Core Concepts
Optimal driving protocols can be derived to minimize Joule losses during memristive switching, both for ideal memristors and more complex memristive systems, through the application of the calculus of variations and optimal control theory.
Abstract
This paper investigates strategies for minimizing Joule losses in resistive random access memory (ReRAM) cells, also known as memristive devices. The authors apply the calculus of variations and optimal control theory to derive optimal driving protocols for memristive switching under various scenarios:
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Unconstrained switching of ideal memristors:
- Minimization of Joule losses within a fixed time interval (Theorem 1: Optimal trajectory has constant power)
- Simultaneous minimization of Joule losses and switching time (Theorem 2: Optimal trajectory has constant power)
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Unconstrained switching of memristive systems:
- Formulation of the Lagrangian function and derivation of the necessary conditions for an extrema
- Optimal control of a threshold-type memristive device
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Constrained switching of ideal memristors:
- Incorporation of Pontryagin's principle to handle current constraints
- Optimization of Joule losses in linear memristors with a current constraint
The authors demonstrate the advantages of their approaches through specific examples and compare the results with those of switching using constant voltage or current. Their findings suggest that voltage or current control can be used to reduce Joule losses in emerging memory devices.
Stats
Equation (12): Qopt = (2/3b^2)[(Rf^(3/2) - Ri^(3/2))^2 / (tf - ti)]
Equation (14): QI=const = (1/2b^2)[(Rf^2 - Ri^2)(Rf - Ri) / (tf - ti)]
Equation (17): QV=const = V(Rf - Ri) / b
Quotes
"Our findings suggest that voltage or current control can be used to reduce Joule losses in emerging memory devices."