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DOE OSTI2020

An Efficient Numerical Algorithm for Solving Data Driven Feedback Control Problems

The goal of this paper is to solve a class of stochastic optimal control problems numerically, in which the state process is governed by an Itô type stochastic differential equation with control process entering both in the drift and the diffusion, and is observed partially. The optimal control of feedback form is determined based on the available observational data. In this work, we call this type of control problems the data driven feedback control. The computational framework that we introduce to solve such type of problems aims to find the best estimate for the optimal control as a conditional expectation given the observational information. To make our method feasible in providing timely feedback to the controlled system from data, we develop an efficient stochastic optimization algorithm to implement our computational framework.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Autonomous Eco-Driving with Traffic Light and Lead Vehicle Constraints: An Application of Best Constrained Interpolation

Eco-Driving is a critical technology for improving automotive transportation efficiency. It is achieved by modifying the driving trajectory over a particular route to minimize required propulsion energy. Eco-Driving can be approached as an optimal control problem subject to driving constraints such as traffic lights and positions of other vehicles. Best interpolation in a strip is a problem in approximation theory and optimal control. The solution to this problem is a cubic spline. In this research, we demonstrate the connection between Eco-Driving and best interpolation in the strip. By exploiting this connection, we are able to generate optimal Eco-Driving trajectories that could be driven with an autonomous system. Using the simulation tool FASTSim, we can evaluate the trajectories using conventional, hybrid electric, and fully electric vehicle models. Our results quantify the energy efficiency improvements that can be achieved with the proposed approach.

Mahmoud, Yara Hazem↗

DOE OSTI2022

Autonomous Eco-Driving with Traffic Light and Lead Vehicle Constraints: An Application of Best Constrained Interpolation

Mahmoud, Yara Hazem↗

DOE OSTI2025

A time-parallel multiple-shooting method for large-scale quantum optimal control

Quantum optimal control plays a crucial role in quantum computing by providing the interface between compiler and hardware. Solving the optimal control problem is particularly challenging for multi-qubit gates, due to the exponential growth in computational complexity with the system's dimensionality and the deterioration of optimization convergence. To ameliorate the computational complexity of time-integration, this paper introduces a multiple-shooting approach in which the time domain is divided into multiple windows and the intermediate states at window boundaries are treated as additional optimization variables. Further, this enables parallel computation of state evolution across time-windows, significantly accelerating objective function and gradient evaluations. Since the initial state matrix in each window is only guaranteed to be unitary upon convergence of the optimization algorithm, the conventional gate trace infidelity is replaced by a generalized infidelity that is convex for non-unitary state matrices. Continuity of the state across window boundaries is enforced by equality constraints. A quadratic penalty optimization method is used to solve the constrained optimal control problem, and an efficient adjoint technique is employed to calculate the gradients in each iteration. We demonstrate the effectiveness of the proposed method through numerical experiments on quantum Fourier transform gates in systems with 2, 3, and 4 qubits, noting a speedup of 80x for evaluating the gradient in the 4-qubit case, highlighting the method's potential for optimizing control pulses in multi-qubit quantum systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Neural network approaches for parameterized optimal control

Here, we consider numerical approaches for deterministic, finite-dimensional optimal control problems whose dynamics depend on unknown or uncertain parameters. We seek to amortize the solution over a set of relevant parameters in an offline stage to enable rapid decision-making and be able to react to changes in the parameter in the online stage. To tackle the curse of dimensionality arising when the state and/or parameter are high-dimensional, we represent the policy using neural networks. We compare two training paradigms: First, our model-based approach leverages the dynamics and definition of the objective function to learn the value function of the parameterized optimal control problem and obtain the policy using a feedback form. Second, we use actor-critic reinforcement learning to approximate the policy in a data-driven way. Using an example involving a two-dimensional convection-diffusion equation, which features high-dimensional state and parameter spaces, we investigate the accuracy and efficiency of both training paradigms. While both paradigms lead to a reasonable approximation of the policy, the model-based approach is more accurate and considerably reduces the number of PDE solves.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Optimizing the fuel efficiency of an opposed piston engine for electric power generation

This paper investigates the optimal crankshaft motion for an opposed piston (OP) engine in a novel hybrid architecture to maximize fuel efficiency. The OP engine was selected for this work due to its inherent thermodynamic benefits and the balanced nature of the engine which can achieve downsizing through reducing the number of cylinders rather than the individual cylinder volume. The typical geartrain required on an OP engine was exchanged for two electric motors, reducing friction loss and decoupling the crankshafts. Using the motors to control the crankshaft motion profiles, this architecture introduces capabilities to dynamically vary compression ratio, combustion volume, and scavenging dynamics. To leverage these opportunities, an optimization scheme was developed utilizing nonlinear optimization of a 0-D model to compute the crankshaft motion profile that maximizes the work generated by the system. This optimization was then iteratively coupled with a high fidelity model which supplies the cylinder flow boundary conditions. This iterative approach reduces the model complexity used in the optimal control problem (OCP) while capturing the gas exchange dynamics critical to the 2-stroke cycle of the OP engine. By using the rate of change of motor torque as the input to the OCP, the torque fluctuation in a single cycle can be limited to ensure tracking feasibility. The results show crankshaft velocity slows during the compression stroke and conversely accelerates during the expansion stroke, reducing the peak motor torque required for control and thus reducing the motor losses. The extended residence time at top dead center, however, leads to an increase in heat transfer, illustrating the trade-off between the work extraction efficiency and the indicated engine efficiency.

Engineering↗

DOE OSTI2021

Parallelized POD-based suboptimal economic model predictive control of a state-constrained Boussinesq approximation

Motivated by an energy efficient building application, we want to optimize a quadratic cost functional subject to the Boussinesq approximation of the Navier-Stokes equations and to bilateral state and control constraints. Since the computation of such an optimal solution is numerically costly, we design an efficient strategy to compute a sub-optimal (but applicationally acceptable) solution with significantly reduced computational effort. We employ an economic Model Predictive Control (MPC) strategy to obtain a feedback control. The MPC sub-problems are based on a linear-quadratic optimal control problem subjected to mixed control and state constraints and a convection-diffusion equation, reduced with proper orthogonal decomposition. Finally, to solve each sub-problem, we apply a primal-dual active set strategy. The method can be fully parallelized, which enables the solution of large problems with real-world parameters.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Sequential linear integer programming for integer optimal control with total variation regularization

We propose a trust-region method that solves a sequence of linear integer programs to tackle integer optimal control problems regularized with a total variation penalty. The total variation penalty implies that the considered integer control problems admit minimizers. We introduce a local optimality concept for the problem, which arises from the infinite-dimensional perspective. In the case of a one-dimensional domain of the control function, we prove convergence of the iterates produced by our algorithm to points that satisfy first-order stationarity conditions for local optimality. We demonstrate the theoretical findings on a computational example.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Robust Optimal Control of Inverter-Based Resources Under Grid-Forming Operation

In this paper, we propose and solve a robust control problem for inverter-based resources under grid-forming operation to regulate the voltage and frequency. One major challenge is to mitigate the effect of unmeasurable load current disturbance, grid and load parametric uncertainties. Moreover, strong coupling between the state variables on both the AC and DC sides, as well as between the modulating control input and the frequency impose additional challenges. To address these challenges, first, a robust control problem is solved at the high level via transformation into an equivalent, but more tractable, optimal control problem. Then, in the middle layer a voltage control law is designed on the one side, and a frequency control law on the other side. Finally, an inverter filter current controller is designed to complete the controller design. Theoretical results are derived to provide stability guarantees for the resulting closed-loop system. Specifically, we show that the inverter current injection error is dissipative, the frequency error is semi-globally asymptotically stable, and the inverter terminal voltage error is globally asymptotically stable, all with provided sufficient conditions. Here, numerical simulation experiments are used to validate the theoretical claims. Furthermore, the developed controller is compared with existing work in literature to show the efficacy of the proposed approach.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Domain Aware Deep-learning Algorithms Integrated with Scientific-computing Technologies (DADAIST)

This technical report summarized the contribution of the DADAIST project funded by the Data Model Convergence Initiative via the Laboratory Directed Research and Development (LDRD) investments at Pacific Northwest National Laboratory (PNNL). Specifically, we report the development of the NeuroMANCER (Neural Modules with Adaptive Nonlinear Constraints and Efficient Regularizations), a new open-source Scientific Machine Learning library for formulating and solving parametric constrained optimization problems, physics-informed system identification, and parametric optimal control problems. NeuroMANCER is using differentiable programming to combine modern data-driven models and optimization modeling language into a coherent algorithmic and software framework. NeuroMANCER is a Pytorch-based framework and adopts much of its philosophy focused on research and development, rapid prototyping, and streamlined deployment. Strong emphasis is given to extensibility, interoperability with the PyTorch ecosystem, and quick adaptability to custom domain problems. Neuromancer repository contains a comprehensive library of differentiable modules, including custom activation functions, matrix factorizations, deep learning architectures, neural differential equations, differential equation solvers, implicit layers such as iterative solvers, high-level API for symbolic expressions, API for modeling and control of dynamical systems, and extensive set of tutorial code examples in the form of python scripts and jupyter notebooks.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Deep reinforcement learning for optimal control of induction welding process

Optimizing induction welding (IW) process parameters for the application of joining thermoplastic composites is challenging as it requires achieving complex spatiotemporal thermal characteristics along the weld-line to obtain desired weld quality. We formulate an optimal control problem which captures these requirements and seeks to optimize the IW coil speed using a fast-acting dynamic IW process model. We develop a novel Deep Reinforcement Learning (DRL) framework to solve this computationally challenging control problem and demonstrate via simulation study that the learned DRL feedback control policy results in better spatiotemporal thermal characteristics as compared to the current state-of-the-art.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Assimilating partial observation to enhance feedback control of stochastic dynamical systems

Here, in this paper, we present a novel methodology to tackle feedback optimal control problems in scenarios where the exact state of the controlled process is unknown. It integrates data assimilation techniques and optimal control solvers to manage partial observation of the state process, a common occurrence in practical scenarios. Traditional stochastic optimal control methods assume full state observation, which is often not feasible in real-world fluid dynamics control problems. Our approach underscores the significance of utilizing observational data to inform control policy design. Specifically, we introduce a kernel learning backward stochastic differential equation (SDE) filter to enhance data assimilation efficiency and propose a sample-wise stochastic optimization method within the stochastic maximum principle framework. We demonstrate the efficacy and accuracy of our method in the control of advection-diffusion-reaction flow problem and the Dubins airplane maneuvering problem with model uncertainty.

data driven↗

DOE OSTI2025

Optimization problems governed by systems of PDEs with uncertainties

This paper reviews current theoretical and numerical approaches to optimization problems governed by partial differential equations (PDEs) that depend on random variables or random fields. Such problems arise in many engineering, science, economics and societal decision-making tasks. This paper focuses on problems in which the governing PDEs are parametrized by the random variables/fields, and the decisions are made at the beginning and are not revised once uncertainty is revealed. Examples of such problems are presented to motivate the topic of this paper, and to illustrate the impact of different ways to model uncertainty in the formulations of the optimization problem and their impact on the solution. A linear–quadratic elliptic optimal control problem is used to provide a detailed discussion of the set-up for the risk-neutral optimization problem formulation, study the existence and characterization of its solution, and survey numerical methods for computing it. Different ways to model uncertainty in the PDE-constrained optimization problem are surveyed in an abstract setting, including risk measures, distributionally robust optimization formulations, probabilistic functions and chance constraints, and stochastic orders. Furthermore, approximation-based optimization approaches and stochastic methods for the solution of the large-scale PDE-constrained optimization problems under uncertainty are described. Some possible future research directions are outlined.

Heinkenschloss, Matthias [Rice Univ., Houston, TX ↗

DOE OSTI2021

Relaxed Multibang Regularization for the Combinatorial Integral Approximation

Multibang regularization and combinatorial integral approximation decompositions are two actively researched techniques for integer optimal control. In this work, we consider a class of polyhedral functions that arise particularly as convex lower envelopes of multibang regularizers and show that they have beneficial properties with respect to regularization of relaxations of integer optimal control problems. We extend the algorithmic framework of the combinatorial integral approximation such that a subsequence of the computed discrete-valued controls converges to the infimum of the regularized integer control problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Multi-Commodity Traffic Signal Control and Routing With Connected Vehicles

We report a real-time traffic management policy that integrates traffic signal control and multi-commodity routing of connected vehicles in networks with multiple destinations is developed. The proposed policy is based on a multi-commodity formulation of the store-and-forward model and assumes all vehicles are able to exchange information with the infrastructure. Vehicles share information about their current location and final destination. Based on this information, the strategy determines both optimized signal timings at every intersection and vehicle-specific routing information at every link of the network. The control actions, i.e., signal times and routing information, are updated at every cycle and delivered by a finite horizon optimal control problem cast into a rolling horizon framework. The underlying optimization problem is convex, and thus the method is suitable for real-time operation in large networks. The method is validated via a micro-simulation study in networks with up to twenty intersections and, in all simulations, outperforms a real-time traffic-responsive signal control strategy that is based on a single-commodity store-and-forward model. The scalable computation effort for increasing network sizes and prediction horizon confirms the computational efficiency of the method.

42 ENGINEERING↗

DOE OSTI2024

Leveraging Multitime Hamilton–Jacobi PDEs for Certain Scientific Machine Learning Problems

Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences. By considering the time variable to be a higher dimensional quantity, HJ PDEs can be extended to the multi-time case. In this paper, we establish a novel theoretical connection between specific optimization problems arising in machine learning and the multi-time Hopf formula, which corresponds to a representation of the solution to certain multi-time HJ PDEs. Through this connection, we increase the interpretability of the training process of certain machine learning applications by showing that when we solve these learning problems, we also solve a multi-time HJ PDE and, by extension, its corresponding optimal control problem. As a first exploration of this connection, we develop the relation between the regularized linear regression problem and the Linear Quadratic Regulator (LQR). We then leverage our theoretical connection to adapt standard LQR solvers (namely, those based on the Riccati ordinary differential equations) to design new training approaches for machine learning. Lastly, we provide some numerical examples that demonstrate the versatility and possible computational advantages of our Riccati-based approach in the context of continual learning, post-training calibration, transfer learning, and sparse dynamics identification.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Real-Time Ecodriving Control in Electrified Connected and Autonomous Vehicles Using Approximate Dynamic Programing

Connected and automated vehicles (CAVs), particularly those with a hybrid electric powertrain, have the potential to significantly improve vehicle energy savings in real-world driving conditions. In particular, the ecodriving problem seeks to design optimal speed and power usage profiles based on available information from connectivity and advanced mapping features to minimize the fuel consumption over an itinerary. This paper presents a hierarchical multilayer model predictive control (MPC) approach for improving the fuel economy of a 48 V mild-hybrid powertrain in a connected vehicle environment. Approximate dynamic programing (DP) is used to solve the receding horizon optimal control problem, whose terminal cost is approximated with the base policy obtained from the long-term optimization. The controller was tested virtually (with deterministic and Monte Carlo simulation) across multiple real-world routes, demonstrating energy savings of more than 20%. The controller was then deployed on a test vehicle equipped with a rapid prototyping embedded controller. In-vehicle testing confirm the energy savings obtained in simulation and demonstrate the real-time ability of the controller.

Automation & Control Systems↗

DOE OSTI2021

Risk-Averse Control of Fractional Diffusion with Uncertain Exponent

In this paper, we introduce and analyze a new class of optimal control problems constrained by elliptic equations with uncertain fractional exponents. We utilize risk measures to formulate the resulting optimization problem. We develop a functional analytic framework, study the existence of solution and rigorously derive the first-order optimality conditions. Additionally, we employ a sample-based approximation for the uncertain exponent and the finite element method to discretize in space. Further, we prove the rate of convergence for the optimal risk neutral controls when using quadrature approximation for the uncertain exponent and conclude with illustrative examples.

finite element method↗