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Control Systems01:10

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Control systems are everywhere in contemporary society, influencing diverse applications from aerospace to automated manufacturing. These systems can be found naturally within biological processes, such as blood sugar regulation and heart rate adjustment in response to stress, as well as in man-made systems like elevators and automated vehicles. A control system is essentially a network of subsystems and processes that collaboratively convert specific inputs into desired outputs.
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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
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Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
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Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
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Optimistic value based optimal control for uncertain linear singular systems and application to a dynamic

Yadong Shu1, Yuanguo Zhu1

  • 1School of Science, Nanjing University of Science and Technology, Nanjing 210094, China.

ISA Transactions
|September 3, 2017
PubMed
Summary

This study addresses optimal control for uncertain singular systems using the optimistic value criterion. It develops methods for both discrete-time and continuous-time systems, providing effective solutions for complex control problems.

Keywords:
Equation of optimalityOptimal controlOptimistic valueRecurrence equationUncertain singular system

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Area of Science:

  • Control Theory
  • Optimization
  • Systems Engineering

Background:

  • Singular systems present unique challenges in control due to their inherent properties.
  • Uncertainty in system parameters complicates the design of effective control strategies.
  • The optimistic value criterion offers a framework for decision-making under uncertainty.

Purpose of the Study:

  • To develop optimal control strategies for uncertain discrete-time and continuous-time singular systems.
  • To apply the optimistic value method to optimize uncertain objective functions in these systems.
  • To provide a systematic approach for solving optimal control problems in singular systems.

Main Methods:

  • Bellman's principle of optimality is utilized to derive a recurrence equation for discrete-time systems.
  • Uncertainty theory and the principle of optimality are combined to derive an equation of optimality for continuous-time systems.
  • The optimistic value method is employed for optimizing uncertain objective functions.

Main Results:

  • A recurrence equation for solving optimal control problems in uncertain discrete-time singular systems.
  • An equation of optimality for optimal control models in uncertain continuous-time singular systems.
  • Demonstrated effectiveness through numerical examples and a dynamic input-output model.

Conclusions:

  • The proposed methods provide effective solutions for optimal control problems in uncertain singular systems.
  • The optimistic value criterion is a viable approach for handling uncertainty in control design.
  • The derived equations offer a pathway to solving complex control challenges in both discrete and continuous time domains.