25 research outputs found
Learning Stable and Robust Linear Parameter-Varying State-Space Models
This paper presents two direct parameterizations of stable and robust linear
parameter-varying state-space (LPV-SS) models. The model parametrizations
guarantee a priori that for all parameter values during training, the allowed
models are stable in the contraction sense or have their Lipschitz constant
bounded by a user-defined value . Furthermore, since the
parametrizations are direct, the models can be trained using unconstrained
optimization. The fact that the trained models are of the LPV-SS class makes
them useful for, e.g., further convex analysis or controller design. The
effectiveness of the approach is demonstrated on an LPV identification problem.Comment: Accepted for the 62nd IEEE Conference on Decision and Control
(CDC2023
Deep-Learning-Based Identification of LPV Models for Nonlinear Systems
The framework of Linear Parameter-Varying (LPV) systems is part of the modern
modeling and control design toolchain for addressing nonlinear system behaviors
through linear surrogate models. Despite the significant research effort spent
on LPV data-driven modeling, a key shortcoming of the current identification
theory is that often the scheduling variable is assumed to be a given measured
signal in the data set. In case of identifying an LPV model of a nonlinear
system, the selection of the scheduling, i.e., the scheduling map that
describes its relation to measurable signals in the system, is put on the
users' shoulder, with only limited supporting tools available. Although, such a
choice greatly affects the usability and the complexity of the resulting LPV
model. This paper presents a deep-learning based approach to provide joint
estimation of a scheduling map and an LPV state-space model of a nonlinear
system from input-output data. The approach has consistency guarantees under
general innovation type of noise conditions, and its efficiency is demonstrated
on the identification problem of a control moment gyroscope.Comment: Submitted to the 61st IEEE Conference on Decision and Contro
LMI-based design of state-feedback controllers for pole clustering of LPV systems in a union of -regions
This paper introduces an approach for the design of a state-feedback controller that achieves pole clustering in a union of DR-regions for linear parameter varying systems. The design conditions, obtained using a partial pole placement theorem, are eventually expressed in terms of linear matrix inequalities. In addition, it is shown that the approach can be modified in a shifting sense. Hence, the controller gain is computed such that different values of the varying parameters imply different regions of the complex plane where the closed-loop poles are situated. This approach enables the online modification of the closed-loop performance. The effectiveness of the proposed method is demonstrated by means of simulations.Peer ReviewedPostprint (author's final draft
A Structured Prediction Approach for Robot Imitation Learning
We propose a structured prediction approach for robot imitation learning from
demonstrations. Among various tools for robot imitation learning, supervised
learning has been observed to have a prominent role. Structured prediction is a
form of supervised learning that enables learning models to operate on output
spaces with complex structures. Through the lens of structured prediction, we
show how robots can learn to imitate trajectories belonging to not only
Euclidean spaces but also Riemannian manifolds. Exploiting ideas from
information theory, we propose a class of loss functions based on the
f-divergence to measure the information loss between the demonstrated and
reproduced probabilistic trajectories. Different types of f-divergence will
result in different policies, which we call imitation modes. Furthermore, our
approach enables the incorporation of spatial and temporal trajectory
modulation, which is necessary for robots to be adaptive to the change in
working conditions. We benchmark our algorithm against state-of-the-art methods
in terms of trajectory reproduction and adaptation. The quantitative evaluation
shows that our approach outperforms other algorithms regarding both accuracy
and efficiency. We also report real-world experimental results on learning
manifold trajectories in a polishing task with a KUKA LWR robot arm,
illustrating the effectiveness of our algorithmic framework
LMI-based design of state-feedback controllers for pole clustering of LPV systems in a union of DR-regions
This paper introduces an approach for the design of a state-feedback controller that achieves pole clustering in a union of DR-regions for linear parameter varying systems. The design conditions, obtained using a partial pole placement theorem, are eventually expressed in terms of linear matrix inequalities. In addition, it is shown that the approach can be modified in a shifting sense. Hence, the controller gain is computed such that different values of the varying parameters imply different regions of the complex plane where the closed-loop poles are situated. This approach enables the online modification of the closed-loop performance. The effectiveness of the proposed method is demonstrated by means of simulations.acceptedVersio
A structured prediction approach for robot imitation learning
We propose a structured prediction approach for robot imitation learning from demonstrations. Among various tools for robot imitation learning, supervised learning has been observed to have a prominent role. Structured prediction is a form of supervised learning that enables learning models to operate on output spaces with complex structures. Through the lens of structured prediction, we show how robots can learn to imitate trajectories belonging to not only Euclidean spaces but also Riemannian manifolds. Exploiting ideas from information theory, we propose a class of loss functions based on the f-divergence to measure the information loss between the demonstrated and reproduced probabilistic trajectories. Different types of f-divergence will result in different policies, which we call imitation modes. Furthermore, our approach enables the incorporation of spatial and temporal trajectory modulation, which is necessary for robots to be adaptive to the change in working conditions. We benchmark our algorithm against state-of-the-art methods in terms of trajectory reproduction and adaptation. The quantitative evaluation shows that our approach outperforms other algorithms regarding both accuracy and efficiency. We also report real-world experimental results on learning manifold trajectories in a polishing task with a KUKA LWR robot arm, illustrating the effectiveness of our algorithmic framework
Meta-State-Space Learning: An Identification Approach for Stochastic Dynamical Systems
Available methods for identification of stochastic dynamical systems from
input-output data generally impose restricting structural assumptions on either
the noise structure in the data-generating system or the possible state
probability distributions. In this paper, we introduce a novel identification
method of such systems, which results in a dynamical model that is able to
produce the time-varying output distribution accurately without taking
restrictive assumptions on the data-generating process. The method is
formulated by first deriving a novel and exact representation of a wide class
of nonlinear stochastic systems in a so-called meta-state-space form, where the
meta-state can be interpreted as a parameter vector of a state probability
function space parameterization. As the resulting representation of the
meta-state dynamics is deterministic, we can capture the stochastic system
based on a deterministic model, which is highly attractive for identification.
The meta-state-space representation often involves unknown and heavily
nonlinear functions, hence, we propose an artificial neural network (ANN)-based
identification method capable of efficiently learning nonlinear
meta-state-space models. We demonstrate that the proposed identification method
can obtain models with a log-likelihood close to the theoretical limit even for
highly nonlinear, highly stochastic systems.Comment: Submitted to Automatic