Optimal control and convex programming.
Optimal control and convex programming, discussing problem of admissible investiment program control for production constraints
OPTIMAL CONTROL↗
SEARCH · Engineering Papers
Results for “convex programming”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Optimal control and convex programming.
Optimal control for investment program, obtaining solution through convex programming
OPTIMAL CONTROL↗
Optimal control and convex programming
Computational scheme for optimal control problem based on convex programming method
PROGRAMMING↗
Higher order sensitivity of solutions to convex programming problems without strict complementarity
Consideration is given to a family of convex programming problems which depend on a vector parameter. It is shown that the solutions of the problems and the associated Lagrange multipliers are arbitrarily many times directionally differentiable functions of the parameter, provided that the data of the problems are sufficiently regular. The characterizations of the respective derivatives are given.
Malanowski, Kazimierz↗
Computable optimal value bounds for generalized convex programs
It has been shown by Fiacco that convexity or concavity of the optimal value of a parametric nonlinear programming problem can readily be exploited to calculate global parametric upper and lower bounds on the optimal value function. The approach is attractive because it involves manipulation of information normally required to characterize solution optimality. A procedure is briefly described for calculating and improving the bounds as well as its extensions to generalized convex and concave functions. Several areas of applications are also indicated.
Fiacco, Anthony V.↗
Enhancements on the Convex Programming Based Powered Descent Guidance Algorithm for Mars Landing
In this paper, we present enhancements on the powered descent guidance algorithm developed for Mars pinpoint landing. The guidance algorithm solves the powered descent minimum fuel trajectory optimization problem via a direct numerical method. Our main contribution is to formulate the trajectory optimization problem, which has nonconvex control constraints, as a finite dimensional convex optimization problem, specifically as a finite dimensional second order cone programming (SOCP) problem. SOCP is a subclass of convex programming, and there are efficient SOCP solvers with deterministic convergence properties. Hence, the resulting guidance algorithm can potentially be implemented onboard a spacecraft for real-time applications. Particularly, this paper discusses the algorithmic improvements obtained by: (i) Using an efficient approach to choose the optimal time-of-flight; (ii) Using a computationally inexpensive way to detect the feasibility/ infeasibility of the problem due to the thrust-to-weight constraint; (iii) Incorporating the rotation rate of the planet into the problem formulation; (iv) Developing additional constraints on the position and velocity to guarantee no-subsurface flight between the time samples of the temporal discretization; (v) Developing a fuel-limited targeting algorithm; (vi) Initial result on developing an onboard table lookup method to obtain almost fuel optimal solutions in real-time.
Guidance↗
Partition-based Feasible Integer Solution Pre-computation for Hybrid Model Predictive Control
For multiparametric mixed-integer convex programming problems such as those encountered in hybrid model predictive control, we propose an algorithm for generating a feasible partition of a subset of the parameter space. The result is a static map from the current parameter to a suboptimal integer solution such that the remaining convex program is feasible. Convergence is proved with a new insight that the overlap among the feasible parameter sets of each integer solution governs the partition complexity. The partition is stored as a tree which makes querying the feasible solution efficient. The algorithm can be used to warm start a mixed integer solver with a real-time guarantee or to provide a reference integer solution in several suboptimal MPC schemes. The algorithm is tested on randomly generated systems with up to six states, demonstrating the effectiveness of the approach.
Bayard, David S.↗
Distributed Spatiotemporal Motion Planning for Spacecraft Swarms in Cluttered Environments
This paper focuses on trajectory planning for spacecraft swarms in cluttered environments, like debris fields or the asteroid belt. Our objective is to reconfigure the spacecraft swarm to a desired formation in a distributed manner while minimizing fuel and avoiding collisions among themselves and with the obstacles. In our prior work we proposed a novel distributed guidance algorithm for spacecraft swarms in static environments.1 In this paper, we present the Multi-Agent Moving-Obstacles Spherical Expansion and Sequential Convex Programming (MAMO SE–SCP) algorithm that extends our prior work to include spatiotemporal constraints such as time-varying, moving obstacles and desired time-varying terminal positions. In the MAMO SE–SCP algorithm, each agent uses a spherical-expansion-based sampling algorithm to cooperatively explore the time-varying environment, a distributed assignment algorithm to agree on the terminal position for each agent, and a sequential-convex-programming-based optimization step to compute the locally-optimal trajectories from the current location to the assigned time-varying terminal position while avoiding collision with other agent and the moving obstacles. Simulations results demonstrate that the proposed distributed algorithm can be used by a spacecraft swarm to achieve a time-varying, desired formation around an object of interest in a dynamic environment with many moving and tumbling obstacles.
Hadaegh, Fred Y.↗
Distributed Spatiotemporal Motion Planning for Spacecraft Swarms in Cluttered Environments
This paper focuses on trajectory planning for spacecraft swarms in cluttered environments, like debris fields or the asteroid belt. Our objective is to reconfigure the spacecraft swarm to a desired formation in a distributed manner while minimizing fuel and avoiding collisions among themselves and with obstacles. In our prior work we proposed a novel distributed guidance algorithm for spacecraft swarms in static environments. In this paper, we present the Multi-Agent Moving-Obstacles Spherical Expansion and Sequential Convex Programming (MAMO SE-SCP) algorithm that extends our prior work to include spatiotemporal constraints such as time-varying, moving obstacles and desired time-varying terminal positions. In the MAMO SE-SCP algorithm, each agent uses a spherical-expansion-based sampling algorithm to cooperatively explore the time-varying environment, a distributed assignment algorithm to agree on the terminal position for each agent, and a sequential-convex-programming-based optimization step to compute the locally-optimal trajectories from the current location to the assigned time-varying terminal position while avoiding collision with other agents and moving obstacles. Simulation results demonstrate that the proposed distributed algorithm can be used by a spacecraft swarm to achieve a time-varying, desired formation around an object of interest in a dynamic environment with many moving and tumbling obstacles.
Bandyopadhyay, Saptarshi↗
Evaluation of Horizon of Viability Optimization Engine for Sustained Power to Critical Infrastructure: Preprint
In the aftermath of increasingly frequent catastrophic events, a typical scenario is Critical Infrastructure (CI) units being supported by available backup sources with a weak power grid that can be intermittent or absent. Such a scenario is significantly challenging in the sense of reliable supply of power to CI units. In this article, an intelligent optimization scheme termed as Horizon of Viability (HoV) engine is developed to guarantee the viability of a sustained reliable supply of power to the CI units over a time-horizon. The proposed HoV engine generates a cost-optimal portfolio of the locally available generation sources and the loads over a time horizon using a mixed-integer convex programming problem. A Controller hardware-in-the-loop (CHIL) platform is developed to evaluate the control performance of the HoV engine. The experimental results corroborates the efficacy in maintaining the viability of the CI units after a grid interruption event. Further, the proposed HoV optimization scheme performs better compared to existing net-load management schemes in the literature.
disaster resiliency↗
Interval Predictor Models with a Formal Characterization of Uncertainty and Reliability
This paper develops techniques for constructing empirical predictor models based on observations. By contrast to standard models, which yield a single predicted output at each value of the model's inputs, Interval Predictors Models (IPM) yield an interval into which the unobserved output is predicted to fall. The IPMs proposed prescribe the output as an interval valued function of the model's inputs, render a formal description of both the uncertainty in the model's parameters and of the spread in the predicted output. Uncertainty is prescribed as a hyper-rectangular set in the space of model's parameters. The propagation of this set through the empirical model yields a range of outputs of minimal spread containing all (or, depending on the formulation, most) of the observations. Optimization-based strategies for calculating IPMs and eliminating the effects of outliers are proposed. Outliers are identified by evaluating the extent by which they degrade the tightness of the prediction. This evaluation can be carried out while the IPM is calculated. When the data satisfies mild stochastic assumptions, and the optimization program used for calculating the IPM is convex (or, when its solution coincides with the solution to an auxiliary convex program), the model's reliability (that is, the probability that a future observation would be within the predicted range of outputs) can be bounded rigorously by a non-asymptotic formula.
Crespo, Luis G.↗
Algorithms for Maneuvering Spacecraft Around Small Bodies
A document describes mathematical derivations and applications of autonomous guidance algorithms for maneuvering spacecraft in the vicinities of small astronomical bodies like comets or asteroids. These algorithms compute fuel- or energy-optimal trajectories for typical maneuvers by solving the associated optimal-control problems with relevant control and state constraints. In the derivations, these problems are converted from their original continuous (infinite-dimensional) forms to finite-dimensional forms through (1) discretization of the time axis and (2) spectral discretization of control inputs via a finite number of Chebyshev basis functions. In these doubly discretized problems, the Chebyshev coefficients are the variables. These problems are, variously, either convex programming problems or programming problems that can be convexified. The resulting discrete problems are convex parameter-optimization problems; this is desirable because one can take advantage of very efficient and robust algorithms that have been developed previously and are well established for solving such problems. These algorithms are fast, do not require initial guesses, and always converge to global optima. Following the derivations, the algorithms are demonstrated by applying them to numerical examples of flyby, descent-to-hover, and ascent-from-hover maneuvers.
Acikmese, A. Bechet↗
Computationally Efficient Motion Planning Algorithms for Agile Autonomous Vehicles in Cluttered Environments
Fast, real-time motion planning of an agile, autonomous vehicle in a cluttered environment, with many geometrically-fixed obstacles, is a very complex problem, especially because of the vehicle dynamics constraints and resource constrained computational capabilities onboard the vehicle. In this paper, we present computationally-efficient versions of our novel motion planning algorithm called the Spherical Expansion and Sequential Convex Programming (SE–SCP) algorithm. The SE–SCP algorithm first uses a spherical-expansion-based randomized sampling algorithm to explore the workspace. Oncea path is found from the start position to the goal position, the algorithm computes a locally optimal trajectory, within its homotopy class for a desired cost function, by solving a sequence of convex optimization problems. Thus, the SE–SCP algorithm is anytime locally optimal and the trajectory is globally optimal if the number of samples tends to infinity. In this paper, we further enhance the computational efficiency of the SE–SCP algorithm using uni-directional and bi-directional rewiring techniques. We also present a detailed proof of the local optimality characteristics of the new SE–SCP algorithms for aspecial case of vehicle dynamics. Simulation examples involving quadrotor and spacecraft help demonstrate the effectiveness of our new algorithms.
Bandyopadhyay, Saptarshi↗
A Smoothed Augmented Lagrangian Framework for Convex Optimization with Nonsmooth Constraints
Augmented Lagrangian (AL) methods have proven remarkably useful in solving optimization problems with complicated constraints. The last decade has seen the development of overall complexity guarantees for inexact AL variants. Yet, a crucial gap persists in addressing nonsmooth convex constraints. To this end, we present a smoothed augmented Lagrangian (AL) framework where nonsmooth terms are progressively smoothed with a smoothing parameter $\eta _k$ . The resulting AL subproblems are $\eta _k$ -smooth, allowing for leveraging accelerated schemes. By a careful selection of the inexactness level $\epsilon _k$ (for inexact subproblem resolution), the penalty parameter $\rho _k$ , and smoothing parameter $\eta _k$ at epoch k, we derive rate and complexity guarantees of $\tilde{\mathcal {O}}(1/{\varepsilon }^{3/2})$ and $\tilde{\mathcal {O}}(1/{\varepsilon })$ in convex and strongly convex regimes for computing an ${\varepsilon }$ -optimal solution, when $\rho _k$ increases at a geometric rate, a significant improvement over the best available guarantees for AL schemes for convex programs with nonsmooth constraints. Analogous guarantees are developed for settings with $\rho _k = \rho$ as well as $\eta _k = \eta$ . Preliminary numerics on a fused Lasso problem display promise.
augmented Lagrangian↗
Optimizing for minimum weight when two different finite element models and analyses are required
The Finite Element Structural Optimization Program's (FESOP) ability to perform minimum weight optimization using two different finite element analyses and models is discussed. FESOP uses the ADS optimizer developed by Dr. Garret Vanderplaats to solve the nonlinear constrained optimization problem. The design optimization problem requires a response spectrum analysis and model to evaluate the stress and displacement constraints. However, the problem needs a frequency analysis and model to calculate the natural frequencies used to evaluate the frequency range constraints. The results of both the successful and unsuccessful approaches used to solve this difficult weight minimization problem are summarized. The results show that no one ADS optimization algorithm worked in all cases. However, the Sequential Convex Programming and Modified Method of Feasible Directions algorithms were the most successful.
Hall, Jeffrey C.↗
Real-time control of connected vehicles in signalized corridors using pseudospectral convex optimization
Recent advances in Connected and Automated Vehicle (CAV) technologies have opened up new opportunities to enable safe, efficient, and sustainable transportation systems. However, developing reliable and rapid speed control algorithms in highly dynamic environments with complex inter-vehicle interactions and nonlinear vehicle dynamics is still a daunting task. In this paper, we develop a novel speed control method for CAVs to produce optimal speed profiles that minimize the fuel consumption and avoid idling at signalized intersections. To this end, an optimal control problem is formulated using the information of the upcoming traffic signal to adapt vehicles' speeds to avoid frequent stop-and-go driving patterns. Here, by applying the pseudospectral discretization method and the sequential convex programming method, the computational efficiency is greatly improved, enabling potential real-time on-vehicle applications. In addition, the algorithm is implemented under a model predictive control framework to ensure online control with instant response for collision avoidance and robust vehicle coordination. The proposed algorithm is verified through numerical simulations of three different traffic scenarios. The convergence and accuracy of the proposed approach are demonstrated by comparing with a popular nonlinear solver. Furthermore, the benefit of the proposed method in both traffic mobility and fuel efficiency is validated using the speed profile determined from a traffic following model in a simulation software as the baseline.
42 ENGINEERING↗
Pseudospectral convex optimization for on-ramp merging control of connected vehicles
It can be a daunting task for human drivers to merge into highways because of the intricate vehicle negotiations and potential risk within limited time and space. Connected vehicle (CV) technologies could be a solution to this problem and offer many benefits to the road safety, traffic mobility, and energy efficiency. However, real-time optimal control of CVs is still an open challenge, due to the nonlinear vehicle dynamics, non-convex fuel consumption model, and highly dynamic uncertain inter-vehicle interactions. To tackle these issues, a novel real-time optimal control approach that balances the computational efficiency and solution optimality is proposed for the purpose of onboard application. To this end, the pseudospectral collocation method is integrated with a sequential convex programming approach to develop two new optimization algorithms, which are implemented within a model predictive control (MPC) framework to allow for real-time generation of optimal merging speed profiles. One algorithm leverages the line search technique to improve convergence, and the other benefits from the trust region method for better computational efficiency. The optimality and convergence process of both proposed algorithms are investigated by comparing their solutions with a popular non-linear solver. Furthermore, simulation results show that the proposed methods outperform the benchmark in terms of computational cost, fuel consumption, and traffic efficiency. In particular, the proposed fuel-economy merging rule can save 57.1% fuel consumption on average on four different traffic volumes. Meanwhile, the proposed optimal control algorithms can reduce 2.2% travel time on average comparing to the “first-in-first-out” merging rule.
33 ADVANCED PROPULSION SYSTEMS↗
Covariant bit threads
We derive several new reformulations of the Hubeny-Rangamani-Takayanagi covariant holographic entanglement entropy formula. These include: (1) a minimax formula, which involves finding a maximal-area achronal surface on a timelike hypersurface homologous to D(A) (the boundary causal domain of the region A whose entropy we are calculating) and minimizing over the hypersurface; (2) a max V-flow formula, in which we maximize the flux through D(A) of a divergenceless bulk 1-form V subject to an upper bound on its norm that is non-local in time; and (3) a min U-flow formula, in which we minimize the flux over a bulk Cauchy slice of a divergenceless timelike 1-form U subject to a lower bound on its norm that is non-local in space. The two flow formulas define convex programs and are related to each other by Lagrange duality. For each program, the optimal configurations dynamically find the HRT surface and the entanglement wedges of A and its complement. The V-flow formula is the covariant version of the Freedman-Headrick bit thread reformulation of the Ryu-Takayanagi formula. We also introduce a measure-theoretic concept of a “thread distribution”, and explain how Riemannian flows, V-flows, and U-flows can be expressed in terms of thread distributions.
79 ASTRONOMY AND ASTROPHYSICS↗