30 research outputs found
On the Finite-Time Behavior of Suboptimal Linear Model Predictive Control
Inexact methods for model predictive control (MPC), such as real-time
iterative schemes or time-distributed optimization, alleviate the computational
burden of exact MPC by providing suboptimal solutions. While the asymptotic
stability of such algorithms is well studied, their finite-time performance has
not received much attention. In this work, we quantify the performance of
suboptimal linear model predictive control in terms of the additional
closed-loop cost incurred due to performing only a finite number of
optimization iterations. Leveraging this novel analysis framework, we propose a
novel suboptimal MPC algorithm with a diminishing horizon length and
finite-time closed-loop performance guarantees. This analysis allows the
designer to plan a limited computational power budget distribution to achieve a
desired performance level. We provide numerical examples to illustrate the
algorithm's transient behavior and computational complexity.Comment: Accepted for Publication at the 62nd IEEE Conference on Decision and
Control (CDC), Singapore, 202
Stochastic Wasserstein Gradient Flows using Streaming Data with an Application in Predictive Maintenance
We study estimation problems in safety-critical applications with streaming
data. Since estimation problems can be posed as optimization problems in the
probability space, we devise a stochastic projected Wasserstein gradient flow
that keeps track of the belief of the estimated quantity and can consume
samples from online data. We show the convergence properties of our algorithm.
Our analysis combines recent advances in the Wasserstein space and its
differential structure with more classical stochastic gradient descent. We
apply our methodology for predictive maintenance of safety-critical processes:
Our approach is shown to lead to superior performance when compared to
classical least squares, enabling, among others, improved robustness for
decision-making.Comment: Accepted for presentation at, and publication in the proceedings of,
the 2023 IFAC World Congres
A Model Predictive Control Framework for Improving Risk-Tolerance of Manufacturing Systems
The need for control strategies that can address dynamic system uncertainty
is becoming increasingly important. In this work, we propose a Model Predictive
Control by quantifying the risk of failure in our system model. The proposed
control scheme uses a Priced Timed Automata representation of the manufacturing
system to promote the fail-safe operation of systems under uncertainties. The
proposed method ensures that in case of unforeseen failure(s), the
optimization-based control strategy can still achieve the manufacturing system
objective. In addition, the proposed strategy establishes a trade-off between
minimizing the cost and reducing failure risk to allow the manufacturing system
to function effectively in the presence of uncertainties. An example from
manufacturing systems is presented to show the application of the proposed
control strategy.Comment: 7 page
Efficient sample selection for safe learning
Ensuring safety in industrial control systems usually involves imposing
constraints at the design stage of the control algorithm. Enforcing constraints
is challenging if the underlying functional form is unknown. The challenge can
be addressed by using surrogate models, such as Gaussian processes, which
provide confidence intervals used to find solutions that can be considered
safe. This in turn involves an exhaustive search on the entire search space.
That approach can quickly become computationally expensive. We reformulate the
exhaustive search as a series of optimization problems to find the next
recommended points. We show that the proposed reformulation allows using a wide
range of available optimization solvers, such as derivative-free methods. We
show that by exploiting the properties of the solver, we enable the
introduction of new stopping criteria into safe learning methods and increase
flexibility in trading off solver accuracy and computational time. The results
from a non-convex optimization problem and an application for controller tuning
confirm the flexibility and the performance of the proposed reformulation
Risk-Averse Model Predictive Control for Priced Timed Automata
In this paper, we propose a Risk-Averse Priced Timed Automata (PTA) Model
Predictive Control (MPC) framework to increase flexibility of cyber-physical
systems. To improve flexibility in these systems, our risk-averse framework
solves a multi-objective optimization problem to minimize the cost and risk,
simultaneously. While minimizing cost ensures the least effort to achieve a
task, minimizing risk provides guarantees on the feasibility of the task even
during uncertainty. Our framework explores the trade-off between these two
qualities to obtain risk-averse control actions. The solution of risk-averse
PTA MPC dynamic decision-making algorithm reacts relatively better to PTA
changes compared to PTA MPC without risk-averse feature. An example from
manufacturing systems is presented to show the application of the proposed
control strategy.Comment: 7 page
Sequential Quadratic Programming-based Iterative Learning Control for Nonlinear Systems
Learning-based control methods for industrial processes leverage the
repetitive nature of the underlying process to learn optimal inputs for the
system. While many works focus on linear systems, real-world problems involve
nonlinear dynamics. In this work, we propose an algorithm for the nonlinear
iterative learning control problem based on sequential quadratic programming, a
well-studied method for nonconvex optimization. We repeatedly solve quadratic
subproblems built using approximate nonlinear models and process measurements,
to find an optimal input for the original system. We demonstrate our method in
a trajectory optimization problem for a precision motion system. We present
simulations to illustrate the performance of the proposed method for linear and
nonlinear dynamics models
Data-Driven Process Optimization of Fused Filament Fabrication based on In Situ Measurements
The tuning of fused filament fabrication parameters is notoriously
challenging. We propose an autonomous data-driven method to select parameters
based on in situ measurements. We use a laser sensor to evaluate the surface
roughness of a printed part. We then correlate the roughness to the mechanical
properties of the part, and show how print quality affects mechanical
performance. Finally, we use Bayesian optimization to search for optimal print
parameters. We demonstrate our method by printing liquid crystal polymer
samples, and successfully find parameters that produce high-performance prints
and maximize the manufacturing process efficiency.Comment: 7 pages, 6 figures. Submitted to IFAC WC 202
Safe Risk-averse Bayesian Optimization for Controller Tuning
Controller tuning and parameter optimization are crucial in system design to
improve both the controller and underlying system performance. Bayesian
optimization has been established as an efficient model-free method for
controller tuning and adaptation. Standard methods, however, are not enough for
high-precision systems to be robust with respect to unknown input-dependent
noise and stable under safety constraints. In this work, we present a novel
data-driven approach, RaGoOSE, for safe controller tuning in the presence of
heteroscedastic noise, combining safe learning with risk-averse Bayesian
optimization. We demonstrate the method for synthetic benchmark and compare its
performance to established BO-based tuning methods. We further evaluate RaGoOSE
performance on a real precision-motion system utilized in semiconductor
industry applications and compare it to the built-in auto-tuning routine
Efficient safe learning for controller tuning with experimental validation
Optimization-based controller tuning is challenging because it requires
formulating optimization problems explicitly as functions of controller
parameters. Safe learning algorithms overcome the challenge by creating
surrogate models from measured data. To ensure safety, such data-driven
algorithms often rely on exhaustive grid search, which is computationally
inefficient. In this paper, we propose a novel approach to safe learning by
formulating a series of optimization problems instead of a grid search. We also
develop a method for initializing the optimization problems to guarantee
feasibility while using numerical solvers. The performance of the new method is
first validated in a simulated precision motion system, demonstrating improved
computational efficiency, and illustrating the role of exploiting numerical
solvers to reach the desired precision. Experimental validation on an
industrial-grade precision motion system confirms that the proposed algorithm
achieves 30% better tracking at sub-micrometer precision as a state-of-the-art
safe learning algorithm, improves the default auto-tuning solution, and reduces
the computational cost seven times compared to learning algorithms based on
exhaustive search
Layer-to-Layer Melt Pool Control in Laser Power Bed Fusion
Additive manufacturing processes are flexible and efficient technologies for
producing complex geometries. However, ensuring reliability and repeatability
is challenging due to the complex physics and various sources of uncertainty in
the process. In this work, we investigate closed-loop control of the melt pool
dimensions in a laser powder bed fusion (LPBF) process. We propose a trajectory
optimization-based layer-to-layer controller that adjusts the laser power input
to the next layer to track a desired melt pool depth and validate our
controller by placing it in closed-loop high-fidelity multi-layer smoothed
particle hydrodynamics simulator of a 2D LPBF process. Detailed numerical case
studies demonstrate successful regulation of the melt pool depth on brick and
overhang geometries and provide first of its kind results on the effectiveness
of layer-to-layer input optimization for the LPBF process as well as detailed
insight into the physics of the controlled process. Computational complexity
and process performance results illustrate the method's effectiveness and
provide an outlook for its implementation onto real systems