This paper applies the classical prediction error method (PEM) to the estimation of nonlinear discrete-time models of neuronal systems subject to input-additive noise. While the nonlinear system exhibits excitability, bifurcations, and limit-cycle oscillations, we prove consistency of the parameter estimation procedure under output feedback. Hence, this paper provides a rigorous framework for the application of conventional nonlinear system identification methods to discrete-time stochastic neuronal systems. The main result exploits the elementary property that conductance-based models of neurons have an exponentially contracting inverse dynamics. This property is implied by the voltage-clamp experiment, which has been the fundamental modeling experiment of neurons ever since the pioneering work of Hodgkin and Huxley.
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 illust…
Building on a recent paper by Georgiou and Lindquist [1] on the problem of rank deficiency of spectral densities and hidden dynamical relations after sampling of continuous-time stochastic processes, this paper is devoted to understanding related questions of feedback and Granger causality that affect stability properties. This then naturally connects to CARMA identification, where we remark on certain oversights in the literature.
We study modeling and identification of stationary processes with a spectral density matrix of low rank. Equivalently, we consider processes having an innovation of reduced dimension for which Prediction Error Methods (PEM) algorithms are not directly applicable. We show that these processes admit a special feedback structure with a deterministic feedback channel which can be used to split the identification in two steps, one of which can be based on standard algorithms while the other is based on a deterministic least squares fit. Identifiability of the feedback system is analyzed and a uniqu…
Focusing on identification, this paper develops techniques to reconstruct zero and nonzero elements of a sparse parameter vector of a stochastic dynamic system under feedback control, for which the current input may depend on the past inputs and outputs, system noises as well as exogenous dithers. First, a sparse parameter identification algorithm is introduced based on L2 norm with L1 regularization, where the adaptive weights are adopted in the optimization variables of L1 term. Second, estimates generated by the algorithm are shown to have both set and parameter convergence. That is, sets o…
This paper considers the problem of closed-loop identification of linear scalar systems with Gaussian process noise, where the system input is determined by a deterministic state feedback policy. The regularized least-square estimate (LSE) algorithm is adopted, seeking to find the best estimate of unknown model parameters based on noiseless measurements of the state. We are interested in the fundamental limitation of the rate at which unknown parameters can be learned, in the sense of the D-optimality scalarization criterion subject to a quadratic control cost. We first establish a novel conne…
This paper proposes a data-driven state feedback controller that enables reference tracking for nonlinear discrete-time systems. The controller is designed based on the identified inverse model of the system and a given reference model, assuming that the identification of the inverse model is carried out using only the system's state/input measurements. When its results are provided, we present conditions that guarantee a certain level of reference tracking performance, regardless of the identification method employed for the inverse model. Specifically, when Gaussian process regression (GPR) …
We study modeling and identification of processes with a spectral density matrix of low rank. Equivalently, we consider processes having an innovation of reduced dimension for which Prediction Error Methods (PEM) algorithms are not directly applicable. We show that these processes admit a special feedback structure with a deterministic feedback channel which can be used to split the identification in two steps, one of which can be based on standard algorithms while the other is based on a deterministic least squares fit.
Model predictive control (MPC) is a widely used modern control technique with numerous successful application in diverse areas. Much of this success is due to the ability of MPC to enforce state and control constraints, which are crucial in many applications of control. In order to avoid the need for an observer, output-feedback model predictive control with online identification (OFMPCOI) uses the block observable canonical form whose state consists of past values of the control inputs and measured outputs. Online identification is performed using recursive least squares (RLS) with variable-r…
Low cost real-time identification of multirotor unmanned aerial vehicle (UAV) dynamics is an active area of research supported by the surge in demand and emerging application domains. Such real-time identification capabilities shorten development time and cost, making UAVs' technology more accessible, and enable a wide variety of advanced applications. In this paper, we present a novel comprehensive approach, called DNN-MRFT, for real-time identification and tuning of multirotor UAVs using the Modified Relay Feedback Test (MRFT) and Deep Neural Networks (DNN). The main contribution is the deve…
Combining control engineering with nonparametric modeling techniques from machine learning allows to control systems without analytic description using data-driven models. Most existing approaches separate learning, i.e. the system identification based on a fixed dataset, and control, i.e. the execution of the model-based control law. This separation makes the performance highly sensitive to the initial selection of training data and possibly requires very large datasets. This article proposes a learning feedback linearizing control law using online closed-loop identification. The employed Gau…
Khalifa University（哈利法大学）；Kingston University London（伦敦金斯顿大学）
Control performance of Unmanned Aerial Vehicles (UAVs) is directly affected by their ability to estimate their states accurately. With the increasing popularity of autonomous UAV solutions in real world applications, it is imperative to develop robust adaptive estimators that can ameliorate sensor noises in low-cost UAVs. Utilizing the knowledge of UAV dynamics in estimation can provide significant advantages, but remains challenging due to the complex and expensive pre-flight experiments required to obtain UAV dynamic parameters. In this paper, we propose two decoupled dynamic model based Ext…
As we transition towards the deployment of data-driven controllers for black-box cyberphysical systems, complying with hard safety constraints becomes a primary concern. Two key aspects should be addressed when input-output data are corrupted by noise: how much uncertainty can one tolerate without compromising safety, and to what extent is the control performance affected? By focusing on finite-horizon constrained linear-quadratic problems, we provide an answer to these questions in terms of the model mismatch incurred during a preliminary identification phase. We propose a control design proc…
In this paper we propose a novel methodology that allows to design, in a purely data-based fashion and for linear single-input and single-output systems, both robustly stable and performing control systems for tracking piecewise constant reference signals. The approach uses both (i) Virtual Reference Feedback Tuning for enforcing suitable performances and (ii) the Set Membership framework for providing a-priori robust stability guarantees. Indeed, an uncertainty set for the system parameters is obtained through Set Membership identification, where an algorithm based on the scenario approach is…
In this paper we consider the joint problems of state estimation and model identification for a class of continuous-time nonlinear systems in output-feedback canonical form. An adaptive observer is proposed that combines an extended high-gain observer and a discrete-time identifier. The extended observer provides the identifier with a data set permitting the identification of the system model and the identifier adapts the extended observer according to the new estimated model. The design of the identifier is approached as a system identification problem and sufficient conditions are presented …
Objective: This paper presents a force control scheme for brief isotonic holds in an isometrically contracted muscle tissue, with minimal overshoot and settling time to measure its shortening velocity, a key parameter of muscle function. Methods: A two-degree-of-freedom control configuration, formed by a feedback controller and a feedforward controller, is explored. The feedback controller is a proportional-integral controller and the feedforward controller is designed using the inverse of a control-oriented model of muscle tissue. A generalized linear model and a nonlinear model of muscle tis…
Fondazione Istituto Italiano di Tecnologia（意大利技术研究院）
The paper contributes towards the modeling, identification, and control of model jet engines. We propose a nonlinear, second order model in order to capture the model jet engines governing dynamics. The model structure is identified by applying sparse identification of nonlinear dynamics, and then the parameters of the model are found via gray-box identification procedures. Once the model has been identified, we approached the control of the model jet engine by designing two control laws. The first one is based on the classical Feedback Linearization technique while the second one on the Slidi…
