Feedback for neuronal system identification

In order to estimate reliable models from noisy input-output data, system identification techniques usually require that the data be generated by a process with a fading memory. Non-equilibrium systems such as neuronal and chaotic models lack a fading memory. Their identification is challenging, in particular in the presence of input noise. In this thesis, we propose a methodology based on the prediction-error method for the identification of neuronal systems subject to input-additive noise. We build on the fundamental observation that while a neuronal model does not have a fading memory, it can be transformed into a fading memory system by output feedback. Our ideas can be generalized to any non-equilibrium system sharing this property. At the core of the methodology is the use of output feedback in experiment design. We provide a theoretical justification for this design choice, which has been exploited in neurophysiology since the invention of the voltage-clamp experiment. To investigate the problem of feedback for identification, we first address the estimation of simple non-equilibrium systems in Lure form, and show that feedback allows estimating the nonlinearity in a static experiment. We then address the estimation of conductance-based models. Assuming that an informed choice can be made on the elements of the model structure, we show that consistent parameter estimates can be obtained when noise is only present at the system input. Finally, we approach the problem from a black-box perspective, and propose identifying the neuronal internal dynamics using a universal approximator with Generalized Orthogonal Basis Functions.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) – Brasil (Finance Code 001

Adaptive observers for biophysical neuronal circuits

This paper presents adaptive observers for online state and parameter estimation of a class of nonlinear systems motivated by biophysical models of neuronal circuits. We first present a linear-in-the-parameters design that solves a classical recursive least-squares problem. Then, building on this simple design, we present an augmented adaptive observer for models with a nonlinearly parameterized internal dynamics, the parameters of which we interpret as structured uncertainty. We present a convergence and robustness analysis based on contraction theory, and illustrate the potential of the approach in neurophysiological applications by means of numerical simulations.Comment: 16 pages. The Julia code used in this paper can be found in https://github.com/thiagoburghi/online-learnin

Feedback for nonlinear system identification

Motivated by neuronal models from neuroscience, we consider the system identification of simple feedback structures whose behaviors include nonlinear phenomena such as excitability, limit-cycles and chaos. We show that output feedback is sufficient to solve the identification problem in a two-step procedure. First, the nonlinear static characteristic of the system is extracted, and second, using a feedback linearizing law, a mildly nonlinear system with an approximately-finite memory is identified. In an ideal setting, the second step boils down to the identification of a LTI system. To illustrate the method in a realistic setting, we present numerical simulations of the identification of two classical systems that fit the assumed model structure.Comment: 18th European Control Conference (ECC), Napoli, Italy, June 25-28 201

Robust online estimation of biophysical neural circuits

The control of neuronal networks, whether biological or neuromorphic, relies on tools for estimating parameters in the presence of model uncertainty. In this work, we explore the robustness of adaptive observers for neuronal estimation. Inspired by biology, we show that decentralization and redundancy help recover the performance of a centralized recursive mean square algorithm in the presence of uncertainty and mismatch on the internal dynamics of the model.Comment: 6 pages, 5 figures, accepted at the 62nd IEEE Conference on Decision and Contro

Distributed online estimation of biophysical neural networks

In this work, we propose a distributed adaptive observer for a class of networked systems inspired by biophysical conductance-based neural network models. Neural systems learn by adjusting intrinsic and synaptic weights in a distributed fashion, with neuronal membrane voltages carrying information from neighbouring neurons in the network. Using contraction analysis, we show that this learning principle can be used to design an adaptive observer based on a decentralized learning rule that greatly reduces the number of observer states required for consistent exponential convergence of parameter estimates. This novel design is relevant for biological, biomedical and neuromorphic applications

Kinematic control design for wheeled mobile robots with longitudinal and lateral slip

The motion control of wheeled mobile robots at high speeds under adverse ground conditions is a difficult task, since the robots' wheels may be subject to different kinds of slip. This work introduces an adaptive kinematic controller that is capable of solving the trajectory tracking problem of a nonholonomic mobile robot under longitudinal and lateral slip. While the controller can effectively compensate for the longitudinal slip, the lateral slip is a more involved problem to deal with, since nonholonomic robots cannot directly produce movement in the lateral direction. To show that the proposed controller is still able to make the mobile robot follow a reference trajectory under lateral and longitudinal time-varying slip, the solutions of the robot's position and orientation error dynamics are shown to be uniformly ultimately bounded. Numerical simulations are presented to illustrate the robot's performance using the proposed adaptive control law