scholarly journals Existence of Optimal Policy for Delay-Differential Control Systems

1974 ◽  
Vol 10 (1) ◽  
pp. 56-62
Author(s):  
Shigeki HATAYAMA
Keyword(s):  
Control Systems ◽  
Optimal Policy ◽  
Delay Differential ◽  
Differential Control

Nonlinear Quasi-differential Control Systems

1992 ◽  
Vol 21 (1-2) ◽  
pp. 65-82
Author(s):  
W. N. Everitt ◽  
L. Markus
Keyword(s):  
Control Systems ◽  
Differential Control

scholarly journals Global Structure of Determining Matrices for a Class of Differential Control Systems

2021 ◽  
Vol 2 (1) ◽  
pp. 88-101
Author(s):  
Chukwunenye Ukwu ◽  
Onyekachukwu Henry Ikeh Ikeh
Keyword(s):  
Control Systems ◽  
Problem Instance ◽  
Computational Process ◽  
Rank Condition ◽  
Small Problem ◽  
Controllability Matrix ◽  
Computing Complexity ◽  
Double Time ◽  
Functional Differential ◽  
Differential Control

This paper developed and established unprecedented global results on the structure of determining matrices of generic double time-delay linear autonomous functional differential control systems, with a view to obtaining the controllability matrix associated with the rank condition for the Euclidean controllability of the system. The computational process and implementation of the controllability matrix were demonstrated on the MATLAB platform to determine the controllability disposition of a small-problem instance. Finally, the work examined the computing complexity of the determining matrices.

Delay-independent Stability of Uncertain Control Systems

2002 ◽  
Vol 124 (2) ◽  
pp. 277-283 ◽  
Author(s):  
Ilhan Tuzcu ◽  
Mehdi Ahmadian
Keyword(s):  
Control Systems ◽  
Uncertain Systems ◽  
Extreme Values ◽  
Sufficient Conditions ◽  
Entire Family ◽  
Active Vibration ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Analytical Expressions

This paper will provide a study of the delay-independent stability of uncertain control systems, represented by a family of quasipolynomials with single time-delays. The uncertain systems that are considered here are delay differential systems whose parameters are known only by their lower and upper bounds. The results are given in the form of necessary and sufficient conditions along with the assumptions for the quasipolynomial families considered. The conditions are transformed into convenient forms, which provide analytical expressions that can be easily checked by commercially available computing tools. For uncertain systems represented by families of quasipolynomials, it is shown that the delay independent stability for the extreme values of parameters is not sufficient for the delay independent stability of the entire family. In addition, the family must satisfy some conditions for the interior values of each parameter within specially constructed frequency ranges. The implementation of the theorem that is suggested is demonstrated on an example system that includes a single degree of freedom system with an active vibration absorber, namely the Delayed Resonator.

scholarly journals Optimising a Microgrid System by Deep Reinforcement Learning Techniques

Energies ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 2830
Author(s):  
David Domínguez-Barbero ◽  
Javier García-González ◽  
Miguel A. Sanz-Bobi ◽  
Eugenio F. Sánchez-Úbeda
Keyword(s):  
Reinforcement Learning ◽  
Control Systems ◽  
Optimal Policy ◽  
Historical Data ◽  
Scaling Up ◽  
Optimal Operation ◽  
Learning Techniques ◽  
Optimisation Model ◽  
The Cost ◽  
Naive Model

The deployment of microgrids could be fostered by control systems that do not require very complex modelling, calibration, prediction and/or optimisation processes. This paper explores the application of Reinforcement Learning (RL) techniques for the operation of a microgrid. The implemented Deep Q-Network (DQN) can learn an optimal policy for the operation of the elements of an isolated microgrid, based on the interaction agent-environment when particular operation actions are taken in the microgrid components. In order to facilitate the scaling-up of this solution, the algorithm relies exclusively on historical data from past events, and therefore it does not require forecasts of the demand or the renewable generation. The objective is to minimise the cost of operating the microgrid, including the penalty of non-served power. This paper analyses the effect of considering different definitions for the state of the system by expanding the set of variables that define it. The obtained results are very satisfactory as it can be concluded by their comparison with the perfect-information optimal operation computed with a traditional optimisation model, and with a Naive model.

SET-VALUED DYNAMICS IN PROBLEMS OF MATHEMATICAL THEORY OF CONTROL PROCESSES

2012 ◽  
Vol 26 (25) ◽  
pp. 1246010 ◽  
Author(s):  
TATIANA FILIPPOVA
Keyword(s):  
Control System ◽  
Differential Equations ◽  
Nonlinear Control ◽  
Control Systems ◽  
Mathematical Theory ◽  
Quadratic System ◽  
Nonlinear Control System ◽  
Reachable Sets ◽  
The Right ◽  
Differential Control

The dynamics and properties of set-valued states of differential control systems with uncertainties in initial data are studied. It is assumed that the dynamical system has a special structure, in which nonlinear terms in the right-hand sides of related differential equations are quadratic in state coordinates. We construct external and internal ellipsoidal estimates of reachable sets of nonlinear control system and find differential equations of proposed ellipsoidal estimates of reachable sets of nonlinear control system. The results obtained for quadratic system nonlinearities are extended to other types of control systems under uncertainty.

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