arXiv subjects

Dominic Liao-McPherson

Publications and source records attributed to Dominic Liao-McPherson.

At least 19 recordsLinked to original sources

arXiv2026

Network Design against the Bullwhip Effect in Complex Supply Chains

This paper studies the bullwhip effect, the amplification of demand fluctuations into larger order fluctuations upstream, in supply chain networks where each firm orders from several suppliers over routes with different lead times. We show that on a directed acyclic network every response from demand to orders is a sum over paths of products of nodal responses, so that the stability and stability margins of the network are determined by those of its individual nodes, and that a node which splits its orders across routes of different lengths gains margin it can spend on a higher gain and a faster response. We then minimize the worst-case amplification of the network by choosing how each firm splits its orders among its suppliers, which route lead times to shorten, and each firm's ordering gain, with gradients from one adjoint pass per demand node and frequency. On a 14-city network the optimized design amplifies 20~dB less than cost-minimal routing and 17~dB less than a design that shortens the longest routes with the same budget, and is better connected than either. Amplification is therefore a property of routing and delay, not only of the ordering policy, and designing against it also makes the network more robust to a lost route.

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arXiv2026

Iterative Learning Control of the Cooling Rate in a Dual-Laser Powder Bed Fusion Process

The thermal history of the melt pool in laser powder bed fusion (LPBF) additive manufacturing processes governs the solidification microstructure and the mechanical properties of the resulting 3D-printed parts. Dual-laser systems offer additional degrees of freedom to control the cooling profile by reheating material behind the melt pool, but calibrating process parameters is challenging due to the complex physics of the process. We present an optimization-based iterative learning controller that determines optimal power, velocity, and offset settings by judiciously combining simulations and experiments: the model supplies search directions while feedback obtained from experiments on the real plant corrects for parameter errors, enabling convergence despite model inaccuracies. The approach is validated in simulation using a high-fidelity thermal model as a plant surrogate, with deliberate mismatches in absorption coefficient, latent heat treatment, and powder-bed effective conductivity between plant and model. Results show that the controller drives the plant cost down by over an order of magnitude and reaches a tight band of low-cost solutions across seeds, while model-only feedforward optimization stalls at a substantially higher plant cost despite appearing to converge on the surrogate.

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arXiv2026

Stability Certificates for Receding Horizon Games

Game-theoretic MPC (or Receding Horizon Games) is an emerging control methodology for multi-agent systems that generates control actions by solving a dynamic game with coupling constraints in a receding-horizon fashion. This control paradigm has recently received increasing attention in various application fields, including robotics, autonomous driving, traffic networks, and energy grids, due to its ability to model the competitive nature of self-interested agents with shared resources while incorporating future predictions, dynamic models, and constraints into the decision-making process. In this work, we present the first formal stability analysis based on dissipativity and monotone operator theory that is valid also for non-potential games. Specifically, we derive LMI-based certificates that ensure asymptotic stability and are numerically verifiable. Moreover, we show that, if the agents have decoupled dynamics, the numerical verification can be performed in a scalable manner. Finally, we present tuning guidelines for the agents' cost function weights to fulfill the certificates and, thus, ensure stability.

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arXiv2026

A Semi-smooth Newton Method for the Constrained Optimal Control of Continuous-Time Linear Systems

This paper details a novel indirect method for solving constrained optimal control problems (OCPs) directly in continuous-time function space. The KKT conditions are embedded in a non-smooth complementarity function, which enables their reformulation as a rootfinding problem in Banach space. This problem is then solved using a non-smooth Newton method. Finally, the paper shows that the Newton update can be obtained by solving a modified differential Riccati equation, where the cost terms are reweighted at every iteration based on the constraint multipliers. Numerical simulations show the effectiveness of the method, which converges superlinearly up to the tolerance of the ODE solver.

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arXiv2025

Integrating Planning and Predictive Control Using the Path Feasibility Governor

The motion planning problem of generating dynamically feasible, collision-free trajectories in non-convex environments is a fundamental challenge for autonomous systems. Decomposing the problem into path planning and path tracking improves tractability, but integrating these components in a theoretically sound and computationally efficient manner is challenging. We propose the Path Feasibility Governor (PathFG), a framework for integrating path planners with nonlinear Model Predictive Control (MPC). The PathFG manipulates the reference passed to the MPC controller, guiding it along a path while ensuring constraint satisfaction, stability, and recursive feasibility. The PathFG is modular, compatible with replanning, and improves computational efficiency and reliability by reducing the need for long prediction horizons. We prove safety and asymptotic stability with a significantly expanded region of attraction, and validate its real-time performance through a simulated case study of quadrotor navigation in a cluttered environment.

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arXiv2024

Layer-to-Layer Melt Pool Control in Laser Powder 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.

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arXiv2024

Receding Horizon Games for Modeling Competitive Supply Chains

The vast majority of products we use daily are supplied to us through complex global supply chains that transform raw materials into finished goods and distribute them to end consumers. This paper proposes a modeling methodology for dynamic competitive supply chains based on game theory and model predictive control. We model each manufacturer in the supply chain as a rational utility maximizing agent that selects their actions by finding an open-loop generalized Nash equilibrium of a multi-stage game. To react to competitors and the state of the market, every agent re-plans their actions in a receding horizon manner based on estimates of market and supplier parameters thereby creating an approximate closed-loop equilibrium policy. We demonstrate through numerical simulations that this modeling approach is computationally tractable and generates economically interpretable behaviors in a variety of settings such as demand spikes, supply shocks, and information asymmetry.

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arXiv2024

Inexact Policy Iteration Methods for Large-Scale Markov Decision Processes

We consider inexact policy iteration methods for large-scale infinite-horizon discounted MDPs with finite spaces, a variant of policy iteration where the policy evaluation step is implemented inexactly using an iterative solver for linear systems. In the classical dynamic programming literature, a similar principle is deployed in optimistic policy iteration, where an a-priori fixed-number of iterations of value iteration is used to inexactly solve the policy evaluation step. Inspired by the connection between policy iteration and semismooth Newton's method, we investigate a class of iPI methods that mimic the inexact variants of semismooth Newton's method by adopting a parametric stopping condition to regulate the level of inexactness of the policy evaluation step. For this class of methods we discuss local and global convergence properties and derive a practical range of values for the stopping-condition parameter that provide contraction guarantees. Our analysis is general and therefore encompasses a variety of iterative solvers for policy evaluation, including the standard value iteration as well as more sophisticated ones such as GMRES. As underlined by our analysis, the selection of the inner solver is of fundamental importance for the performance of the overall method. We therefore consider different iterative methods to solve the policy evaluation step and analyze their applicability and contraction properties when used for policy evaluation. We show that the contraction properties of these methods tend to be enhanced by the specific structure of policy evaluation and that there is margin for substantial improvement in terms of convergence rate. Finally, we study the numerical performance of different instances of inexact policy iteration on large-scale MDPs for the design of health policies to control the spread of infectious diseases in epidemiology.

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arXiv2024

A Log-domain Interior Point Method for Convex Quadratic Games

In this paper, we propose an equilibrium-seeking algorithm for finding generalized Nash equilibria of non-cooperative monotone convex quadratic games. Specifically, we recast the Nash equilibrium-seeking problem as variational inequality problem that we solve using a log-domain interior point method and provide a general purpose solver based on this algorithm. This approach is suitable for non-potential, general sum games and does not require extensive structural assumptions. We demonstrate the efficiency and versatility of our method using three benchmark games and demonstrate our algorithm is especially effective on small to medium scale problems.

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arXiv2024

Online Feedback Equilibrium Seeking

This paper proposes a unifying design framework for dynamic feedback controllers that track solution trajectories of time-varying generalized equations, such as local minimizers of nonlinear programs or competitive equilibria (e.g., Nash) of non-cooperative games. Inspired by the feedback optimization paradigm, the core idea of the proposed approach is to re-purpose classic iterative algorithms for solving generalized equations (e.g., Josephy--Newton, forward-backward splitting) as dynamic feedback controllers by integrating online measurements of the continuous-time nonlinear plant. Sufficient conditions for closed-loop stability and robustness of the algorithm-plant cyber-physical interconnection are derived in a sampled-data setting by combining and tailoring results from (monotone) operator, fixed-point, and nonlinear systems theory. Numerical simulations on smart building automation and competitive supply-chain management are presented to support the theoretical findings.

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arXiv2023

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.

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arXiv2023

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.

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arXiv2023

Stability and Robustness of Distributed Suboptimal Model Predictive Control

In distributed model predictive control (MPC), the control input at each sampling time is computed by solving a large-scale optimal control problem (OCP) over a finite horizon using distributed algorithms. Typically, such algorithms require several (virtually, infinite) communication rounds between the subsystems to converge, which is a major drawback both computationally and from an energetic perspective (for wireless systems). Motivated by these challenges, we propose a suboptimal distributed MPC scheme in which the total communication burden is distributed also in time, by maintaining a running solution estimate for the large-scale OCP and updating it at each sampling time. We demonstrate that, under some regularity conditions, the resulting suboptimal MPC control law recovers the qualitative robust stability properties of optimal MPC, if the communication budget at each sampling time is large enough.

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arXiv2022

Drone-based Volume Estimation in Indoor Environments

Volume estimation in large indoor spaces is an important challenge in robotic inspection of industrial warehouses. We propose an approach for volume estimation for autonomous systems using visual features for indoor localization and surface reconstruction from 2D-LiDAR measurements. A Gaussian Process-based model incorporates information collected from measurements given statistical prior information about the terrain, from which the volume estimate is computed. Our algorithm finds feasible trajectories which minimize the uncertainty of the volume estimate. We show results in simulation for the surface reconstruction and volume estimate of topographic data.

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arXiv2022

Inexact GMRES Policy Iteration for Large-Scale Markov Decision Processes

Policy iteration enjoys a local quadratic rate of contraction, but its iterations are computationally expensive for Markov decision processes (MDPs) with a large number of states. In light of the connection between policy iteration and the semismooth Newton method and taking inspiration from the inexact variants of the latter, we propose \textit{inexact policy iteration}, a new class of methods for large-scale finite MDPs with local contraction guarantees. We then design an instance based on the deployment of GMRES for the approximate policy evaluation step, which we call inexact GMRES policy iteration. Finally, we demonstrate the superior practical performance of inexact GMRES policy iteration on an MDP with 10000 states, where it achieves a $\times 5.8$ and $\times 2.2$ speedup with respect to policy iteration and optimistic policy iteration, respectively.

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arXiv2022

Data-driven Reference Trajectory Optimization for Precision Motion Systems

We propose a data-driven optimization-based pre-compensation method to improve the contour tracking performance of precision motion stages by modifying the reference trajectory and without modifying any built-in low-level controllers. The position of the precision motion stage is predicted with data-driven models, a linear low-fidelity model is used to optimize traversal time, by changing the path velocity and acceleration profiles then a non-linear high-fidelity model is used to refine the previously found time-optimal solution. We experimentally demonstrate that the proposed method is capable of simultaneously improving the productivity and accuracy of a high precision motion stage. Given the data-based nature of the models, the proposed method can easily be adapted to a wide family of precision motion systems.

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arXiv2022

Dynamic Programming Through the Lens of Semismooth Newton-Type Methods (Extended Version)

Policy iteration and value iteration are at the core of many (approximate) dynamic programming methods. For Markov Decision Processes with finite state and action spaces, we show that they are instances of semismooth Newton-type methods to solve the Bellman equation. In particular, we prove that policy iteration is equivalent to the exact semismooth Newton method and enjoys local quadratic convergence rate. This finding is corroborated by extensive numerical evidence in the fields of control and operations research, which confirms that policy iteration generally requires few iterations to achieve convergence even when the number of policies is vast. We then show that value iteration is an instance of the fixed-point iteration method. In this spirit, we develop a novel locally accelerated version of value iteration with global convergence guarantees and negligible extra computational costs.

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arXiv2022

Receding Horizon Games with Coupling Constraints for Demand-Side Management

Distributed energy storage and flexible loads are essential tools for ensuring stable and robust operation of the power grid in spite of the challenges arising from the integration of volatile renewable energy generation and increasing peak loads due to widespread electrification. This paper proposes a demand-side management policy to coordinate self-interested energy prosumers based on receding horizon games, i.e., a closed-loop receding-horizon implementation of game-theoretic day-ahead planning. Practical stability and recursive constraint satisfaction of the proposed feedback control policy is proven under symmetric pricing assumptions using tools from game theory and economic model predictive control. Our numerical studies show that the proposed approach is superior to standard open-loop day-head implementations in terms of peak-shaving, disturbance rejection, and control performance.

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