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Congestion on highways has become a significant social problem due to the increasing number of vehicles, leading to considerable waste of time and pollution. Regulating the outflow from the Service Station can help alleviate this congestion. Notably, traffic flows follow recurring patterns over days and weeks, allowing for the application of Iterative Learning Control (ILC). Building on these insights, we propose an ILC approach based on the Cell Transmission Model with service stations (CTM-s). It is shown that ILC can effectively compensate for potential inaccuracies in model parameter estimates by leveraging historical data.

In this paper, we consider the problem of predicting unknown targets from data. We propose Online Residual Learning (ORL), a method that combines online adaptation with offline-trained predictions. At a lower level, we employ multiple offline predictions generated before or at the beginning of the prediction horizon. We augment every offline prediction by learning their respective residual error concerning the true target state online, using the recursive least squares algorithm. At a higher level, we treat the augmented lower-level predictors as experts, adopting the Prediction with Expert Advice framework. We utilize an adaptive softmax weighting scheme to form an aggregate prediction and provide guarantees for ORL in terms of regret. We employ ORL to boost performance in the setting of online pedestrian trajectory prediction. Based on data from the Stanford Drone Dataset, we show that ORL can demonstrate best-of-both-worlds performance., Comment: Accepted to CDC 2024, v2: fixed certain typos

Open-loop control of laser powder bed fusion (LPBF) additive manufacturing (AM) has enabled the production of complex, high-criticality parts for various industries. This method relies on static parameter sets from extensive experimentation and simulations, hoping they remain stable and defect-free in production. Closed-loop control of LPBF can further enhance process stability and reduce defects despite complex thermal histories, process noise, hardware drift, and unexpected perturbations. Controller performance depends on parameter tuning, traditionally a manual, expertise-driven process with no guarantee of optimal performance and limited transferability between systems. This study proposes Bayesian Optimization (BO) to automate in-layer controller tuning by leveraging LPBF's layer-to-layer repetitive nature. Two approaches are introduced: online tuning, adjusting parameters iteratively during the process, and offline tuning, conducted in a setup such as laser exposures on a bare metal plate. These methods are experimentally implemented on an in-layer PI controller, and the performance is investigated on two wedge geometries prone to overheating. Results show that BO effectively tunes controllers using either method, significantly reducing overheating in controlled wedge specimens compared to uncontrolled ones. This study presents the first printed parts controlled by an in-layer controller subjected to microstructural analysis. Findings reveal partial presence of lack-of-fusion porosities due to insufficient laser power assigned by the controller, highlighting a significant challenge for utilizing laser power controllers. In summary, BO presents a promising method for automatic in-layer controller tuning in LPBF, enhancing control precision and mitigating overheating in production parts.

Controller tuning and parameter optimization are crucial in system design to improve closed-loop system performance. Bayesian optimization has been established as an efficient model-free controller tuning and adaptation method. However, Bayesian optimization methods are computationally expensive and therefore difficult to use in real-time critical scenarios. In this work, we propose a real-time purely data-driven, model-free approach for adaptive control, by online tuning low-level controller parameters. We base our algorithm on GoOSE, an algorithm for safe and sample-efficient Bayesian optimization, for handling performance and stability criteria. We introduce multiple computational and algorithmic modifications for computational efficiency and parallelization of optimization steps. We further evaluate the algorithm's performance on a real precision-motion system utilized in semiconductor industry applications by modifying the payload and reference stepsize and comparing it to an interpolated constrained optimization-based baseline approach.

In this study, we present a novel swarm-based approach for generating optimized stress-aligned trajectories for 3D printing applications. The method utilizes swarming dynamics to simulate the motion of virtual agents along the stress produced in a loaded part. Agent trajectories are then used as print trajectories. With this approach, the complex global trajectory generation problem is subdivided into a set of sequential and computationally efficient quadratic programs. Through comprehensive evaluations in both simulation and experiments, we compare our method with state-of-the-art approaches. Our results highlight a remarkable improvement in computational efficiency, achieving a 115x faster computation speed than existing methods. This efficiency, combined with the possibility to tune the trajectories spacing to match the deposition process constraints, makes the potential integration of our approach into existing 3D printing processes seamless. Additionally, the open-hole tensile specimen produced on a conventional fused filament fabrication set-up with our algorithm achieve a notable ~10% improvement in specific modulus compared to existing trajectory optimization methods., Comment: To be submitted to IEEE Access

Continuous-time adaptive controllers for systems with a matched uncertainty often comprise an online parameter estimator and a corresponding parameterized controller to cancel the uncertainty. However, such methods are often impossible to implement directly, as they depend on an unobserved estimation error. We consider the equivalent discrete-time setting with a causal information structure, and propose a novel, online proximal point method-based adaptive controller, that under a sufficient excitation (SE) condition is asymptotically stable and achieves finite regret, scaling only with the time required to fulfill the SE. We show the same also for the widely-used recursive least squares with exponential forgetting controller under a stronger persistence of excitation condition., Comment: Accepted at the 63rd IEEE Conference on Decision and Control (CDC) 2024

The quality of 3D prints often varies due to different conditions inherent to each print, such as filament type, print speed, and nozzle size. Closed-loop process control methods improve the accuracy and repeatability of 3D prints. However, optimal tuning of controllers for given process parameters and design geometry is often a challenge with manually tuned controllers resulting in inconsistent and suboptimal results. This work employs Bayesian optimization to identify the optimal controller parameters. Additionally, we explore transfer learning in the context of 3D printing by leveraging prior information from past trials. By integrating optimized extrusion force control and transfer learning, we provide a novel framework for closed-loop 3D printing and propose an automated calibration routine that produces high-quality prints for a desired combination of print settings, material, and shape., Comment: Submitted to IEEE CASE 2024

In material extrusion additive manufacturing, the extrusion process is commonly controlled in a feed-forward fashion. The amount of material to be extruded at each printing location is pre-computed by a planning software. This approach is inherently unable to adapt the extrusion to external and unexpected disturbances, and the quality of the results strongly depends on a number of modeling and tuning parameters. To overcome these limitations, we propose the first framework for Force Controlled Printing for material extrusion additive manufacturing. We utilize a custom-built extruder to measure the extrusion force in real time, and use this quantity as feedback to continuously control the material flow in closed-loop. We demonstrate the existence of a strong correlation between extrusion force and line width, which we exploit to deposit lines of desired width in a width range of 33 % up to 233 % of the nozzle diameter. We also show how Force Controlled Printing outperforms conventional feed-forward extrusion in print quality and disturbance rejection, while requiring little tuning and automatically adapting to changes in the hardware settings. With no adaptation, Force Controlled Printing can deposit lines of desired width under severe disturbances in bed leveling, such as at layer heights ranging between 20 % and 200 % of the nominal height., Comment: Preprint to be submitted to Elsevier Additive Manufacturing

This work introduces the Data-Enabled Predictive iteRative Control (DeePRC) algorithm, a direct data-driven approach for iterative LTI systems. The DeePRC learns from previous iterations to improve its performance and achieves the optimal cost. By utilizing a tube-based variation of the DeePRC scheme, we propose a two-stage approach that enables safe active exploration using a left-kernel-based input disturbance design. This method generates informative trajectories to enrich the historical data, which extends the maximum achievable prediction horizon and leads to faster iteration convergence. In addition, we present an end-to-end formulation of the two-stage approach, integrating the disturbance design procedure into the planning phase. We showcase the effectiveness of the proposed algorithms on a numerical experiment.

It is well known that ignoring the presence of stochastic disturbances in the identification of stochastic Wiener models leads to asymptotically biased estimators. On the other hand, optimal statistical identification, via likelihood-based methods, is sensitive to the assumptions on the data distribution and is usually based on relatively complex sequential Monte Carlo algorithms. We develop a simple recursive online estimation algorithm based on an output-error predictor, for the identification of continuous-time stochastic parametric Wiener models through stochastic approximation. The method is applicable to generic model parameterizations and, as demonstrated in the numerical simulation examples, it is robust with respect to the assumptions on the spectrum of the disturbance process.

Model mismatch and process noise are two frequently occurring phenomena that can drastically affect the performance of model predictive control (MPC) in practical applications. We propose a principled way to tune the cost function and the constraints of linear MPC schemes to improve the closed-loop performance and robust constraint satisfaction on uncertain nonlinear dynamics with additive noise. The tuning is performed using a novel MPC tuning algorithm based on backpropagation developed in our earlier work. Using the scenario approach, we provide probabilistic bounds on the likelihood of closed-loop constraint violation over a finite horizon. We showcase the effectiveness of the proposed method on linear and nonlinear simulation examples.

In this paper, we study the problem of online tracking in linear control systems, where the objective is to follow a moving target. Unlike classical tracking control, the target is unknown, non-stationary, and its state is revealed sequentially, thus, fitting the framework of online non-stochastic control. We consider the case of quadratic costs and propose a new algorithm, called predictive linear online tracking (PLOT). The algorithm uses recursive least squares with exponential forgetting to learn a time-varying dynamic model of the target. The learned model is used in the optimal policy under the framework of receding horizon control. We show the dynamic regret of PLOT scales with $\mathcal{O}(\sqrt{TV_T})$, where $V_T$ is the total variation of the target dynamics and $T$ is the time horizon. Unlike prior work, our theoretical results hold for non-stationary targets. We implement PLOT on a real quadrotor and provide open-source software, thus, showcasing one of the first successful applications of online control methods on real hardware., Comment: ICML 2024 (spotlight)

Model predictive control (MPC) is pervasive in research and industry. However, designing the cost function and the constraints of the MPC to maximize closed-loop performance remains an open problem. To achieve optimal tuning, we propose a backpropagation scheme that solves a policy optimization problem with nonlinear system dynamics and MPC policies. We enforce the system dynamics using linearization and allow the MPC problem to contain elements that depend on the current system state and on past MPC solutions. Moreover, we propose a simple extension that can deal with losses of feasibility. Our approach, unlike other methods in the literature, enjoys convergence guarantees., Comment: Improved simulation results, corrected typos, extended theory

Suboptimal methods in optimal control arise due to a limited computational budget, unknown system dynamics, or a short prediction window among other reasons. Although these methods are ubiquitous, their transient performance remains relatively unstudied. We consider the control of discrete-time, nonlinear time-varying dynamical systems and establish sufficient conditions to analyze the finite-time closed-loop performance of such methods in terms of the additional cost incurred due to suboptimality. Finite-time guarantees allow the control design to distribute a limited computational budget over a time horizon and estimate the on-the-go loss in performance due to suboptimality. We study exponential incremental input-to-state stabilizing policies and show that for nonlinear systems, under some mild conditions, this property is directly implied by exponential stability without further assumptions on global smoothness. The analysis is showcased on a suboptimal model predictive control use case.

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.

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.

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.

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.

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, 2023

Online learning algorithms for dynamical systems provide finite time guarantees for control in the presence of sequentially revealed cost functions. We pose the classical linear quadratic tracking problem in the framework of online optimization where the time-varying reference state is unknown a priori and is revealed after the applied control input. We show the equivalence of this problem to the control of linear systems subject to adversarial disturbances and propose a novel online gradient descent based algorithm to achieve efficient tracking in finite time. We provide a dynamic regret upper bound scaling linearly with the path length of the reference trajectory and a numerical example to corroborate the theoretical guarantees., Comment: Published at the IEEE Control Systems Letters

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 pages

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 Congress

When manufacturing parts using material extrusion additive manufacturing and anisotropic polymers, the mechanical properties of a manufactured component are strongly dependent on the print trajectory orientation. We conduct non-planar slicing and optimize the print trajectories to maximize the alignment between the material deposition direction and the stress flow induced by a predefined load case. The trajectory optimization framework considers manufacturability constraints in the form of uniform layer height and line spacing. We demonstrate the method by manufacturing a load bearing mechanical bracket using a 5-axis 3D printer and a liquid crystal polymer material. The failure strength and stiffness of the optimized bracket are improved by a factor of 44 and 6 respectively when compared with conventional printing., Comment: Accepted and published on Elsevier Additive Manufacturing

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.

The setting of an agent making decisions under uncertainty and under dynamic constraints is common for the fields of optimal control, reinforcement learning, and recently also for online learning. In the online learning setting, the quality of an agent's decision is often quantified by the concept of regret, comparing the performance of the chosen decisions to the best possible ones in hindsight. While regret is a useful performance measure, when dynamical systems are concerned, it is important to also assess the stability of the closed-loop system for a chosen policy. In this work, we show that for linear state feedback policies and linear systems subject to adversarial disturbances, linear regret implies asymptotic stability in both time-varying and time-invariant settings. Conversely, we also show that bounded input bounded state stability and summability of the state transition matrices imply linear regret., Comment: Accepted for presentation at the IFAC World Congress 2023, Yokohama, Japan

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 2023

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 pages

In this paper, we consider a cyber-physical manufacturing system (CPMS) scenario containing physical components (robots, sensors, and actuators), operating in a digitally connected, constrained environment to perform industrial tasks. The CPMS has a centralized control plane with digital twins (DTs) of the physical resources, computational resources, and a network manager that allocates network resources. Existing approaches for allocation of network resources are typically fixed with respect to controller-dependent run-time specifications, which may impact the performance of physical processes. We propose a dynamic network management framework, where the network resource allocation schemes are controller-aware. The information about the controllers of the physical resources is implemented at the DT level, and metrics, such as regret bounds, take the process performance measures into account. The proposed network management schemes optimize physical system performance by balancing the shared resources between the physical assets on the plant floor, and by considering their control requirements, providing a new perspective for dynamic resource allocation. A simulation study is provided to illustrate the performance of the proposed network management approaches and compare their efficiencies.