61,899 research outputs found
Set-based state estimation and fault diagnosis using constrained zonotopes and applications
This doctoral thesis develops new methods for set-based state estimation and
active fault diagnosis (AFD) of (i) nonlinear discrete-time systems, (ii)
discrete-time nonlinear systems whose trajectories satisfy nonlinear equality
constraints (called invariants), (iii) linear descriptor systems, and (iv)
joint state and parameter estimation of nonlinear descriptor systems. Set-based
estimation aims to compute tight enclosures of the possible system states in
each time step subject to unknown-but-bounded uncertainties. To address this
issue, the present doctoral thesis proposes new methods for efficiently
propagating constrained zonotopes (CZs) through nonlinear mappings. Besides,
this thesis improves the standard prediction-update framework for systems with
invariants using new algorithms for refining CZs based on nonlinear
constraints. In addition, this thesis introduces a new approach for set-based
AFD of a class of nonlinear discrete-time systems. An affine parametrization of
the reachable sets is obtained for the design of an optimal input for set-based
AFD. In addition, this thesis presents new methods based on CZs for set-valued
state estimation and AFD of linear descriptor systems. Linear static
constraints on the state variables can be directly incorporated into CZs.
Moreover, this thesis proposes a new representation for unbounded sets based on
zonotopes, which allows to develop methods for state estimation and AFD also of
unstable linear descriptor systems, without the knowledge of an enclosure of
all the trajectories of the system. This thesis also develops a new method for
set-based joint state and parameter estimation of nonlinear descriptor systems
using CZs in a unified framework. Lastly, this manuscript applies the proposed
set-based state estimation and AFD methods using CZs to unmanned aerial
vehicles, water distribution networks, and a lithium-ion cell.Comment: My PhD Thesis from Federal University of Minas Gerais, Brazil. Most
of the research work has already been published in DOIs
10.1109/CDC.2018.8618678, 10.23919/ECC.2018.8550353,
10.1016/j.automatica.2019.108614, 10.1016/j.ifacol.2020.12.2484,
10.1016/j.ifacol.2021.08.308, 10.1016/j.automatica.2021.109638,
10.1109/TCST.2021.3130534, 10.1016/j.automatica.2022.11042
Online Optimization of Dynamical Systems with Deep Learning Perception
This paper considers the problem of controlling a dynamical system when the
state cannot be directly measured and the control performance metrics are
unknown or partially known. In particular, we focus on the design of
data-driven controllers to regulate a dynamical system to the solution of a
constrained convex optimization problem where: i) the state must be estimated
from nonlinear and possibly high-dimensional data; and, ii) the cost of the
optimization problem -- which models control objectives associated with inputs
and states of the system -- is not available and must be learned from data. We
propose a data-driven feedback controller that is based on adaptations of a
projected gradient-flow method; the controller includes neural networks as
integral components for the estimation of the unknown functions. Leveraging
stability theory for perturbed systems, we derive sufficient conditions to
guarantee exponential input-to-state stability (ISS) of the control loop. In
particular, we show that the interconnected system is ISS with respect to the
approximation errors of the neural network and unknown disturbances affecting
the system. The transient bounds combine the universal approximation property
of deep neural networks with the ISS characterization. Illustrative numerical
results are presented in the context of control of robotics and epidemics.Comment: This is an extended version of the paper submitted to the IEEE Open
Journal of Control Systems - Special Section on Machine Learning with
Control, containing proof
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
Identification of Structured LTI MIMO State-Space Models
The identification of structured state-space model has been intensively
studied for a long time but still has not been adequately addressed. The main
challenge is that the involved estimation problem is a non-convex (or bilinear)
optimization problem. This paper is devoted to developing an identification
method which aims to find the global optimal solution under mild computational
burden. Key to the developed identification algorithm is to transform a
bilinear estimation to a rank constrained optimization problem and further a
difference of convex programming (DCP) problem. The initial condition for the
DCP problem is obtained by solving its convex part of the optimization problem
which happens to be a nuclear norm regularized optimization problem. Since the
nuclear norm regularized optimization is the closest convex form of the
low-rank constrained estimation problem, the obtained initial condition is
always of high quality which provides the DCP problem a good starting point.
The DCP problem is then solved by the sequential convex programming method.
Finally, numerical examples are included to show the effectiveness of the
developed identification algorithm.Comment: Accepted to IEEE Conference on Decision and Control (CDC) 201
Bayesian model predictive control: Efficient model exploration and regret bounds using posterior sampling
Tight performance specifications in combination with operational constraints
make model predictive control (MPC) the method of choice in various industries.
As the performance of an MPC controller depends on a sufficiently accurate
objective and prediction model of the process, a significant effort in the MPC
design procedure is dedicated to modeling and identification. Driven by the
increasing amount of available system data and advances in the field of machine
learning, data-driven MPC techniques have been developed to facilitate the MPC
controller design. While these methods are able to leverage available data,
they typically do not provide principled mechanisms to automatically trade off
exploitation of available data and exploration to improve and update the
objective and prediction model. To this end, we present a learning-based MPC
formulation using posterior sampling techniques, which provides finite-time
regret bounds on the learning performance while being simple to implement using
off-the-shelf MPC software and algorithms. The performance analysis of the
method is based on posterior sampling theory and its practical efficiency is
illustrated using a numerical example of a highly nonlinear dynamical
car-trailer system
Concurrent Learning Adaptive Model Predictive Control with Pseudospectral Implementation
This paper presents a control architecture in which a direct adaptive control
technique is used within the model predictive control framework, using the
concurrent learning based approach, to compensate for model uncertainties. At
each time step, the control sequences and the parameter estimates are both used
as the optimization arguments, thereby undermining the need for switching
between the learning phase and the control phase, as is the case with
hybrid-direct-indirect control architectures. The state derivatives are
approximated using pseudospectral methods, which are vastly used for numerical
optimal control problems. Theoretical results and numerical simulation examples
are used to establish the effectiveness of the architecture.Comment: 21 pages, 13 figure
Robust Adaptive Control Barrier Functions: An Adaptive & Data-Driven Approach to Safety (Extended Version)
A new framework is developed for control of constrained nonlinear systems
with structured parametric uncertainties. Forward invariance of a safe set is
achieved through online parameter adaptation and data-driven model estimation.
The new adaptive data-driven safety paradigm is merged with a recent adaptive
control algorithm for systems nominally contracting in closed-loop. This
unification is more general than other safety controllers as closed-loop
contraction does not require the system be invertible or in a particular form.
Additionally, the approach is less expensive than nonlinear model predictive
control as it does not require a full desired trajectory, but rather only a
desired terminal state. The approach is illustrated on the pitch dynamics of an
aircraft with uncertain nonlinear aerodynamics.Comment: Added aCBF non-Lipschitz example and discussion on approach
implementatio
Reducing “Structure from Motion”: a general framework for dynamic vision. 1. Modeling
The literature on recursive estimation of structure and motion from monocular image sequences comprises a large number of apparently unrelated models and estimation techniques. We propose a framework that allows us to derive and compare all models by following the idea of dynamical system reduction. The “natural” dynamic model, derived from the rigidity constraint and the projection model, is first reduced by explicitly decoupling structure (depth) from motion. Then, implicit decoupling techniques are explored, which consist of imposing that some function of the unknown parameters is held constant. By appropriately choosing such a function, not only can we account for models seen so far in the literature, but we can also derive novel ones
Model predictive control techniques for hybrid systems
This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non-fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.Ministerio de EduaciĂłn y Ciencia DPI2007-66718-C04-01Ministerio de EduaciĂłn y Ciencia DPI2008-0581
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