114,676 research outputs found
Determination of the adjoint state evolution for the efficient operation of a hybrid electric vehicle
To minimize the fuel consumption in hybrid electric vehicles, it is necessary to define a strategy for the management of the power flows within the vehicle. Under the assumption that the velocity to be developed by the vehicle is known a priori, this problem may be posed as a nonlinear optimal control problem with control and state constraints. We find the solution to this problem using the optimality conditions given by the Pontryagin Maximum Principle. This leads to boundary value problems that we solve using a software tool named PASVA4. On real time operation, the velocity to be developed by the vehicle is not known in advance. We show how the adjoint state obtained from the former problem may be used as a weighing factor, called ‘‘equivalent consumption’’. This weighing factor may be used to design suboptimal real time algorithms for power management.Fil: Perez, Laura Virginia. Universidad Nacional de Rio Cuarto. Facultad de IngenierÃa. Grupo de Electronica Aplicada; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: de Angelo, Cristian Hernan. Universidad Nacional de Rio Cuarto. Facultad de IngenierÃa. Grupo de Electronica Aplicada; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Pereyra, VÃctor. San Diego State University; Estados Unido
A Homotopy-Based Method for Optimization of Hybrid High-Low Thrust Trajectories
Space missions require increasingly more efficient trajectories to provide payload transport and mission goals by means of lowest fuel consumption, a strategic mission design key-point. Recent works demonstrated that the combined (or hybrid) use of chemical and electrical propulsion can give important advantages in terms of fuel consumption, without losing the ability to reach other mission objectives: as an example the Hohmann Spiral Transfer, applied in the case of a transfer to GEO orbit, demonstrated a fuel mass saving between 5-10% of the spacecraft wet mass, whilst satisfying a pre-set boundary constraint for the time of flight. Nevertheless, methods specifically developed for optimizing space trajectories considering the use of hybrid high-low thrust propulsion systems have not been extensively developed, basically because of the intrinsic complexity in the solution of optimal problem equations with existent numerical methods. The study undertaken and presented in this paper develops a numerical strategy for the optimization of hybrid high-low thrust space trajectories. An indirect optimization method has been developed, which makes use of a homotopic approach for numerical convergence improvement. The adoption of a homotopic approach provides a relaxation to the optimal problem, transforming it into a simplest problem to solve in which the optimal problem presents smoother equations and the shooting function acquires an increased convergence radius: the original optimal problem is then reached through a homotopy parameter continuation. Moreover, the use of homotopy can make possible to include a high thrust impulse (treated as velocity discontinuity) to the low thrust optimal control obtained from the indirect method. The impulse magnitude, location and direction are obtained following from a numerical continuation in order to minimize the problem cost function. The initial study carried out in this paper is finally correlated with particular test cases, in order to validate the work developed and to start investigating in which cases the effectiveness of hybrid-thrust propulsion subsists
Maximum-principle preserving space-time isogeometric analysis
In this work we propose a nonlinear stabilization technique for
convection-diffusion-reaction and pure transport problems discretized with
space-time isogeometric analysis. The stabilization is based on a
graph-theoretic artificial diffusion operator and a novel shock detector for
isogeometric analysis. Stabilization in time and space directions are performed
similarly, which allow us to use high-order discretizations in time without any
CFL-like condition. The method is proven to yield solutions that satisfy the
discrete maximum principle (DMP) unconditionally for arbitrary order. In
addition, the stabilization is linearity preserving in a space-time sense.
Moreover, the scheme is proven to be Lipschitz continuous ensuring that the
nonlinear problem is well-posed. Solving large problems using a space-time
discretization can become highly costly. Therefore, we also propose a
partitioned space-time scheme that allows us to select the length of every time
slab, and solve sequentially for every subdomain. As a result, the
computational cost is reduced while the stability and convergence properties of
the scheme remain unaltered. In addition, we propose a twice differentiable
version of the stabilization scheme, which enjoys the same stability properties
while the nonlinear convergence is significantly improved. Finally, the
proposed schemes are assessed with numerical experiments. In particular, we
considered steady and transient pure convection and convection-diffusion
problems in one and two dimensions
An hybrid system approach to nonlinear optimal control problems
We consider a nonlinear ordinary differential equation and want to control
its behavior so that it reaches a target by minimizing a cost function. Our
approach is to use hybrid systems to solve this problem: the complex dynamic is
replaced by piecewise affine approximations which allow an analytical
resolution. The sequence of affine models then forms a sequence of states of a
hybrid automaton. Given a sequence of states, we introduce an hybrid
approximation of the nonlinear controllable domain and propose a new algorithm
computing a controllable, piecewise convex approximation. The same way the
nonlinear optimal control problem is replaced by an hybrid piecewise affine
one. Stating a hybrid maximum principle suitable to our hybrid model, we deduce
the global structure of the hybrid optimal control steering the system to the
target
On Minimum-time Paths of Bounded Curvature with Position-dependent Constraints
We consider the problem of a particle traveling from an initial configuration
to a final configuration (given by a point in the plane along with a prescribed
velocity vector) in minimum time with non-homogeneous velocity and with
constraints on the minimum turning radius of the particle over multiple regions
of the state space. Necessary conditions for optimality of these paths are
derived to characterize the nature of optimal paths, both when the particle is
inside a region and when it crosses boundaries between neighboring regions.
These conditions are used to characterize families of optimal and nonoptimal
paths. Among the optimality conditions, we derive a "refraction" law at the
boundary of the regions that generalizes the so-called Snell's law of
refraction in optics to the case of paths with bounded curvature. Tools
employed to deduce our results include recent principles of optimality for
hybrid systems. The results are validated numerically.Comment: Expanded version of paper in Automatic
Hybrid control for low-regular nonlinear systems: application to an embedded control for an electric vehicle
This note presents an embedded automatic control strategy for a low
consumption vehicle equipped with an "on/off" engine. The main difficulties are
the hybrid nature of the dynamics, the non smoothness of the dynamics of each
mode, the uncertain environment, the fast changing dynamics, and low cost/ low
consumption constraints for the control device. Human drivers of such vehicles
frequently use an oscillating strategy, letting the velocity evolve between
fixed lower and upper bounds. We present a general justification of this very
simple and efficient strategy, that happens to be optimal for autonomous
dynamics, robust and easily adaptable for real-time control strategy. Effective
implementation in a competition prototype involved in low-consumption races
shows that automatic velocity control achieves performances comparable with the
results of trained human drivers. Major advantages of automatic control are
improved robustness and safety. The total average power consumption for the
control device is less than 10 mW
An indirect numerical method for a time-optimal state-constrained control problem in a steady two-dimensional fluid flow
This article concerns the problem of computing solutions to state-constrained
optimal control problems whose trajectory is affected by a flow field. This
general mathematical framework is particularly pertinent to the requirements
underlying the control of Autonomous Underwater Vehicles in realistic scenarii.
The key contribution consists in devising a computational indirect method which
becomes effective in the numerical computation of extremals to optimal control
problems with state constraints by using the maximum principle in Gamkrelidze's
form in which the measure Lagrange multiplier is ensured to be continuous. The
specific problem of time-optimal control of an Autonomous Underwater Vehicle in
a bounded space set, subject to the effect of a flow field and with bounded
actuation, is used to illustrate the proposed approach. The corresponding
numerical results are presented and discussed
On Weak Topology for Optimal Control of Switched Nonlinear Systems
Optimal control of switched systems is challenging due to the discrete nature
of the switching control input. The embedding-based approach addresses this
challenge by solving a corresponding relaxed optimal control problem with only
continuous inputs, and then projecting the relaxed solution back to obtain the
optimal switching solution of the original problem. This paper presents a novel
idea that views the embedding-based approach as a change of topology over the
optimization space, resulting in a general procedure to construct a switched
optimal control algorithm with guaranteed convergence to a local optimizer. Our
result provides a unified topology based framework for the analysis and design
of various embedding-based algorithms in solving the switched optimal control
problem and includes many existing methods as special cases
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