arXiv subjects

Dominic Liao-McPherson

Publications and source records attributed to Dominic Liao-McPherson.

34 records · Page 2Linked to original sources

arXiv2022

On Robustness in Optimization-Based Constrained Iterative Learning Control

Iterative learning control (ILC) is a control strategy for repetitive tasks wherein information from previous runs is leveraged to improve future performance. Optimization-based ILC (OB-ILC) is a powerful design framework for constrained ILC where measurements from the process are integrated into an optimization algorithm to provide robustness against noise and modelling error. This paper proposes a robust ILC controller for constrained linear processes based on the forward-backward splitting algorithm. It demonstrates how structured uncertainty information can be leveraged to ensure constraint satisfaction and provides a rigorous stability analysis in the iteration domain by combining concepts from monotone operator theory and robust control. Numerical simulations of a precision motion stage support the theoretical results.

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arXiv2022

Cross-layer Design for Real-Time Grid Operation: Estimation, Optimization and Power Flow

In this paper, we propose a combined Online Feedback Optimization (OFO) and dynamic estimation approach for a real-time power grid operation under time-varying conditions. A dynamic estimation uses grid measurements to generate the information required by an OFO controller, that incrementally steers the controllable power injections set-points towards the solutions of a time-varying AC Optimal Power Flow (AC-OPF) problem. More concretely, we propose a quadratic programming-based OFO that guarantees satisfying the grid operational constraints, like admissible voltage limits. Within the estimation, we design an online power flow solver that efficiently computes power flow approximations in real time. Finally, we certify the stability and convergence of this combined approach under time-varying conditions, and we validate its effectiveness on a simulation with a test feeder and high resolution consumption data.

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arXiv2022

In-layer Thermal Control of a Multi-layer Selective Laser Melting Process

Selective Laser Melting (SLM) is an additive manufacturing technology that builds three dimensional parts by melting layers of metal powder together with a laser that traces out a desired geometry. SLM is popular in industry, however the inherent melting and re-solidification of the metal during the process can, if left uncontrolled, cause excessive residual stress, porosity, and other defects in the final printed parts. This paper presents a control-oriented thermal model of a multi-layer SLM process and proposes a structured model reduction methodology with an associated reduced order model based in-layer controller to track temperature references. Simulation studies demonstrate that the controller is able to prevent layer-to-layer heat buildup and that good closed-loop performance is possible using relatively low-order models.

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arXiv2021

Sampled-Data Online Feedback Equilibrium Seeking: Stability and Tracking

This paper proposes a general framework for constructing feedback controllers that drive complex dynamical systems to "efficient" steady-state (or slowly varying) operating points. Efficiency is encoded using generalized equations which can model a broad spectrum of useful objectives, such as optimality or equilibria (e.g. Nash, Wardrop, etc.) in noncooperative games. The core idea of the proposed approach is to directly implement iterative solution (or equilibrium seeking) algorithms in closed loop with physical systems. Sufficient conditions for closed-loop stability and robustness are derived; these also serve as the first closed-loop stability results for sampled-data feedback-based optimization. Numerical simulations of smart building automation and game-theoretic robotic swarm coordination support the theoretical results.

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arXiv2021

Feasibility Governor for Linear Model Predictive Control

This paper introduces the Feasibility Governor (FG): an add-on unit that enlarges the region of attraction of Model Predictive Control by manipulating the reference to ensure that the underlying optimal control problem remains feasible. The FG is developed for linear systems subject to polyhedral state and input constraints. Offline computations using polyhedral projection algorithms are used to construct the feasibility set. Online implementation relies on the solution of a convex quadratic program that guarantees recursive feasibility. The closed-loop system is shown to satisfy constraints, achieve asymptotic stability, and exhibit zero-offset tracking.

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arXiv2021

An Analysis of Closed-Loop Stability for Linear Model Predictive Control Based on Time-Distributed Optimization

Time-distributed Optimization (TDO) is an approach for reducing the computational burden of Model Predictive Control (MPC). When using TDO, optimization iterations are distributed over time by maintaining a running solution estimate and updating it at each sampling instant. In this paper, TDO applied to input constrained linear MPC is studied in detail, and analytic expressions for the system gains and a bound on the number of optimization iterations per sampling instant required to guarantee closed-loop stability is derived. Further, it is shown that the closed-loop stability of TDO-based MPC can be guaranteed using multiple mechanisms including increasing the number of solver iterations, preconditioning the optimal control problem, adjusting the MPC cost matrices, and reducing the length of the receding horizon. These results in a linear system setting also provide insights and guidelines that could be more broadly applicable, e.g., to nonlinear MPC.

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arXiv2020

A Feasibility Governor for Enlarging the Region of Attraction of Linear Model Predictive Controllers

This paper proposes a method for enlarging the region of attraction of Linear Model Predictive Controllers (MPC) when tracking piecewise-constant references in the presence of pointwise-in-time constraints. It consists of an add-on unit, the Feasibility Governor (FG), that manipulates the reference command so as to ensure that the optimal control problem that underlies the MPC feedback law remains feasible. Offline polyhedral projection algorithms based on multi-objective linear programming are employed to compute the set of feasible states and reference commands. Online, the action of the FG is computed by solving a convex quadratic program. The closed-loop system is shown to satisfy constraints, be asymptotically stable, exhibit zero-offset tracking, and display finite-time convergence of the reference.

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arXiv2020

Suboptimal Nonlinear Model Predictive Control Strategies for Tracking Near Rectilinear Halo Orbits

Near Rectilinear Halo Orbits (NRHOs), a subclass of halo orbits around the L1 and L2 Lagrange points, are promising candidates for future lunar gateways in cis-lunar space and as staging orbits for lunar missions. Closed-loop control is beneficial to compensate orbital perturbations and potential instabilities while maintaining spacecraft on NRHOs and performing relative motion maneuvers. This paper investigates the use of nonlinear model predictive control (NMPC) coupled with low-thrust actuators for station-keeping on NRHOs. It is demonstrated through numerical simulations that NMPC is able to stabilize a spacecraft to a reference orbit and handle control constraints. Further, it is shown that the computational burden of NMPC can be managed using specialized optimization routines and suboptimal approaches without jeopardizing closed-loop performance.

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arXiv2019

Time Distributed Optimization for Model Predictive Control: Stability, Robustness, and Constraint Satisfaction

Time distributed optimization is an implementation strategy that can significantly reduce the computational burden of model predictive control by exploiting its robustness to incomplete optimization. When using this strategy, optimization iterations are distributed over time by maintaining a running solution estimate for the optimal control problem and updating it at each sampling instant. The resulting controller can be viewed as a dynamic compensator which is placed in closed-loop with the plant. This paper presents a general systems theoretic analysis framework for time distributed optimization. The coupled plant-optimizer system is analyzed using input-to-state stability concepts and sufficient conditions for stability and constraint satisfaction are derived. When applied to time distributed sequential quadratic programming, the framework significantly extends the existing theoretical analysis for the real-time iteration scheme. Numerical simulations are presented that demonstrate the effectiveness of the scheme.

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arXiv2019

Sensitivity-based Warmstarting for Nonlinear Model Predictive Control with Polyhedral State and Control Constraints

Model predictive control (MPC) is of increasing interest in applications for constrained control of multivariable systems. However, one of the major obstacles to its broader use is the computation time and effort required to solve a possibly non-convex optimal control problem (OCP) online. This paper introduces a sensitivity-based warmstarting strategy for systems with nonlinear dynamics and polyhedral constraints with the goal of reducing the computational footprint of MPC controllers. It predicts changes in the solution of the parameterized OCP as the parameter varies, by calculating the semiderivative of the solution mapping. The main novelty of the paper is that the polyhedrality of the constraints allows us to avoid imposing any constraint qualification conditions or strict complementarity assumptions. A numerical study featuring MPC applied to unmanned aerial vehicles illustrates the proposed approach.

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arXiv2019

FBstab: A Stabilized Semismooth Quadratic Programming Algorithm with Applications in Model Predictive Control

This paper introduces the proximally stabilized Fischer-Burmeister method (FBstab); a new algorithm for convex quadratic programming that synergistically combines the proximal point algorithm with a primal-dual semismooth Newton-type method. FBstab is numerically robust, easy to warmstart, handles degenerate primal-dual solutions, detects infeasibility/unboundedness and requires only that the Hessian matrix be positive semidefinite. We outline the algorithm, provide convergence and convergence rate proofs, report some numerical results from model predictive control benchmarks, and also include experimental results. We show that FBstab is competitive with and often superior to, state of the art methods, has attractive scaling properties, and is especially promising for model predictive control applications.

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arXiv2019

A Semismooth Predictor Corrector Method for Suboptimal Model Predictive Control

Suboptimal model predictive control is a technique that can reduce the computational cost of model predictive control (MPC) by exploiting its robustness to incomplete optimization. Instead of solving the optimal control problem exactly, this method maintains an estimate of the optimal solution and updates it at each sampling instance. The resulting controller can be viewed as a dynamic compensator which runs in parallel with the plant. This paper explores the use of the semismooth predictor-corrector method to implement suboptimal MPC. The dynamic interconnection of the combined plant-optimizer system is studied using the input-to-state stability framework and sufficient conditions for closed-loop asymptotic stability and constraint enforcement are derived using small gain arguments. Numerical simulations demonstrate the efficacy of the scheme.

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arXiv2019

Spacecraft Attitude Control with Nonconvex Constraints: An Explicit Reference Governor Approach

This paper introduces a novel attitude controller for spacecraft subject to actuator saturation and multiple exclusion cone constraints. The proposed solution relies on a two-layer approach where the first layer prestabilizes the system dynamics whereas the second layer enforces constraint satisfaction by suitably manipulating the reference of the prestabilized system. In particular, constraint satisfaction is guaranteed by taking advantage of set invariance properties, whereas asymptotic convergence is achieved by implementing a non-conservative navigation field which is devoid of undesired stagnation points. Multiple numerical examples illustrate the good behavior of the proposed scheme.

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arXiv2018

A Semismooth Predictor Corrector Method for Real-Time Constrained Parametric Optimization with Applications in Model Predictive Control

Real-time optimization problems are ubiquitous in control and estimation, and are typically parameterized by incoming measurement data and/or operator commands. This paper proposes solving parameterized constrained nonlinear programs using a semismooth predictor-corrector (SSPC) method. Nonlinear complementarity functions are used to reformulate the first order necessary conditions of the optimization problem into a parameterized non-smooth root-finding problem. Starting from an approximate solution, a semismooth Euler-Newton algorithm is proposed for tracking the trajectory of the primal-dual solution as the parameter varies over time. Active set changes are naturally handled by the SSPC method, which only requires the solution of linear systems of equations. The paper establishes conditions under which the solution trajectories of the root-finding problem are well behaved and provides sufficient conditions for ensuring boundedness of the tracking error. Numerical case studies featuring the application of the SSPC method to nonlinear model predictive control are reported and demonstrate the advantages of the proposed method.

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arXiv2018

A Regularized and Smoothed Fischer-Burmeister Method for Quadratic Programming with Applications to Model Predictive Control

This paper considers solving convex quadratic programs (QPs) in a real-time setting using a regularized and smoothed Fischer-Burmeister method (FBRS). The Fischer-Burmeister function is used to map the optimality conditions of the quadratic program to a nonlinear system of equations which is solved using Newton's method. Regularization and smoothing are applied to improve the practical performance of the algorithm and a merit function is used to globalize convergence. FBRS is simple to code, easy to warmstart, robust to early termination, and has attractive theoretical properties, making it appealing for real-time and embedded applications. Numerical experiments using several predictive control examples show that the proposed method is competitive with other state of the art solvers.

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arXiv2017

Embedding Constrained Model Predictive Control in a Continuous-Time Dynamic Feedback

This paper introduces a continuous-time constrained nonlinear control scheme which implements a model predictive control strategy as a continuous-time dynamic system. The approach is based on the idea that the solution of the optimal control problem can be embedded into the internal states of a dynamic control law which runs in parallel to the system. Using input to state stability arguments, it is shown that if the controller dynamics are sufficiently fast with respect to the plant dynamics, the interconnection between the two systems is asymptotically stable. Additionally, it is shown that, by augmenting the proposed scheme with an add-on unit known as an Explicit Reference Governor, it is possible to drastically increase the set of initial conditions that can be steered to the desired reference without violating the constraints. Numerical examples demonstrate the effectiveness of the proposed scheme.

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