Critical speed control of a solar car
type: Item
instance of: scholarly article
title: Critical speed control of a solar car
zbMATH Open document ID: 1080.49506
DOI: 10.1023/A:1020907101234
author: P. J. Pudney
author: Phil Howlett
published in: Optimization and Engineering
publication date: 2003-03-12T00:00:00Z
review text: The following optimal control problem is presented: The World Solar Challenge is a 3000 km race for solar powered cars across the Australian continent from Darwin to Adelaide. Each car is powered by a panel of photovoltaic cells which convert sunlight into electrical power. The power can be used directly to drive the car or stored in a battery for later use. Previous papers [\textit{P. G. Howlett, P. J. Pudney, T. Tarnopolskaya}, and \textit{D. Gates}, IMA J. Math. Appl. Bus. Ind. 8, 59--81 (1997; Zbl 0893.49025), \textit{P.G. Howlett} and \textit{P.J. Pudney}, Dyn. Contin. Discrete Impulsive Syst. 4, 553--567 (1998; Zbl 0914.49024)] using a simplified model of the battery, have shown that the optimal strategy is essentially a speedholding strategy. In this paper, with a more realistic model of the battery, they show that the optimal driving strategy is a critical speed strategy. For an optimal journey with no beginning and no ending the solar car must always travel at the critical speed. For an optimal journey of finite length the speed must be close to the critical speed for most of the journey. The critical speed depends on the solar power and will normally vary slowly with time. The mathematical model for this problem is described as follows. Assume that the force generated by the wheels of the driving vehicle is \(F = \frac{p}{v}\) where \(p\) is the power applied to the drive system and \(v\) the velocity of the car. Let \(R(v)\) be the resistive force increasing in \(v\) and suppose that \(\varphi (v) := v R(v)\) is convex. Then the equation of motion of the car is modeled by \[ \frac{d x}{d t} = v,\quad \frac{d v}{d t} = \frac{1}{m} \Big[\frac{p}{v}-R(v)\Big] \] with mass \(m\) and initial-boundary conditions \[ x(0) = x_0, \quad v(0) = v_0, \quad v(T) = v_T . \] Set \(p = b + s\) where \(s\) is the power coming from the solar array (\(b\) battery power). Additionally, the energy storage equations are supposed to be \[ \frac{d q}{d t} = - I(b), \quad q(0)=q_…
reviewed by: Henri Schurz
Mathematics Subject Classification ID: 49N90
Mathematics Subject Classification ID: 49L20
Mathematics Subject Classification ID: 93C95
Mathematics Subject Classification ID: 90B99
Mathematics Subject Classification ID: 93E20
zbMATH DE Number: 1880490
zbMATH Keywords: solar car problem
zbMATH Keywords: stochastic optimal control
zbMATH Keywords: Bellman principle of dynamic programming
zbMATH Keywords: Markov processes
zbMATH Keywords: optimal control strategy
zbMATH Keywords: control policy
zbMATH Keywords: critical speed control
MaRDI profile type: Publication
full work available at URL: a:1020907101234
OpenAlex ID: W1697120458
description: scientific article; zbMATH DE number 1880490