10,663 research outputs found
Extremum Seeking-based Iterative Learning Model Predictive Control (ESILC-MPC)
In this paper, we study a tracking control problem for linear time-invariant
systems, with model parametric uncertainties, under input and states
constraints. We apply the idea of modular design introduced in Benosman et al.
2014, to solve this problem in the model predictive control (MPC) framework. We
propose to design an MPC with input-to-state stability (ISS) guarantee, and
complement it with an extremum seeking (ES) algorithm to iteratively learn the
model uncertainties. The obtained MPC algorithms can be classified as iterative
learning control (ILC)-MPC
Sample Efficient Path Integral Control under Uncertainty
We present a data-driven optimal control framework that can be viewed as a
generalization of the path integral (PI) control approach. We find iterative
feedback control laws without parameterization based on probabilistic
representation of learned dynamics model. The proposed algorithm operates in a
forward-backward manner which differentiate from other PI-related methods that
perform forward sampling to find optimal controls. Our method uses
significantly less samples to find optimal controls compared to other
approaches within the PI control family that relies on extensive sampling from
given dynamics models or trials on physical systems in model-free fashions. In
addition, the learned controllers can be generalized to new tasks without
re-sampling based on the compositionality theory for the linearly-solvable
optimal control framework. We provide experimental results on three different
systems and comparisons with state-of-the-art model-based methods to
demonstrate the efficiency and generalizability of the proposed framework
Reinforcement Learning for Batch Bioprocess Optimization
Bioprocesses have received a lot of attention to produce clean and
sustainable alternatives to fossil-based materials. However, they are generally
difficult to optimize due to their unsteady-state operation modes and
stochastic behaviours. Furthermore, biological systems are highly complex,
therefore plant-model mismatch is often present. To address the aforementioned
challenges we propose a Reinforcement learning based optimization strategy for
batch processes.
In this work, we applied the Policy Gradient method from batch-to-batch to
update a control policy parametrized by a recurrent neural network. We assume
that a preliminary process model is available, which is exploited to obtain a
preliminary optimal control policy. Subsequently, this policy is updatedbased
on measurements from thetrueplant. The capabilities of our proposed approach
were tested on three case studies (one of which is nonsmooth) using a more
complex process model for thetruesystemembedded with adequate process
disturbance. Lastly, we discussed the advantages and disadvantages of this
strategy compared against current existing approaches such as nonlinear model
predictive control
Stochastic trajectory optimization for mechanical systems with parametric uncertainties
In this paper we develop a novel, discrete-time optimal control framework for
mechanical systems with uncertain model parameters. We consider finite-horizon
problems where the performance index depends on the statistical moments of the
stochastic system. Our approach constitutes an extension of the original
Differential Dynamic Programming method and handles uncertainty through
generalized Polynomial Chaos (gPC) theory. The developed iterative scheme is
capable of controlling the probabilistic evolution of the dynamic system and
can be used in planning and control. Moreover, its scalable and fast converging
nature play a key role when dealing with complex, high-dimensional problems.
Based on Lagrangian mechanics principles, we also prove that Variational
Integrators can be designed to properly propagate and linearize the gPC
representations of stochastic, forced mechanical systems in discrete time. We
utilize this benefit to further improve the efficiency of our
trajectory-optimization methodology. Numerical simulations are included to
validate the applicability of our approach
Modeling and identification of uncertain-input systems
In this work, we present a new class of models, called uncertain-input
models, that allows us to treat system-identification problems in which a
linear system is subject to a partially unknown input signal. To encode prior
information about the input or the linear system, we use Gaussian-process
models. We estimate the model from data using the empirical Bayes approach: the
input and the impulse responses of the linear system are estimated using the
posterior means of the Gaussian-process models given the data, and the
hyperparameters that characterize the Gaussian-process models are estimated
from the marginal likelihood of the data. We propose an iterative algorithm to
find the hyperparameters that relies on the EM method and results in simple
update steps. In the most general formulation, neither the marginal likelihood
nor the posterior distribution of the unknowns is tractable. Therefore, we
propose two approximation approaches, one based on Markov-chain Monte Carlo
techniques and one based on variational Bayes approximation. We also show
special model structures for which the distributions are treatable exactly.
Through numerical simulations, we study the application of the uncertain-input
model to the identification of Hammerstein systems and cascaded linear systems.
As part of the contribution of the paper, we show that this model structure
encompasses many classical problems in system identification such as classical
PEM, Hammerstein models, errors-in-variables problems, blind system
identification, and cascaded linear systems. This allows us to build a
systematic procedure to apply the algorithms proposed in this work to a wide
class of classical problems.Comment: 27 Pages, submitted to Automatic
New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems
This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use
Active Sampling for Constrained Simulation-based Verification of Uncertain Nonlinear Systems
Increasingly demanding performance requirements for dynamical systems
motivates the adoption of nonlinear and adaptive control techniques. One
challenge is the nonlinearity of the resulting closed-loop system complicates
verification that the system does satisfy the requirements at all possible
operating conditions. This paper presents a data-driven procedure for efficient
simulation-based, statistical verification without the reliance upon exhaustive
simulations. In contrast to previous work, this approach introduces a method
for online estimation of prediction accuracy without the use of external
validation sets. This work also develops a novel active sampling algorithm that
iteratively selects additional training points in order to maximize the
accuracy of the predictions while still limited to a sample budget. Three case
studies demonstrate the utility of the new approach and the results show up to
a 50% improvement over state-of-the-art techniques.Comment: 8 pages, submitted to ACC 201
Optimization under Uncertainty in the Era of Big Data and Deep Learning: When Machine Learning Meets Mathematical Programming
This paper reviews recent advances in the field of optimization under
uncertainty via a modern data lens, highlights key research challenges and
promise of data-driven optimization that organically integrates machine
learning and mathematical programming for decision-making under uncertainty,
and identifies potential research opportunities. A brief review of classical
mathematical programming techniques for hedging against uncertainty is first
presented, along with their wide spectrum of applications in Process Systems
Engineering. A comprehensive review and classification of the relevant
publications on data-driven distributionally robust optimization, data-driven
chance constrained program, data-driven robust optimization, and data-driven
scenario-based optimization is then presented. This paper also identifies
fertile avenues for future research that focuses on a closed-loop data-driven
optimization framework, which allows the feedback from mathematical programming
to machine learning, as well as scenario-based optimization leveraging the
power of deep learning techniques. Perspectives on online learning-based
data-driven multistage optimization with a learning-while-optimizing scheme is
presented
Fractional-order Generalized Principle of Self-Support (FOG PSS) in Control Systems Design
This paper reviews research that studies the principle of self-support (PSS)
in some control systems and proposes a fractional-order generalized PSS
framework for the first time. The existing PSS approach focuses on practical
tracking problem of integer-order systems including robotic dynamics, high
precision linear motor system, multi-axis high precision positioning system
with unmeasurable variables, imprecise sensor information, uncertain parameters
and external disturbances. More generally, by formulating the fractional PSS
concept as a new generalized framework, we will focus in the possible fields on
the fractional-order control problems such as practical tracking,
-tracking, etc. of robot systems, multiple mobile agents, discrete
dynamical systems, time delay systems and other uncertain nonlinear systems.
Finally, the practical tracking of a first-order uncertain model of automobile
is considered as a simple example to demonstrate the efficiency of the
fractional-order generalized principle of self-support (FOGPSS) control
strategy
Direct Synthesis of Iterative Algorithms With Bounds on Achievable Worst-Case Convergence Rate
Iterative first-order methods such as gradient descent and its variants are
widely used for solving optimization and machine learning problems. There has
been recent interest in analytic or numerically efficient methods for computing
worst-case performance bounds for such algorithms, for example over the class
of strongly convex loss functions. A popular approach is to assume the
algorithm has a fixed size (fixed dimension, or memory) and that its structure
is parameterized by one or two hyperparameters, for example a learning rate and
a momentum parameter. Then, a Lyapunov function is sought to certify robust
stability and subsequent optimization can be performed to find optimal
hyperparameter tunings. In the present work, we instead fix the constraints
that characterize the loss function and apply techniques from robust control
synthesis to directly search over algorithms. This approach yields stronger
results than those previously available, since the bounds produced hold over
algorithms with an arbitrary, but finite, amount of memory rather than just
holding for algorithms with a prescribed structure.Comment: American Control Conference, 202
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