Improved robust control of nonlinear stochastic systems using uncertain models

We introduce a technique for quantifying and then exploiting uncertainty in nonlinear stochastic control systems. The approach is suboptimal though robust and relies upon the approximation of the forward and inverse plant models by neural networks, which also estimate the intrinsic uncertainty. Sampling from the resulting Gaussian distributions of the inversion based neurocontroller allows us to introduce a control law which is demonstrably more robust than traditional adaptive controllers.

Robust control of nonlinear stochastic systems by modelling conditional distributions of control signals

We introduce a novel inversion-based neuro-controller for solving control problems involving uncertain nonlinear systems that could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. In this work a novel robust inverse control approach is obtained based on importance sampling from these distributions. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The performance of the new algorithm is illustrated through simulations with example systems.

Q parameter estimation using numerical simulations for linear and nonlinear transmission systems

We compare the Q parameter obtained from scalar, semi-analytical and full vector models for realistic transmission systems. One set of systems is operated in the linear regime, while another is using solitons at high peak power. We report in detail on the different results obtained for the same system using different models. Polarisation mode dispersion is also taken into account and a novel method to average Q parameters over several independent simulation runs is described. © 2006 Elsevier B.V. All rights reserved.

Semi-analytical Q parameter estimate in linear and nonlinear transmission systems

We compare the Q parameter obtained from the semi-analytical model with scalar and vector models for two realistic transmission systems. First a linear system with a compensated dispersion map and second a soliton transmission system.

Intermediate asymptotics in nonlinear optical systems

Using a fiber laser system as a specific illustrative example, we introduce the concept of intermediate asymptotic states in finite nonlinear optical systems. We show that intermediate asymptotics of nonlinear equations (e.g., coherent structures with a finite lifetime or distance) can be used in applications similar to those of truly stable asymptotic solutions, such as, e.g., solitons and dissipative nonlinear waves. Applying this general idea to a particular, albeit practically important, physical system, we demonstrate a novel type of nonlinear pulse-shaping regime in a mode-locked fiber laser leading to the generation of linearly chirped pulses with a triangular distribution of the intensity.

Intermediate asymptotics in nonlinear optical systems

Using a fiber laser system as a specific illustrative example, we introduce the concept of intermediate asymptotic states in finite nonlinear optical systems. We show that intermediate asymptotics of nonlinear equations (e.g., coherent structures with a finite lifetime or distance) can be used in applications similar to those of truly stable asymptotic solutions, such as, e.g., solitons and dissipative nonlinear waves. Applying this general idea to a particular, albeit practically important, physical system, we demonstrate a novel type of nonlinear pulse-shaping regime in a mode-locked fiber laser leading to the generation of linearly chirped pulses with a triangular distribution of the intensity.

Fully probabilistic control for stochastic nonlinear control systems with input dependent noise

Robust controllers for nonlinear stochastic systems with functional uncertainties can be consistently designed using probabilistic control methods. In this paper a generalised probabilistic controller design for the minimisation of the Kullback-Leibler divergence between the actual joint probability density function (pdf) of the closed loop control system, and an ideal joint pdf is presented emphasising how the uncertainty can be systematically incorporated in the absence of reliable systems models. To achieve this objective all probabilistic models of the system are estimated from process data using mixture density networks (MDNs) where all the parameters of the estimated pdfs are taken to be state and control input dependent. Based on this dependency of the density parameters on the input values, explicit formulations to the construction of optimal generalised probabilistic controllers are obtained through the techniques of dynamic programming and adaptive critic methods. Using the proposed generalised probabilistic controller, the conditional joint pdfs can be made to follow the ideal ones. A simulation example is used to demonstrate the implementation of the algorithm and encouraging results are obtained.

Dissipative parametric modulation instability and pattern formation in nonlinear optical systems

We present the essential features of the dissipative parametric instability, in the universal complex Ginzburg- Landau equation. Dissipative parametric instability is excited through a parametric modulation of frequency dependent losses in a zig-zag fashion in the spectral domain. Such damping is introduced respectively for spectral components in the +ΔF and in the -ΔF region in alternating fashion, where F can represent wavenumber or temporal frequency depending on the applications. Such a spectral modulation can destabilize the homogeneous stationary solution of the system leading to growth of spectral sidebands and to the consequent pattern formation: both stable and unstable patterns in one- and in two-dimensional systems can be excited. The dissipative parametric instability provides an useful and interesting tool for the control of pattern formation in nonlinear optical systems with potentially interesting applications in technological applications, like the design of mode- locked lasers emitting pulse trains with tunable repetition rate; but it could also find realizations in nanophotonics circuits or in dissipative polaritonic Bose-Einstein condensates.

Probabilistic DHP adaptive critic for nonlinear stochastic control systems

Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Kárnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained.

Probability distribution modelling to improve stability in nonlinear MIMO control

We consider the direct adaptive inverse control of nonlinear multivariable systems with different delays between every input-output pair. In direct adaptive inverse control, the inverse mapping is learned from examples of input-output pairs. This makes the obtained controller sub optimal, since the network may have to learn the response of the plant over a larger operational range than necessary. Moreover, in certain applications, the control problem can be redundant, implying that the inverse problem is ill posed. In this paper we propose a new algorithm which allows estimating and exploiting uncertainty in nonlinear multivariable control systems. This approach allows us to model strongly non-Gaussian distribution of control signals as well as processes with hysteresis. The proposed algorithm circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider.

Coherent propagation and energy transfer in low-dimension nonlinear arrays

We present a theory of coherent propagation and energy or power transfer in a low-dimension array of coupled nonlinear waveguides. It is demonstrated that in the array with nonequal cores (e.g., with the central core) stable steady-state coherent multicore propagation is possible only in the nonlinear regime, with a power-controlled phase matching. The developed theory of energy or power transfer in nonlinear discrete systems is rather generic and has a range of potential applications including both high-power fiber lasers and ultrahigh-capacity optical communication systems. © 2012 American Physical Society.

Nonlinear semi-analytical model for simulation of few-mode fiber transmission

In this letter, a nonlinear semi-analytical model (NSAM) for simulation of few-mode fiber transmission is proposed. The NSAM considers the mode mixing arising from the Kerr effect and waveguide imperfections. An analytical explanation of the model is presented, as well as simulation results for the transmission over a two mode fiber (TMF) of 112 Gb/s using coherently detected polarization multiplexed quadrature phase-shift-keying modulation. The simulations show that by transmitting over only one of the two modes on TMFs, long-haul transmission can be realized without increase of receiver complexity. For a 6000-km transmission link, a small modal dispersion penalty is observed in the linear domain, while a significant increase of the nonlinear threshold is observed due to the large core of TMF. © 2006 IEEE.

Enhanced information transmission with signal dependent noise in an array of LIF neurons

Sensory cells usually transmit information to afferent neurons via chemical synapses, in which the level of noise is dependent on an applied stimulus. Taking into account such dependence, we model a sensory system as an array of LIF neurons with a common signal. We show that information transmission is enhanced by a nonzero level of noise. Moreover, we demonstrate a phenomenon similar to suprathreshold stochastic resonance with additive noise. We remark that many properties of information transmission found for the LIF neurons was predicted by us before with simple binary units [Phys. Rev. E 75, 021121 (2007)]. This confirmation of our predictions allows us to point out identical roots of the phenomena found in the simple threshold systems and more complex LIF neurons.