Stochastic optimal control of a solar car (Q2776668)

This paper discusses the solar car problem, which is related to the 3000 km race of solar powered cars across the Australian continent, known as World Solar Challenge. Each solar vehicle is powered by a panel of photovoltic cells that convert solar irradiance to electrical power used for driving or storage. It is assumed that the solar radiation follows a Markov process with known transition matrix and that the distance travelled is a known function of the energy used. The state variables for this problem are the number of days remaining in the race, the amount of energy in the battery and the amount of solar energy collected on the previous day. The control variable is the amount of energy to be used on any given day. The authors consider the following mathematical problem related to the described model: Find a driving strategy that maximizes the expected value of the total distance to be travelled by the solar car on the remaining days for each allowable configuration of the state variables. For its solution, the Bellman principle of dynamic programming is applied. It is shown that the long term strategy to use the same amount of energy each day maximizes the expected total distance to be travelled on the remaining days at least in some special cases. It is well known that long term strategies must be sustainable. Therefore, the energy used each day should be equal to the average daily solar radiation. The authors formulate a conjecture for ergodic systems. An effective calculation of recursive equations is found to determine the optimal energy used. The implication for the driving strategy is as follows. At the start of the race, the optimal daily energy usage is approximately equal to the average daily power received. Towards the end of the race, the exact solution to the found recursive equations can be computed on a daily basis.NEWLINENEWLINEFor the entire collection see [Zbl 0974.00048].