We present a dynamic model for the optimal control problem (OCP) of hydrogen blending into natural gas pipeline networks subject to inequality constraints. The dynamic model is derived using the first principles parti...
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ISBN:
(纸本)9798350382662;9798350382655
We present a dynamic model for the optimal control problem (OCP) of hydrogen blending into natural gas pipeline networks subject to inequality constraints. The dynamic model is derived using the first principles partial differential equations (PDEs) for the transport of heterogeneous gas mixtures through long distance pipes. Hydrogen concentration is tracked together with the pressure and mass flow dynamics within the pipelines, as well as mixing and compatibility conditions at nodes, actuation by compressors, and injection of hydrogen or natural gas into the system or withdrawal of the mixture from the network. We implement a lumped parameter approximation to reduce the full PDE model to a differential algebraic equation (DAE) system that can be easily discretized and solved using nonlinear optimization or programming (NLP) solvers. We examine a temporal discretization that is advantageous for time-periodic boundary conditions, parameters, and inequality constraint bound values. The method is applied to solve case studies for a single pipe and a multi-pipe network with time-varying parameters in order to explore how mixing of heterogeneous gases affects pipeline transient optimization.
Direct shooting is an efficient method to solve numerical optimal control. It utilizes the Runge-Kutta scheme to discretize a continuous-time optimal control problem making the problem solvable by nonlinear programmin...
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ISBN:
(纸本)9798331540920;9783907144107
Direct shooting is an efficient method to solve numerical optimal control. It utilizes the Runge-Kutta scheme to discretize a continuous-time optimal control problem making the problem solvable by nonlinear programming solvers. However, conventional direct shooting raises a contradictory dynamics issue when using an augmented state to handle high-order systems. This paper fills the research gap by considering the direct shooting method for high-order systems. We derive the modified Euler and Runge-Kutta-4 methods to transcribe the system dynamics constraint directly. Additionally, we provide the global error upper bounds of our proposed methods. A set of benchmark optimal control problems shows that our methods provide more accurate solutions than existing approaches.
In this paper, we study an augmented Lagrangian-type algorithm called the Dislocation Hyperbolic Augmented Lagrangian Algorithm (DHALA), which solves an inequality nonconvex optimization problem. We show that the sequ...
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In this paper, we study an augmented Lagrangian-type algorithm called the Dislocation Hyperbolic Augmented Lagrangian Algorithm (DHALA), which solves an inequality nonconvex optimization problem. We show that the sequence generated by DHALA converges to a Karush-Kuhn-Tucker (KKT) point under the Mangasarian-Fromovitz constraint qualification. The contribution of our work is to consider a constraint qualification into this algorithm. Finally, we present some computational illustrations to demonstrate the performance our algorithm works.
On the surface of the earth's sphere, the shortest path of an unmanned surface vehicle's (USV's) voyage across an ocean is a great circle arc rather than a rhumb line segment. To plan the great circle path...
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ISBN:
(纸本)9798331540845;9789887581598
On the surface of the earth's sphere, the shortest path of an unmanned surface vehicle's (USV's) voyage across an ocean is a great circle arc rather than a rhumb line segment. To plan the great circle paths fitting to USV dynamics, this paper develops a great-circle-based nonlinear programming (GCNLP) approach for USV voyages across oceans with irregular static obstacles. We formulate the path planning problem as an optimization problem whose feasible solutions are the USV control vector consisting of force in surge and moment in yaw, which generates a USV planned path. The objective function of the optimization problem is the sum of all the great circle arc lengths between the adjacent waypoints in a USV planned path, such that an optimal USV planned path is the shortest. The constraints of the optimization problem are formulated using a new irregular static obstacle geometric model and the dynamic model of USVs, such that a USV planned path bypasses irregular static obstacles and fits to the USV dynamics. Using a nonlinear programming technique to search for the optimal solution of the optimization problem, we obtain the USV great circle planned path. Path planning and comparison results with the A* path planning method demonstrate that the USV great circle planned path under our proposed GCNLP approach is shorter. Our proposed GCNLP approach can be applied to the USV sailing in different waters using the corresponding irregular static obstacle data.
This paper focuses on the control of a fuel cell system, for which an optimization model is proposed to control the oxygen excess ratio in order to tackle the fuel cell starvation phenomenon and increase the net power...
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This paper focuses on the control of a fuel cell system, for which an optimization model is proposed to control the oxygen excess ratio in order to tackle the fuel cell starvation phenomenon and increase the net power production of the system. The optimization problem considers the detailed nonlinear dynamics of the stack and the air supply sub -system as constraints and upper and lower bounds to consider the technical limitations in the system's operation. The goal is to maintain the oxygen excess ratio at its reference value, using the compressor input voltage as a control variable, under several load variations of the current demand, considered as the external noise to the system. The proposed nonlinear optimization problem has been applied to a 75 kW stack used in the Ford P2000 fuel cell prototype vehicles, and results have been compared to the proportional -integral (PI) control technique. The proposed control approach has shown a significant enhancement in the control performance of the oxygen excess ratio.
The aim of this paper is to deepen the study of solution methods for rank-two nonconvex problems with polyhedral feasible region, expressed by means of equality, inequality and box constraints, and objective function ...
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The aim of this paper is to deepen the study of solution methods for rank-two nonconvex problems with polyhedral feasible region, expressed by means of equality, inequality and box constraints, and objective function in the form of phi c T x + c 0 , d T x + d 0 b T x + b 0 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi \left( c<^>Tx+c_0,\frac{d<^>Tx+d_0}{b<^>Tx+b_0}\right) $$\end{document} or phi over bar c over bar T y + c over bar 0 a T y + a 0 , d T y + d 0 b T y + b 0 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{\phi }\left( \frac{\bar{c}<^>Ty+\bar{c}_0}{a<^>Ty+a_0}, \frac{d<^>Ty+d_0}{b<^>Ty+b_0}\right) $$\end{document} . These problems arise in bicriteria programs, quantitative management science, data envelopment analysis, efficiency analysis and performance measurement. Theoretical results are proved and applied to propose a solution algorithm. Computational results are provided, comparing various splitting criteria.
This paper introduces an approach for synthesizing feasible safety indices to derive safe control laws under state-dependent control spaces. The problem, referred to as Safety Index Synthesis (SIS), is challenging bec...
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ISBN:
(纸本)9798350382662;9798350382655
This paper introduces an approach for synthesizing feasible safety indices to derive safe control laws under state-dependent control spaces. The problem, referred to as Safety Index Synthesis (SIS), is challenging because it requires the existence of feasible control input in all states and leads to an infinite number of constraints. The proposed method leverages Positivstellensatz to formulate SIS as a nonlinear programming (NP) problem. We formally prove that the NP solutions yield safe control laws with two imperative guarantees: forward invariance within user-defined safe regions and finite-time convergence to those regions. A numerical study validates the effectiveness of our approach.
The advent of Urban Air Mobility (UAM) presents the scope for a transformative shift in the domain of urban transportation. However, its widespread adoption and economic viability depends in part on the ability to opt...
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ISBN:
(数字)9781624107160
ISBN:
(纸本)9781624107160
The advent of Urban Air Mobility (UAM) presents the scope for a transformative shift in the domain of urban transportation. However, its widespread adoption and economic viability depends in part on the ability to optimally schedule the fleet of aircraft across vertiports in a UAM network, under uncertainties attributed to airspace congestion, changing weather conditions, and varying demands. This paper presents a comprehensive optimization formulation of the fleet scheduling problem, while also identifying the need for alternate solution approaches, since directly solving the resulting integer nonlinear programming (INLP) problem is computationally prohibitive for daily fleet scheduling. Previous work has shown the effectiveness of using (graph) reinforcement learning (RL) approaches to train real-time executable policy models for fleet scheduling. However, such policies can often be brittle on out-of-distribution scenarios or edge cases. Moreover, training performance also deteriorates as the complexity (e.g., number of constraints) of the problem increases. To address these issues, this paper presents an imitation learning approach where the RL-based policy exploits expert demonstrations yielded by solving the exact optimization using a Genetic Algorithm. The policy model comprises Graph Neural Network (GNN) based encoders that embed the space of vertiports and aircraft, Transformer networks to encode demand, passenger fare and transport cost profiles, and a Multi-head attention (MHA) based decoder. Expert demonstrations are used through the Generative Adversarial Imitation Learning (GAIL) algorithm. Interfaced with a UAM simulation environment involving 8 vertiports and 40 aircrafts, in terms of the daily profits earned reward, the new imitative approach achieves better mean performance and remarkable improvement in the case of unseen worst-case scenarios, compared to pure RL results.
Event cameras are an interesting visual exteroceptive sensor that reacts to brightness changes rather than integrating absolute image intensities. Owing to this design, the sensor exhibits strong performance in situat...
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ISBN:
(纸本)9798350377712;9798350377705
Event cameras are an interesting visual exteroceptive sensor that reacts to brightness changes rather than integrating absolute image intensities. Owing to this design, the sensor exhibits strong performance in situations of challenging dynamics and illumination conditions. While event-based simultaneous tracking and mapping remains a challenging problem, a number of recent works have pointed out the sensor's suitability for prior map-based tracking. By making use of cross-modal registration paradigms, the camera's ego-motion can be tracked across a large spectrum of illumination and dynamics conditions on top of accurate maps that have been created a priori by more traditional sensors. The present paper follows up on a recently introduced event-based geometric semi-dense tracking paradigm, and proposes the addition of inertial signals in order to robustify the estimation. More specifically, the added signals provide strong cues for pose initialization as well as regularization during windowed, multi-frame tracking. As a result, the proposed framework achieves increased performance under challenging illumination conditions as well as a reduction of the rate at which intermediate event representations need to be registered in order to maintain stable tracking across highly dynamic sequences. Our evaluation focuses on a diverse set of real world sequences and comprises a comparison of our proposed method against a purely event-based alternative running at different rates.
We guarantee the strong duality and the existence of a saddle point of the hyperbolic augmented Lagrangian function (HALF) in convex optimization. To guarantee these results, we assume a set of convexity hypothesis an...
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We guarantee the strong duality and the existence of a saddle point of the hyperbolic augmented Lagrangian function (HALF) in convex optimization. To guarantee these results, we assume a set of convexity hypothesis and the Slater condition. Finally, we computationally illustrate our theoretical results obtained in this work.
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