An indirectoptimization method is applied to orbit transfers in LEO, considering almost circular orbits and the influence of J2 perturbation. An approach based on Edelbaum's approximation is employed to solve tra...
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An indirectoptimization method is applied to orbit transfers in LEO, considering almost circular orbits and the influence of J2 perturbation. An approach based on Edelbaum's approximation is employed to solve transfers with change of semimajor axis, inclination and right ascension of ascending node. The spacecraft employs electric propulsion either alone or in combination with a drag sail that can be deployed and retracted. The proposed formulation is simple and effective and is capable of treating both minimum-time (thruster is always on) and minimum-propellant (coasting arcs are introduced) problems, while also dealing with the presence of altitude constraints. Convergence to the optimal solution is fast and straightforward, making the proposed approach suitable for the preliminary evaluation of large sets of available transfers (e.g., multiple debris removal).
An indirectoptimization procedure is presented to minimize the propellant consumption for finite-burn transfers with two practical thrust control models, namely, inertially fixed thrust and fixed-plane linearly varyi...
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An indirectoptimization procedure is presented to minimize the propellant consumption for finite-burn transfers with two practical thrust control models, namely, inertially fixed thrust and fixed-plane linearly varying thrust direction. The optimality equations are derived with theory of optimal control and the consequent boundary value problem is solved with a procedure based on Newton's method. A homotopic approach is used to find suitable tentative solutions and assure convergence. The method is applied to the optimization of Moon escape trajectories with accurate dynamic models and proves to be fast and accurate.
Nonlinear model predictive control (NMPC) is an important tool for the real-time optimization of batch and semi-batch processes. Direct methods are often the methods of choice to solve the corresponding optimal contro...
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Nonlinear model predictive control (NMPC) is an important tool for the real-time optimization of batch and semi-batch processes. Direct methods are often the methods of choice to solve the corresponding optimal control problems, in particular for large-scale problems. However, the matrix factorizations associated with large prediction horizons can be computationally demanding. In contrast, indirectmethods can be competitive for smaller-scale problems. Furthermore, the interplay between states and co-states in the context of Pontryagin's Minimum Principle (PMP) might turn out to be computationally quite efficient. This work proposes to use an indirect solution technique in the context of shrinking-horizon NMPC. In particular, the technique deals with path constraints via indirect adjoining, which allows meeting active path constraints explicitly at each iteration. Uncertainties are handled by the introduction of time-varying backoff terms for the path constraints. The resulting NMPC algorithm is applied to a two-phase semi-batch reactor for the hydroformylation of 1-dodecene in the presence of uncertainty, and its performance is compared to that of NMPC that uses a direct simultaneous optimization method. The results show that the proposed algorithm (i) can enforce feasible operation for different uncertainty realizations both within batch or from batch to batch, and (ii) is significantly faster than direct simultaneous NMPC, especially at the beginning of the batch. In addition, a modification of the PMP-based NMPC scheme is proposed to enforce active constraints via tracking. (C) 2017 Elsevier Ltd. All rights reserved.
This work considers the numerical optimization of constrained batch and semi-batch processes, for which direct as well as indirectmethods exist. Direct methods are often the methods of choice, but they exhibit certai...
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This work considers the numerical optimization of constrained batch and semi-batch processes, for which direct as well as indirectmethods exist. Direct methods are often the methods of choice, but they exhibit certain limitations related to the compromise between feasibility and computational burden. indirectmethods, such as Pontryagin's Minimum Principle (PMP), reformulate the optimization problem. The main solution technique is the shooting method, which however often leads to convergence problems and instabilities caused by the integration of the co-state equations forward in time. This study presents an alternative indirect solution technique. Instead of integrating the states and co-states simultaneously forward in time, the proposed algorithm parameterizes the inputs, and integrates the state equations forward in time and the co-state equations backward in time, thereby leading to a gradient-based optimization approach. Constraints are handled by indirect adjoining to the Hamiltonian function, which allows meeting the active constraints explicitly at every iteration step. The performance of the solution strategy is compared to direct methods through three different case studies. The results show that the proposed PMP-based quasi-Newton strategy is effective in dealing with complicated constraints and is quite competitive computationally. (C) 2017 Elsevier Ltd. All rights reserved.
Abstract indirectmethods solve optimal control problems for hybrid systems with high precision, but they are difficult to initialize. To overcome the initialization difficulties, two different concepts based on direc...
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Abstract indirectmethods solve optimal control problems for hybrid systems with high precision, but they are difficult to initialize. To overcome the initialization difficulties, two different concepts based on direct methods are presented. In the first approach, the hybrid optimal control problem is solved by a direct method until the precision is sufficient for a successful initialization of the indirect method. The second approach decomposes the hybrid optimal control problem into non-hybrid subproblems, where each subproblem can be initialized separately by a direct method. This results in a significantly higher robustness of the initialization compared to the first approach. However, the precision of the solution with the indirect method achieved in the first approach is higher. The two concepts are compared in a numerical example.
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