
Vol 20 (2) ◽  
pp. 301-312
Author(s):  
T.R. Jefferson ◽  
C.H. Scott
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
State Constraints ◽  
Strong Duality ◽  
State Constraint ◽  
Continuous Functions ◽  
Control Problems ◽  
Absolutely Continuous Functions ◽  
Pure State Constraints ◽  
Constrained Control Problems

For convex optimal control problems without explicit pure state constraints, the structure of dual problems is now well known. However, when these constraints are present and active, the theory of duality is not highly developed. The major difficulty is that the dual variables are not absolutely continuous functions as a result of singularities when the state trajectory hits a state constraint. In this paper we recognize this difficulty by formulating the dual probram in the space of measurable functions. A strong duality theorem is derived. This pairs a primal, state constrained convex optimal control problem with a dual convex control problem that is unconstrained with respect to state constraints. In this sense, the dual problem is computationally more attractive than the primal.

scholarly journals Production and process management: An optimal control approach

2016 ◽  
Vol 26 (3) ◽  
pp. 331-342 ◽  
Author(s):  
Haider Biswas ◽  
Ahad Ali
Keyword(s):  
Optimal Control ◽  
Process Management ◽  
Nonlinear Dynamical Systems ◽  
State Constraint ◽  
Control Technique ◽  
Optimal Control Strategy ◽  
Nonlinear Dynamical ◽  
Control Approach ◽  
Time Operation ◽  
Operation Process

Optimal control and efficient management of industrial products are the key for sustainable development in industrial and process engineering. It is well-known that proper maintenance of process performance, ensuring the quality products after a long time operation of the system, is desirable in any industry. Nonlinear dynamical systems may play crucial role to appropriately design the model and obtain optimal control strategy in production and process management. This paper deals with a mathematical model in terms of ordinary differential equations (ODEs) that describe control of production and process arising in industrial engineering. The optimal control technique in the form of maximum principle, used to control the quality products in the operation processes, is applied to analyze the model. It is shown that the introduction of state constraint can be advantageous for obtaining good products during the longer operation process. We investigate the model numerically, using some known nonlinear optimal control solvers, and we present the simulation results to illustrate the significance of introducing state constraint onto the dynamics of the model.

Optimal control strategy for the immunotherapeutic treatment of HIV infection with state constraint

2019 ◽  
Vol 40 (4) ◽  
pp. 807-818 ◽  
Author(s):  
Md. Haider Ali Biswas ◽  
Md. Mohidul Haque ◽  
Uzzwal Kumar Mallick
Keyword(s):  
Optimal Control ◽  
Hiv Infection ◽  
Control Strategy ◽  
State Constraint ◽  
Optimal Control Strategy

Human Driver Modeling Based on Analytical Optimal Solutions: Stopping Behaviors at the Intersections

2020 ◽  
Vol 1 (1) ◽  
Author(s):  
Jihun Han ◽  
Dominik Karbowski ◽  
Namdoo Kim ◽  
Aymeric Rousseau
Keyword(s):  
Optimal Control ◽  
State Constraint ◽  
Driver Model ◽  
Optimal Solutions ◽  
Driving Behaviors ◽  
Human Driver ◽  
Proposed Model ◽  
Wide Range ◽  
Instrumented Vehicle ◽  
Road Testing

Abstract Safe and energy-efficient driving of connected and automated vehicles (CAVs) must be influenced by human-driven vehicles. Thus, to properly evaluate the energy impacts of CAVs in a simulation framework, a human driver model must capture a wide range of real-world driving behaviors corresponding to the surrounding environment. This paper formulates longitudinal human driving as an optimal control problem with a state constraint imposed by the vehicle in front. Deriving analytically optimal solutions by employing optimal control theory can capture longitudinal human driving behaviors with low computational burden, and adding the state constraint can assist with describing car-following features while anticipating behaviors of the vehicle in front. We also use on-road testing data collected by an instrumented vehicle to validate the proposed human driver model for stop scenarios at intersections. Results show that vehicle stopping trajectories of the proposed model are well matched with those of experimental data.

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