Supervisory observer for parameter and state estimation of nonlinear systems using the DIRECT algorithm

A supervisory observer is a multiple-model architecture, which estimates the parameters and the states of nonlinear systems. It consists of a bank of state observers, where each observer is designed for some nominal parameter values sampled in a known parameter set. A selection criterion is used to select a single observer at each time instant, which provides its state estimate and parameter value. The sampling of the parameter set plays a crucial role in this approach. Existing works require a sufficiently large number of parameter samples, but no explicit lower bound on this number is provided. The aim of this work is to overcome this limitation by sampling the parameter set automatically using an iterative global optimisation method, called DIviding RECTangles (DIRECT). Using this sampling policy, we start with 1 + 2np parameter samples where np is the dimension of the parameter set. Then, the algorithm iteratively adds samples to improve its estimation accuracy. Convergence guarantees are provided under the same assumptions as in previous works, which include a persistency of excitation condition. The efficacy of the supervisory observer with the DIRECT sampling policy is illustrated on a model of neural populations

Economic Games as Estimators

Discrete event games are discrete time dynamical systems whose state transitions are discrete events caused by actions taken by agents within the game. The agents’ objectives and associated decision rules need not be known to the game designer in order to impose struc- ture on a game’s reachable states. Mechanism design for discrete event games is accomplished by declaring desirable invariant properties and restricting the state transition functions to conserve these properties at every point in time for all admissible actions and for all agents, using techniques familiar from state-feedback control theory. Building upon these connections to control theory, a framework is developed to equip these games with estimation properties of signals which are private to the agents playing the game. Token bonding curves are presented as discrete event games and numerical experiments are used to investigate their signal processing properties with a focus on input-output response dynamics.Series: Working Paper Series / Institute for Cryptoeconomics / Interdisciplinary Researc

A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Adaptive control of time-invariant systems with discrete delays subject to multiestimation

This paper deals with a robustly stable adaptive pole-placement-based controller for time-delay linear systems with unknown point delays within known intervals of sufficiently small lengths under unmodeled dynamics and bounded disturbances. A multiestimation scheme is used to improve the identification error and then to deal with possible errors between the true basic delays compared to that used in the regressor of the adaptive scheme. Each estimation scheme possess a relative dead zone for each estimation scheme which freezes the adaptation for small sizes of the adaptation error compared with the estimated size of the contribution of the uncertainties to the filtered output. All the estimation schemes run in parallel but only that, which is currently in operation, parameterizes the adaptive controller to generate the plant input at each time. A supervisory scheme chooses in real time the appropriate estimator subject to a minimum residence time which is the tool to ensure closed-loop stability under switching between the estimators in the estimation scheme. The dead zone adaptation mechanism prevents the closed-loop system against potential instability caused by uncertainties

Sparse Model Identification and Learning for Ultra-high-dimensional Additive Partially Linear Models

The additive partially linear model (APLM) combines the flexibility of nonparametric regression with the parsimony of regression models, and has been widely used as a popular tool in multivariate nonparametric regression to alleviate the "curse of dimensionality". A natural question raised in practice is the choice of structure in the nonparametric part, that is, whether the continuous covariates enter into the model in linear or nonparametric form. In this paper, we present a comprehensive framework for simultaneous sparse model identification and learning for ultra-high-dimensional APLMs where both the linear and nonparametric components are possibly larger than the sample size. We propose a fast and efficient two-stage procedure. In the first stage, we decompose the nonparametric functions into a linear part and a nonlinear part. The nonlinear functions are approximated by constant spline bases, and a triple penalization procedure is proposed to select nonzero components using adaptive group LASSO. In the second stage, we refit data with selected covariates using higher order polynomial splines, and apply spline-backfitted local-linear smoothing to obtain asymptotic normality for the estimators. The procedure is shown to be consistent for model structure identification. It can identify zero, linear, and nonlinear components correctly and efficiently. Inference can be made on both linear coefficients and nonparametric functions. We conduct simulation studies to evaluate the performance of the method and apply the proposed method to a dataset on the Shoot Apical Meristem (SAM) of maize genotypes for illustration

Data-driven fault diagnosis of awind farm benchmark model

The fault diagnosis of wind farms has been proven to be a challenging task, and motivates the research activities carried out through this work. Therefore, this paper deals with the fault diagnosis of a wind park benchmark model, and it considers viable solutions to the problem of earlier fault detection and isolation. The design of the fault indicator involves data-driven approaches, as they can represent effective tools for coping with poor analytical knowledge of the system dynamics, noise, uncertainty, and disturbances. In particular, the proposed data-driven solutions rely on fuzzy models and neural networks that are used to describe the strongly nonlinear relationships between measurement and faults. The chosen architectures rely on nonlinear autoregressive with exogenous input models, as they can represent the dynamic evolution of the system over time. The developed fault diagnosis schemes are tested by means of a high-fidelity benchmark model that simulates the normal and the faulty behaviour of a wind farm installation. The achieved performances are also compared with those of a model-based approach relying on nonlinear differential geometry tools. Finally, a Monte-Carlo analysis validates the robustness and reliability of the proposed solutions against typical parameter uncertainties and disturbances.The fault diagnosis of wind farms has been proven to be a challenging task, and motivates the research activities carried out through this work. Therefore, this paper deals with the fault diagnosis of a wind park benchmark model, and it considers viable solutions to the problem of earlier fault detection and isolation. The design of the fault indicator involves data-driven approaches, as they can represent effective tools for coping with poor analytical knowledge of the system dynamics, noise, uncertainty, and disturbances. In particular, the proposed data-driven solutions rely on fuzzy models and neural networks that are used to describe the strongly nonlinear relationships between measurement and faults. The chosen architectures rely on nonlinear autoregressive with exogenous input models, as they can represent the dynamic evolution of the system over time. The developed fault diagnosis schemes are tested by means of a high-fidelity benchmark model that simulates the normal and the faulty behaviour of a wind farm installation. The achieved performances are also compared with those of a model-based approach relying on nonlinear differential geometry tools. Finally, a Monte-Carlo analysis validates the robustness and reliability of the proposed solutions against typical parameter uncertainties and disturbances