A near-optimal decentralized control approach for polynomial nonlinear interconnected systems

2020 ◽  
pp. 014233122097743
Author(s):  
Mohamed Sadok Attia ◽  
Mohamed Karim Bouafoura ◽  
Naceur Benhadj Braiek
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Open Loop ◽  
System Stability ◽  
Gronwall Lemma ◽  
Interconnected System ◽  
Control Approach ◽  
State Dependent ◽  
And Control

This article tackles the decentralized near-optimal control problem for the class of nonlinear polynomial interconnected system based on a shifted Legendre polynomials direct approach. The proposed method converts the interconnected optimal control problems into a nonlinear programming one with multiple constraints. In light of the formulated NLP optimization, state and control coefficients are used to design a nonlinear decentralized state feedback controller. Overall closed-loop system stability sufficient conditions are investigated with the help of Grönwall lemma. The triple inverted pendulum case is considered for simulation. Satisfactory results are obtained in both open-loop and closed-loop schemes with comparison to collocation and state-dependent Riccati equation techniques.

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.

A New Iterative Identification and Control Method of Closed-Loop Power System Based on Ambient Signals

2015 ◽  
Vol 798 ◽  
pp. 261-265
Author(s):  
Miao Yu ◽  
Chao Lu
Keyword(s):  
Power System ◽  
Closed Loop ◽  
Control Method ◽  
Controller Design ◽  
Design Method ◽  
Stability Margin ◽  
System Stability ◽  
Iterative Identification ◽  
Effective Performance ◽  
And Control

Identification and control are important problems of power system based on ambient signals. In order to avoid the model error influence of the controller design, a new iterative identification and control method is proposed in this paper. This method can solve model set and controller design of closed-loop power system. First, an uncertain model of power system is established. Then, according to the stability margin of power system, stability theorem is put forward. And then controller design method and the whole algorithm procedure are given. Simulation results show the effective performance of the proposed method based on the four-machine-two-region system.

Computers: Applications to the Quantification of Human Behavior

1964 ◽  
Vol 6 (6) ◽  
pp. 585-605
Author(s):  
Gustave J. Rath ◽  
William P. Allman
Keyword(s):  
Human Behavior ◽  
Closed Loop ◽  
Data Gathering ◽  
Open Loop ◽  
Behavioral Analysis ◽  
On Line ◽  
Analysis System ◽  
Response Collection ◽  
And Control ◽  
Computing Machines

This paper discusses the use of computing machines in the biological and social sciences, namely the ultilization of computerized behavior analysis systems in the quantification of human behavior. Only systems of which living human organisms are a part are considered. Some specific functional uses of computers for stimulus preparation and presentation, response collection, and apparatus scheduling and control are presented. All of these functions may be performed by automated systems characterized by the amount of experimental integration and control performed by the computer. Systems types include on-line open-loop, on-line closed loop single or multiple purpose, and off-line. The multiple-man, multiple-purpose system which permits numerous automated investigations upon different source subjects to occur simultaneously is highlighted as the culmination of current automated behavioral analysis systems. But the possibility of behavioral scientists “tapping” into operating systems is presented as possibly having revolutionary consequences with respect to the data gathering of human behaviour. Finally, a general automated behavioral analysis system schematic assists in discussing current advantages, potential advances, and impending limitations of contributions of computers to the quantification of human behavior.

The Optimal Regulator Problem for a Stationary Linear System With State-Dependent Noise

1970 ◽  
Vol 92 (2) ◽  
pp. 363-368 ◽  
Author(s):  
P. J. McLane
Keyword(s):  
Linear System ◽  
Sufficient Conditions ◽  
Quadratic Functional ◽  
Optimal Controls ◽  
Final Time ◽  
State Dependent ◽  
Continuous Dynamic ◽  
The Stability ◽  
And Control ◽  
Stationary Linear System

The problem of minimizing a quadratic functional of the system outputs and control for a stationary linear system with state-dependent noise is solved in this paper. Both the finite final time and infinite final time versions of the problem are treated. For the latter case existence conditions are obtained using the second method of Lyapunov. The optimal controls for both problems are obtained using Bellman’s continuous dynamic programming. In light of this, the system dynamics are assumed to determine a diffusion process. For the infinite final time version of the problem noted above, sufficient conditions are obtained for the stability of the optimal system and uniqueness of the optimal control law. In addition, for this problem, an example is treated. The computational results for this example illustrate some of the qualitative features of regulators for linear, stationary systems with state-dependent disturbances.

The Effect of Local Force Control on Punch Forces During Panel Forming

2018 ◽  
Author(s):  
William J. Emblom
Keyword(s):  
Closed Loop ◽  
Force Transducer ◽  
Open Loop ◽  
Control Panel ◽  
Closed Loop Control ◽  
Punch Force ◽  
Blank Holder ◽  
Loop Control ◽  
Operational Envelope ◽  
And Control

Methods for improving the robustness of panel forming including the introduction of process sensing and feedback and control has resulted in significant gains in the quality of parts and reduced failures. Initial efforts in implementing closed-loop control during panel forming used active tool elements to ensure that the total punch force followed prescribed trajectories. However, more recently local forces within the tooling have been demonstrated to not only follow desired force trajectories but have been shown to increase the operational envelope of the tooling compared to open-loop tests and even closed-loop test where the total punch force had been controlled. However, what has not been examined is the effect of local force, especially during closed-loop control panel forming operations on the total punch force measured during forming. This paper addresses this by comparing the results of both open-loop tests and closed-loop tests and examining the effects on both local and total punch forces. It was found that while open-loop forming with various constant draw bead depths resulted in varying total punch forces, once closed-loop control was implemented the total punch forces followed virtually identical trajectories. The tooling for this project included local force transducers and a total punch force transducer. In addition, active draw beads could be controlled during forming and a flexible blank holder with variable blank holder forces were part of the setup.

Adaptive Identification and Control for Small Modular Reactors

2011 ◽  
Author(s):  
Daniel G. Cole
Keyword(s):  
Adaptive Control ◽  
Control System ◽  
Adaptive System ◽  
Operating Conditions ◽  
System Stability ◽  
Peak Performance ◽  
Model Matching ◽  
Adaptive Identification ◽  
Control Approach ◽  
And Control

This paper discusses adaptive identification and control (AID&C) techniques to enable automated online identification and control of SMRs. Adaptive system ID allows engineers to rapidly measure system dynamics, calibrate sensors channels, determine loop processes, and quantify actuator authority for the various reactor control loops. Adaptive control can automatically tune these loops and adjust plant processes to optimize conditions for peak performance and power production. Another advantage of the adaptive ID and control approach is that these tools can be used during reactor operation to monitor active and passive components. Adaptive system ID techniques are used to measure loop-transfer characteristics. Presented is a practical approach that uses adaptive model-matching tools to identify the coprime factors of the local loops. This has the advantage over model based approaches since coprime factors can be identified on the real system using real data. Adaptive control enables auto-tuning of controller parameters to meet operational specifications. Using the coprime factors, all controllers that stabilize the plant can be parametrized by a free Q-parameter that can be changed to meet control system objectives and improve performance, and the tuning is performed using adaptive techniques. The controller architecture presented provides several desirable and necessary features: e.g., a default fail-safe mode of operation, stability in the presence of communications failures, guaranteed stability, and robustness. An advantage of the adaptive structure presented here is that control system stability can be guaranteed, even during adaptation by ensuring certain norm conditions on the Q-parameter and estimated plant uncertainty. More importantly, the Q-parameter can be monitored during operation, providing a real-time estimate of the changes in the plant resulting from changes in the reactor itself. This signal monitors the dynamics of each loop, providing information about the reactor from the perspective of the control process. Online monitoring using AID&C can be used to better track control system transients that result in reactor trip, thus avoiding undesirable reactor trips and diversion events. And, there is a potential that the system can better adapt to changing operating conditions during plant transients including load following procedures.

scholarly journals Dynamic Analysis of a Two-Language Competitive Model with Control Strategies

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Lin-Fei Nie ◽  
Zhi-Dong Teng ◽  
Juan J. Nieto ◽  
Il Hyo Jung
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Numerical Simulations ◽  
Control Strategy ◽  
Sufficient Conditions ◽  
Positive Order ◽  
State Dependent ◽  
Competitive Model ◽  
The Impact

The dynamic behavior of a two-language competitive model is analyzed systemically in this paper. By the linearization and the Bendixson-Dulac theorem on dynamical system, some sufficient conditions on the globally asymptotical stability of the trivial equilibria and the existence and the stability of the positive equilibrium of this model are presented. Nextly, in order to protect the endangered language, an optimal control problem relative to this model is explored. We derive some necessary conditions to solve the optimal control problem and present some numerical simulations using a Runge-Kutta fourth-order method. Finally, the languages competitive model is extended to this model assessing the impact of state-dependent pulse control strategy. Using the Poincaré map, differential inequality, and method of qualitative analysis, we prove the existence and stability of positive order-1 periodic solution for this control model. Numerical simulations are carried out to illustrate the main results and the feasibility of state-dependent impulsive control strategy.

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