scholarly journals Approximately Optimal Control of Nonlinear Dynamic Stochastic Problems with Learning: The OPTCON Algorithm

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 181
Author(s):  
Dmitri Blueschke ◽  
Viktoria Blueschke-Nikolaeva ◽  
Reinhard Neck
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Numerical Solutions ◽  
Optimization Problems ◽  
Economic Models ◽  
Open Loop ◽  
Parameter Uncertainties ◽  
Information Patterns ◽  
Loop Feedback ◽  
Dynamic Stochastic

OPTCON is an algorithm for the optimal control of nonlinear stochastic systems which is particularly applicable to economic models. It delivers approximate numerical solutions to optimum control (dynamic optimization) problems with a quadratic objective function for nonlinear economic models with additive and multiplicative (parameter) uncertainties. The algorithm was first programmed in C# and then in MATLAB. It allows for deterministic and stochastic control, the latter with open loop (OPTCON1), passive learning (open-loop feedback, OPTCON2), and active learning (closed-loop, dual, or adaptive control, OPTCON3) information patterns. The mathematical aspects of the algorithm with open-loop feedback and closed-loop information patterns are presented in more detail in this paper.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

Passive optimal feedback control of an articulated flexible arm

2020 ◽  
pp. 107754632095676
Author(s):  
Raja Tebbikh ◽  
Hicham Tebbikh ◽  
Sihem Kechida
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Closed Loop ◽  
Open Loop ◽  
Optimal Feedback Control ◽  
Convolution Operators ◽  
High Frequencies ◽  
Zero Initial Condition ◽  
Flexible Arm ◽  
Euler Bernoulli Beam

This article deals with stabilization and optimal control of an articulated flexible arm by a passive approach. This approach is based on the boundary control of the Euler–Bernoulli beam by means of wave-absorbing feedback. Due to the specific propagative properties of the beam, such controls involve long-memory, non-rational convolution operators. Diffusive realizations of these operators are introduced and used for elaborating an original and efficient wave-absorbing feedback control. The globally passive nature of the closed-loop system gives it the unconditional robustness property, even with the parameters uncertainties of the system. This is not the case in active control, where the system is unstable, because the energy of high frequencies is practically uncontrollable. Our contribution comes in the achievement of optimal control by the diffusion equation. The proposed approach is original in considering a non-zero initial condition of the diffusion as an optimization variable. The optimal arm evolution, in a closed loop, is fixed in an open loop by optimizing a criterion whose variable is the initial diffusion condition. The obtained simulation results clearly illustrate the effectiveness and robustness of the optimal diffusive control.

scholarly journals Linear-Quadratic Stackelberg Game for Mean-Field Backward Stochastic Differential System and Application

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Kai Du ◽  
Zhen Wu
Keyword(s):  
Optimal Control ◽  
Differential System ◽  
Optimization Problems ◽  
Stackelberg Game ◽  
Mean Field ◽  
Open Loop ◽  
Stackelberg Equilibrium ◽  
Linear Quadratic ◽  
Stackelberg Differential Game ◽  
Lq Optimal Control

This paper is concerned with a new kind of Stackelberg differential game of mean-field backward stochastic differential equations (MF-BSDEs). By means of four Riccati equations (REs), the follower first solves a backward mean-field stochastic LQ optimal control problem and gets the corresponding open-loop optimal control with the feedback representation. Then the leader turns to solve an optimization problem for a 1×2 mean-field forward-backward stochastic differential system. In virtue of some high-dimensional and complicated REs, we obtain the open-loop Stackelberg equilibrium, and it admits a state feedback representation. Finally, as applications, a class of stochastic pension fund optimization problems which can be viewed as a special case of our formulation is studied and the open-loop Stackelberg strategy is obtained.

Feedback and Mapping Control of Natural Gas Engines

2002 ◽  
Author(s):  
Greg Sorge
Keyword(s):  
Natural Gas ◽  
Control Systems ◽  
Closed Loop ◽  
Open Loop ◽  
Natural Gas Engines ◽  
Feedback Type ◽  
History Of ◽  
Loop Feedback ◽  
Closed Loop Feedback ◽  
The 19Th Century

Automatic controls have been used on all types of machinery since the first complicated machines became popular in the 19th century. Controls are used to maintain pressures, temperatures, operating speeds, flows and many other operating parameters. Natural gas engines have used a variety of controls for various purposes since the first natural gas engines were produced. This paper will discuss the history of mechanical controls used on natural gas engines and the introduction and application of electronic controls. The paper will discuss open loop (mapping) and closed loop (feedback) type controls and common applications of each. Mechanical control systems such as governors, fuel regulators, fuel mixing valves, thermostats, and turbocharger wastegates will be discussed and classified as open or closed loop controls. Electronic control systems such as governors, air/fuel ratio controls, detonation controls, and turbocharger controls will also be discussed and classified. This paper will also discuss state of the art controls which perform numerous functions to get desired performance, and can be communicated with remotely.

scholarly journals Closed-loop feedback control for microfluidic systems through automated capacitive fluid height sensing

2017 ◽  
Author(s):  
L. R. Soenksen ◽  
T. Kassis ◽  
M. Noh ◽  
L.G. Griffith ◽  
D.L. Trumper
Keyword(s):  
Feedback Control ◽  
Closed Loop ◽  
Cost Effective ◽  
Capacitive Sensor ◽  
Open Loop ◽  
Small Scale ◽  
Microfluidic Systems ◽  
Wide Range ◽  
Loop Feedback ◽  
Closed Loop Feedback

AbstractPrecise fluid height sensing in open-channel microfluidics has long been a desirable feature for a wide range of applications. However, performing accurate measurements of the fluid level in small-scale reservoirs (<1mL) has proven to be an elusive goal, especially if direct fluid-sensor contact needs to be avoided. In particular, gravity-driven systems used in several microfluidic applications to establish pressure gradients and impose flow remain open-loop and largely unmonitored due to these sensing limitations. Here we present an optimized self-shielded coplanar capacitive sensor design and automated control system to provide submillimeter fluid-height resolution (~250 μm) and control of small-scale open reservoirs without the need for direct fluid contact. Results from testing and validation of our optimized sensor and system also suggest that accurate fluid height information can be used to robustly characterize, calibrate and dynamically control a range of microfluidic systems with complex pumping mechanisms, even in cell culture conditions. Capacitive sensing technology provides a scalable and cost-effective way to enable continuous monitoring and closed-loop feedback control of fluid volumes in small-scale gravity-dominated wells in a variety of microfluidic applications.

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.

Approximating open-loop and closed-loop optimal control by model predictive control

2020 ◽  
Author(s):  
Asen L. Dontchev ◽  
Ilya V. Kolmanovsky ◽  
Mikhail I. Krastanov ◽  
Vladimir M. Veliova
Keyword(s):  
Optimal Control ◽  
Model Predictive Control ◽  
Predictive Control ◽  
Closed Loop ◽  
Open Loop

Comparison of closed-loop and open-loop feedback schemes of message decoding using chaotic laser diodes

2003 ◽  
Vol 28 (22) ◽  
pp. 2168 ◽  
Author(s):  
Min Won Lee ◽  
Jon Paul ◽  
Sivaraman Sivaprakasam ◽  
K. Alan Shore
Keyword(s):  
Closed Loop ◽  
Laser Diodes ◽  
Open Loop ◽  
Chaotic Laser ◽  
Loop Feedback
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