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State Space Representation01:27

State Space Representation

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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.
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Chemistry is the study of matter and the changes it undergoes. Matter is anything that has mass and occupies space. Matter is all around us; the air, water, soil, mountains, even our bodies are all examples of matter. Matter is divided into three states — solid, liquid, and gas — that are commonly found on earth. The fourth state of matter, plasma, occurs naturally in the interiors of stars. 
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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.
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Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
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Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
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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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Liquid State Machine on SpiNNaker for Spatio-Temporal Classification Tasks.

Alberto Patiño-Saucedo1,2, Horacio Rostro-González1,3, Teresa Serrano-Gotarredona2

  • 1Department of Electronics Engineering, University of Guanajuato, Salamanca, Mexico.

Frontiers in Neuroscience
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Summary
This summary is machine-generated.

Liquid State Machines (LSMs) effectively classify visual events on the SpiNNaker neuromorphic processor. This approach achieves state-of-the-art results on the N-MNIST dataset with reduced memory usage.

Keywords:
Liquid State MachineN-MNISTSpiNNakerneuromorphic hardwarespiking neural network

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Area of Science:

  • Computational Neuroscience
  • Neuromorphic Engineering
  • Artificial Intelligence

Background:

  • Liquid State Machines (LSMs), utilizing Spiking Neural Networks (SNNs), offer biological plausibility and efficient training for pattern recognition.
  • Implementing LSMs for complex tasks like event-based vision on large-scale neuromorphic hardware remains challenging.

Purpose of the Study:

  • To demonstrate the efficacy of offline-trained LSMs on the SpiNNaker neuromorphic processor for event-based visual classification.
  • To evaluate the impact of transferring LSMs from deep learning frameworks to neuromorphic hardware and assess the effect of weight quantization.

Main Methods:

  • Offline training of LSMs using an adaptation of back-propagation-through-time (BPTT) for SNNs.
  • Deployment of trained LSMs onto the SpiNNaker neuromorphic processor for visual event classification.
  • Performance evaluation on the N-MNIST dataset and analysis of weight quantization effects.

Main Results:

  • Achieved state-of-the-art performance in classifying visual events on the N-MNIST dataset.
  • Demonstrated that mapping LSMs from deep learning frameworks to SpiNNaker does not degrade classification accuracy.
  • Confirmed that weight quantization significantly reduces memory footprint with minimal impact on performance.

Conclusions:

  • Offline-trained LSMs are a viable and high-performing solution for event-based visual processing on neuromorphic hardware.
  • The SpiNNaker platform effectively supports LSMs for complex tasks, bridging deep learning frameworks and neuromorphic implementation.
  • Weight quantization presents a practical method for optimizing LSMs for memory-constrained neuromorphic systems.