The optimality of an easily implementable feedback control system: An inverse problem in optimal control theory

AIChE Journal ◽  
1967 ◽  
Vol 13 (5) ◽  
pp. 926-931 ◽  
Author(s):  
Morton M. Denn
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Control System ◽  
Feedback Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Feedback Control System

Feedback control for non-stationary 3D Navier–Stokes–Voigt equations

2020 ◽  
Vol 25 (12) ◽  
pp. 2210-2221
Author(s):  
Biao Zeng
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Feedback Control ◽  
Optimal Control Problem ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Feedback Control System ◽  
Boundedness Result

The goal of this article is to study the feedback control for non-stationary three-dimensional Navier–Stokes–Voigt equations. Based on the existence, uniqueness, and boundedness result of the weak solutions to the equations, we obtain the existence of solutions to the feedback control system. An existence result for an optimal control problem is also given. We illustrate our main result with an evolutionary hemivariational inequality.

scholarly journals A velocity plan with internal feedback control best explains modulation of saccade kinematics during eye-hand coordination

2020 ◽  
Author(s):  
Varsha V ◽  
Atul Gopal ◽  
Sumitash Jana ◽  
Radhakant Padhi ◽  
Aditya Murthy
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Hand Movement ◽  
Control Model ◽  
Internal Feedback ◽  
Endpoint Control ◽  
Saccade Velocity ◽  
Velocity Tracking

ABSTRACTFast movements like saccadic eye movements that occur in the absence of sensory feedback are often thought to be under internal feedback control. In this framework, a desired input in the form of desired displacement signal is widely believed to be encoded in a spatial map of the superior colliculus (SC). This is then converted into a dynamic velocity signal that drives the oculomotor neurons. However, recent evidence has shown the presence of a dynamic signal within SC neurons, which correlates with saccade velocity. Hence, we used models based on optimal control theory to test whether saccadic execution could be achieved by a velocity based internal feedback controller. We compared the ability of a trajectory control model based on velocity to that of an endpoint control model based on final displacement to capture saccade behavior of modulation of peak saccade velocity by the hand movement, independent of the saccade amplitude. The trajectory control model tracking the desired velocity in optimal feedback control framework predicted this saccade velocity modulation better than an endpoint control model. These results suggest that the saccadic system has the flexibility to incorporate a velocity plan based internal feedback control that is imposed by task context.NEW & NOTEWORTHYWe show that the saccade generation system may use an explicit velocity tracking controller when demand arises. Modulation of peak saccade velocity due to modulation of the velocity of the accompanying hand movement was better captured using a velocity tracking stochastic optimal control model compared to an endpoint model of saccade control. This is the first evidence of trajectory planning and control for the saccadic system based on optimal control theory.

Optimization of pyrolytic chromium carbide coating properties

2020 ◽  
pp. 55-64
Author(s):  
N. N. Schitov ◽  
A. A. Lozovan
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Control Theory ◽  
Abrasive Wear ◽  
Chromium Carbide ◽  
Optimal Control Theory ◽  
Direct Problem ◽  
Specific Interaction ◽  
Young Modulus ◽  
Quality Criterion

The paper discusses ways to optimize the properties of pyrolytic chromium carbide coatings (PCCC) for different industries. PCCC applications include protecting surfaces of different parts and units made of various materials against corrosion, sticking, high temperatures, and various types of wear. Such versatility of PCCCs is explained partly by the peculiarities of their structure that is generally a «superlattice» of alternating relatively hard and soft layers of different composition and, accordingly, functional characteristics such as microhardness and Young modulus. These structures with specific periods and layer thickness ratios correspond to the maximum quality criterion of the optimal control theory (OCT) problem, an inverse problem stated on the class of solutions for a direct problem simulating specific interaction, e.g. abrasive wear. At the same time, the direct problem itself, e.g. an indentation description, is an incorrect inverse problem of mathematical physics, and it needs its own optimal strategy to be solved. This results in a hierarchy of optimization algorithms that can be used to obtain best PCCC functional properties. When an abrasive-wear type direct problem cannot be formalized, it is suggested to use a computational-experimental method elaborated by the authors that is also based on OCT. The main focus is on the improvement of the PCCC deposition technology for every specific application using the optimal control theory. To obtain PCCCs that meet these conditions, it is required to take into account the physical and chemical features of precursor pyrolysis as well as the effect of different additives or catalysts in the process development.

scholarly journals Optimal control of feedback control systems governed by systems of evolution hemivariational inequalities

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5205-5220 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Zhenhai Liu ◽  
Jen-Chih Yao ◽  
Yonghong Yao
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Feedback Control ◽  
Control Systems ◽  
Existence Result ◽  
Sufficient Conditions ◽  
Hemivariational Inequalities ◽  
Feedback Control System ◽  
Feedback Control Systems ◽  
Evolution Hemivariational Inequalities

In this paper, we introduce and consider a feedback control system governed by the system of evolution hemivariational inequalities. Several sufficient conditions are formulated by virtue of the properties of multimaps and partial Clarke?s subdifferentials such that the existence result of feasible pairs of the feedback control systems is guaranteed. Moreover, an existence result of optimal control pairs for an optimal control system is also established.

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