Optimal Control for Multi-mode Systems with Discrete Costs

This paper studies optimal time-bounded control in multi-mode systems with discrete costs. Multi-mode systems are an important subclass of linear hybrid systems, in which there are no guards on transitions and all invariants are global. Each state has a continuous cost attached to it, which is linear in the sojourn time, while a discrete cost is attached to each transition taken. We show that an optimal control for this model can be computed in NEXPTIME and approximated in PSPACE. We also show that the one-dimensional case is simpler: although the problem is NP-complete (and in LOGSPACE for an infinite time horizon), we develop an FPTAS for finding an approximate solution.Comment: extended version of a FORMATS 2017 pape

Optimisation in multi-mode systems

We study cost optimisation in multi-mode systems with discrete costs. We first solve the problem in one dimension and next we study it in multiple dimensions. As a motivating example, we study the temperature control in buildings using heating, ventilation and air-conditioning system HVAC while paying the minimal cost as possible. By optimising the behaviour of the HVAC systems, lots of energy could be saved. We are interested in finding optimal solutions as well as approximate solutions with guarantees