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Observer Design for Interconnected Systems and Implementation via Differential-Algebraic Equations
A new approach to the design of observers of nonlinear dynamical systems is presented. Generally, linear or nonlinear control systems are expressed as explicit systems of differential equations and solved either analytically or numerically. If numerically, they are implemented using standard ordinary differential equation (ODE) solvers. In this thesis, a system is decomposed and modeled as an interconnection between two observer subsystems, particularly, as canonical DAE observers. In general, control design engineers may be faced with a formidable problem of solving this system analytically or in obtaining closed-form solutions. To attest to the complexity and complications in treating a system of interconnected DAE observer systems, a scaled-down version of a publication on “Small-Gain Theorem” is included in the appendix for the reader’s perusal. (A brief introduction to “Small-Gain Theorem” can be found in Chapter 4). The premise of this thesis is to demonstrate that, where the design of an observer plays a major role involving output feedback, there may be advantages in formulating a control system as a differential-algebraic equation (DAE), especially in the case of interconnected subsystems. An implicit system of interconnected DAE observers is considered and shown implementable using an existing DAE solver, whose resolution allows one the capability of computing input and output bounds. This is based on fixed or variable timesteps within the operating interval of each subsystem to ensure input-output stability (IOS) and the observability property of the interconnected observer system. The observer design method is based on the extended linearization approach. The basic background is provided for the design process of an interconnected observer system using DAE. Note, the application of the new approach has not been considered previously for the case of an interconnected DAE observer system
Interval Prediction for Continuous-Time Systems with Parametric Uncertainties
The problem of behaviour prediction for linear parameter-varying systems is
considered in the interval framework. It is assumed that the system is subject
to uncertain inputs and the vector of scheduling parameters is unmeasurable,
but all uncertainties take values in a given admissible set. Then an interval
predictor is designed and its stability is guaranteed applying Lyapunov
function with a novel structure. The conditions of stability are formulated in
the form of linear matrix inequalities. Efficiency of the theoretical results
is demonstrated in the application to safe motion planning for autonomous
vehicles.Comment: 6 pages, CDC 2019. Website:
https://eleurent.github.io/interval-prediction
Contracting Nonlinear Observers: Convex Optimization and Learning from Data
A new approach to design of nonlinear observers (state estimators) is
proposed. The main idea is to (i) construct a convex set of dynamical systems
which are contracting observers for a particular system, and (ii) optimize over
this set for one which minimizes a bound on state-estimation error on a
simulated noisy data set. We construct convex sets of continuous-time and
discrete-time observers, as well as contracting sampled-data observers for
continuous-time systems. Convex bounds for learning are constructed using
Lagrangian relaxation. The utility of the proposed methods are verified using
numerical simulation.Comment: conference submissio
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
LMI-Based Reset Unknown Input Observer for State Estimation of Linear Uncertain Systems
This paper proposes a novel kind of Unknown Input Observer (UIO) called Reset
Unknown Input Observer (R-UIO) for state estimation of linear systems in the
presence of disturbance using Linear Matrix Inequality (LMI) techniques. In
R-UIO, the states of the observer are reset to the after-reset value based on
an appropriate reset law in order to decrease the norm and settling time
of estimation error. It is shown that the application of the reset theory to
the UIOs in the LTI framework can significantly improve the transient response
of the observer. Moreover, the devised approach can be applied to both SISO and
MIMO systems. Furthermore, the stability and convergence analysis of the
devised R-UIO is addressed. Finally, the efficiency of the proposed method is
demonstrated by simulation results
Robust fault detection for vehicle lateral dynamics: Azonotope-based set-membership approach
© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksIn this work, a model-based fault detection layoutfor vehicle lateral dynamics system is presented. The majorfocus in this study is on the handling of model uncertainties andunknown inputs. In fact, the vehicle lateral model is affectedby several parameter variations such as longitudinal velocity,cornering stiffnesses coefficients and unknown inputs like windgust disturbances. Cornering stiffness parameters variation isconsidered to be unknown but bounded with known compactset. Their effect is addressed by generating intervals for theresiduals based on the zonotope representation of all possiblevalues. The developed fault detection procedure has been testedusing real driving data acquired from a prototype vehicle.Index Terms— Robust fault detection, interval models,zonotopes, set-membership, switched uncertain systems, LMIs,input-to-state stability, arbitrary switching.Peer ReviewedPostprint (author's final draft
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