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Related Concept Videos

State Space Representation01:27

State Space Representation

324
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
324
State Space to Transfer Function01:21

State Space to Transfer Function

346
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
346
Transfer Function to State Space01:23

Transfer Function to State Space

450
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...
450
Open and closed-loop control systems01:17

Open and closed-loop control systems

1.1K
Control systems are foundational elements in automation and engineering. They are broadly categorized into open-loop and closed-loop systems. These classifications hinge on the presence or absence of feedback mechanisms, significantly influencing the system's performance, complexity, and application.
An open-loop control system operates without feedback from the output. It consists of two primary elements: the controller and the controlled process. The controller receives an input signal...
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Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

198
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.
In the absence...
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BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

575
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
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Maximum-Likelihood State Estimators in Probabilistic Boolean Control Networks.

Mitsuru Toyoda, Yuhu Wu

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    This study presents new algorithms for state estimation in probabilistic Boolean control networks (PBCNs), enabling accurate predictions from partial or output data using dynamic programming and shortest path methods.

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    Area of Science:

    • Systems Biology
    • Control Theory
    • Computational Biology

    Background:

    • Probabilistic Boolean control networks (PBCNs) introduce stochasticity into Boolean networks, necessitating advanced statistical methods for state estimation.
    • Estimating states in PBCNs is challenging due to the inherent randomness in their logical update functions.

    Purpose of the Study:

    • To develop efficient algorithms for state estimation in PBCNs from both partial state measurements and output data.
    • To design novel observer methods for PBCNs based on the developed estimation algorithms.

    Main Methods:

    • Maximum-likelihood estimation formulated as an optimization problem.
    • Efficient algorithms based on dynamic programming.
    • Dijkstra-type algorithms utilizing best-first search to solve equivalent shortest path problems.

    Main Results:

    • The study successfully applies dynamic programming and Dijkstra-type algorithms to solve state estimation and observer design problems for PBCNs.
    • Novel observer design methods for PBCNs are derived from the proposed algorithms.
    • Algorithms are validated through practical sensor reduction problems and gene regulatory network models (apoptosis, Lac operon).

    Conclusions:

    • The developed algorithms provide effective solutions for state estimation and observer design in PBCNs.
    • The methods are applicable to complex biological systems, aiding in understanding gene regulatory networks.
    • The approach facilitates sensor reduction in practical applications.