Comparing different nonlinearities in readout systems for optical neuromorphic computing networks

Nonlinear activation is a crucial building block of most machine-learning systems. However, unlike in the digital electrical domain, applying a saturating nonlinear function in a neural network in the analog optical domain is not as easy, especially in integrated systems. In this paper, we first investigate in detail the photodetector nonlinearity in two main readout schemes: electrical readout and optical readout. On a 3-bit-delayed XOR task, we show that optical readout trained with backpropagation gives the best performance. Furthermore, we propose an additional saturating nonlinearity coming from a deliberately non-ideal voltage amplifier after the detector. Compared to an all-optical nonlinearity, these two kinds of nonlinearities are extremely easy to obtain at no additional cost, since photodiodes and voltage amplifiers are present in any system. Moreover, not having to design ideal linear amplifiers could relax their design requirements. We show through simulation that for long-distance nonlinear fiber distortion compensation, using only the photodiode nonlinearity in an optical readout delivers BER improvements over three orders of magnitude. Combined with the amplifier saturation nonlinearity, we obtain another three orders of magnitude improvement of the BER.

All-Fiber Optical Nonreciprocity Based on Parity-Time-Symmetric Fabry-Perot Resonators

Nonreciprocal light transmission in an all-fiber device with remotely tunable isolation ratio and switchable isolation direction is proposed and demonstrated. Three cascaded fiber Bragg gratings (FBGs) are inscribed in an erbium-ytterbium co-doped fiber (EYDF) to form two mutually coupled Fabry-Perot (FP) resonators. The two FP resonators have an identical geometry, but the gain and loss of the FP resonators, and their mutual coupling are manipulated by controlling the pumping power to realize broken parity-time (PT) symmetry. Strong optical nonreciprocity is achieved due to gain saturation nonlinearity that is enhanced by the broken PT symmetry. The proposed device is fabricated, and its operation is experimentally evaluated. Nonreciprocal light transmission with an isolation ratio of 8.58 dB at 1550 nm and a 3-dB bandwidth of 125 MHz is experimentally demonstrated. Our study also indicates, by optimizing the design, an isolation ratio up to 33 dB can be achieved. The proposed approach provides an all-fiber solution for a remotely tunable and optically controlled isolator, which may find great applications in software-defined optical networks.

Adaptive Robust Tracker Design for Nonlinear Sandwich Systems Subject to Saturation Nonlinearities

SUMMARY This paper addresses the tracking problem for uncertain nonlinear sandwich systems that consist of two nonlinear subsystems and saturation nonlinearity, which is sandwiched between the subsystems. The considered sandwich system is also subject to a nonsymmetric input saturation constraint. Due to the nonsmooth characteristics of sandwiched saturation nonlinearity and also the input saturation function, the design procedure deals with hard challenges. To overcome these difficulties, a recursive approach is suggested that consists of two phases. For the implementation of the proposed approach, a tracking problem is solved in each phase. In the first phase, the second subsystem with sandwiched saturation nonlinearity is considered and the output tracking problem of the desired time-varying reference signal is solved using backstepping method. The outcome of the first phase is the desired reference signal that should be tracked by the first subsystem in the next phase. In the second phase, the robust control input is designed for the first subsystem by employing adaptive sliding mode technique such that, despite the nonsymmetric input saturation constraint, model uncertainty and external disturbances, the output of the first subsystem follows the desired signal that is obtained in the previous phase. The simulation results for a mechanical sandwich system are illustrated to verify the effectiveness of the proposed control method.

Design of nonlinear anti-windup compensator for time-delayed systems based on triple Lyapunov Functional

In this paper, an internal model control based anti-windup compensator (AWC) is designed for nonlinear systems subjected to time-varying delay and input saturation. By using Lyapunov Krasvoskii Functional, less conservative linear matrix inequality (LMI) based delay-dependent stability condition is derived by utilizing the information of delay. Triple integral Lyapunov Functional is used for finding the gains of AWC to guarantee the closed loop stability of the system and reduce the conservatism. The saturation nonlinearity is taken into account by using sector condition. Finally, the efficacy of proposed approach is shown by numerical examples.

Asymmetrically Dynamic Coupling Hysteresis in Piezoelectric Actuators: Modeling Identification and Experimental Assessments

An asymmetrically dynamic coupling hysteresis (ADCH) model is proposed as an extension of the Prandtl–Ishlinskii (PI) model to characterize the hysteretic nonlinearities in piezoelectric actuators (PEAs). When subject to two-input: dynamic excitation and external loads. In this model, the developed asymmetrically one-side play operator helps to represent the saturation, nonlinearity, and centrally asymmetric properties of PEAs employed inverse hyperbolic envelope functions. The dynamic threshold functions are put in place to characterize the width of rate-dependent hysteresis property. Introductions of continuously coupled density functions are beneficial to the cross-coupled hysteresis behaviors of external load/excitation voltage-to-expansion. Besides, the proposed ADCH model is verified to satisfy indeed the wiping-out property and equal vertical chords property, which means that it can be regarded as well-suited in modeling the complicated hysteresis nonlinearity of PEAs. Furthermore, this paper also tackles the identification issue of the proposed ADCH model by using a global research method, which possesses satisfactory accuracy without strict requirements for the initially iterative value.