This paper presents an automatic procedure to enhance the accuracy of the numerical solution of an optimal control problem (OCP) discretized via direct collocation at Gauss–Legendre points. First, a numerical solutio...
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This paper presents an automatic procedure to enhance the accuracy of the numerical solution of an optimal control problem (OCP) discretized via direct collocation at Gauss–Legendre points. First, a numerical solution is obtained by solving a nonlinear program (NLP). Then, the method evaluates its accuracy and adaptively changes both the degree of the approximating polynomial within each mesh interval and the number of mesh intervals until a prescribed accuracy is met. The number of mesh intervals is increased for all state vector components alike, in a classical fashion. Instead, improving on state-of-the-art procedures, the degrees of the polynomials approximating the different components of the state vector are allowed to assume, in each finite element, distinct values. This explains thepnhdefinition, wherenis the state dimension. With respect to the approaches found in the literature, where the degree is always raised to the highest order for all the state components, our methods allow a sensible reduction of the overall number of variables of the resulting NLP, with a corresponding reduction of the computational burden. Numerical tests on three OCP problems highlight that, under the same maximum allowable error, by independently selecting the degree of the polynomial for each state, our method effectively picks lower degrees for some of the states, thus reducing the overall number of variables in the NLP. Accordingly, various advantages are brought about, the most remarkable being: (i) an increased computational efficiency for the final enhanced mesh with solution accuracy still within the prescribed tolerance, (ii) a reduced risk of being trapped by local minima due to the reduced NLP size, and (iii) a gain of the robustness of the convergence process due to the better-behaved solution landscapes.
Here we study an optimal control problem involving energy management of a hybrid-fuel Unmanned Aerial Vehicle (UAV). The planning problem for a hybrid-fuel platform involves determining the path while managing the ene...
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Here we study an optimal control problem involving energy management of a hybrid-fuel Unmanned Aerial Vehicle (UAV). The planning problem for a hybrid-fuel platform involves determining the path while managing the energy resources, which includes a policy for power modality switching whenever applicable. The hybrid-fuel platform considered here involves a generator and battery pack combined in a series fashion as energy sources on-board a UAV. Also included in the problem are the noise restrictions, which place constraints on generator operation depending on the airspace location. These emulate possible restrictions on UAV noise that occur in military surveillance missions or in urban path planning, where the collective noise of many UAVs, some with combustion engines, may be restricted in certain areas or times of the day. We present a hybrid methodology which starts from an initial path and generator pattern obtained from a mixed integer linear program (MILP) solution. The generator pattern from the discrete solution is then refined in an optimal control framework with an objective to minimize fuel usage, while considering the nonlinear battery and generator dynamics and noise-restriction constraints. Optimal control problem is solved with a nonlinear program solver, IPOPT. Numerical results are presented and analyzed with varying path lengths and scenarios. This work aims to serve as an initial study of this hybrid-fuel UAV problem within an optimal control framework, which can be extended to refinement of both the generator pattern and the trajectory in tandem, while considering vehicle and power dynamics that are often ignored in discrete path planning solutions.
Oxygen starvation is one of the key technical challenges in proton exchange membrane (PEM) fuel cells operation. It impacts the system's durability, performance, and safety, especially under severe variability of ...
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The Interval Branch and Bound (IBB) method is a widely used approach for solving nonlinear programming problems where a rigorous solution is required. The method uses Interval Arithmetic (IA) to handle rounding errors...
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This paper introduces a traffic evacuation model for railway disruptions to improve resilience. The research focuses on the problem of failure of several nodes or lines on the railway network topology. We proposed a h...
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Mathematical programming approaches, such as Lagrangian relaxation, have the advantage of computational efficiency when the optimization problems are decomposable. Lagrangian relaxation belongs to a class of primal-du...
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ISBN:
(纸本)9781467330374;9781467330367
Mathematical programming approaches, such as Lagrangian relaxation, have the advantage of computational efficiency when the optimization problems are decomposable. Lagrangian relaxation belongs to a class of primal-dual algorithms. Subgradient-based optimization methods can be used to optimize the dual functions in Lagrangian relaxation. In this paper, three subgradient-based methods, the subgradient (SG), the surrogate subgradient (SSG) and the surrogate modified subgradient (SMSG), are adopted to solve a demonstrative nonlinear programming problem to assess the performances on optimality in order to demonstrate its applicability to the realistic problem.
This paper proposes a comprehensive approach to improve the computational efficiency of Reinforcement Learning (RL) based Model Predictive Controller (MPC). Although MPC will ensure controller safety and RL can genera...
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This paper proposes a comprehensive approach to improve the computational efficiency of Reinforcement Learning (RL) based Model Predictive Controller (MPC). Although MPC will ensure controller safety and RL can generate optimal control policies, combining the two requires substantial time and computational effort, particularly for larger data sets. In a typical RL-based MPC and Q- learning workflow, two not-so-different MPC problems must be evaluated at each RL iteration, i.e. one for the action-value and one for the value function, which is time-consuming and prohibitively expensive in terms of computations. We employ nonlinear programming (NLP) sensitivities to approximate the action-value function using the optimal solution from the value function, reducing computational time. The proposed approach can achieve comparable performance to the conventional method but with significantly lower computational time. We demonstrate the proposed approach on two examples: Linear Quadratic Regulator (LQR) problem and Continuously Stirred Tank Reactor (CSTR).
A modified form of Legendre-Gauss orthogonal direct collocation is developed for solving optimal control problems whose solutions are nonsmooth due to control discontinuities. This new method adds switch-time variable...
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We propose a novel method for spatiotemporal multi-camera calibration using freely moving people in multiview videos. Since calibrating multiple cameras and finding matches across their views are inherently interdepen...
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We present a new framework for the simultaneous optimiziation of both the topology as well as the relative density grading of cellular structures and materials, also known as lattices. Due to manufacturing constraints...
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