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**1 - 2**of**2**### Optimal Control with Regular Objectives Using an Abstraction-Refinement Approach

"... Abstract—This paper presents a method to synthesize a se-quence of control inputs for a discrete-time switched linear system equipped with a cost function, such that the controlled system behavior satisfies a linear-time temporal objective with minimal cost. An abstract finite state weighted transit ..."

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Abstract—This paper presents a method to synthesize a se-quence of control inputs for a discrete-time switched linear system equipped with a cost function, such that the controlled system behavior satisfies a linear-time temporal objective with minimal cost. An abstract finite state weighted transition system is constructed, such that the cost of the optimal control on the abstract system provides an upper bound on the cost of the system is constructed from finite partitions of the state and input spaces by solving certain optimization problems, and a sequence of controllers is obtained by considering a sequence of uniformly refined partitions. Under mild assumptions on the optimal control for the switched system, the costs of the sequence of controllers constructed converges to the cost of the optimal control for the switched system. The abstraction refinement algorithm is implemented in the tool OptCAR. The feasibility of this approach is illustrated on two different examples, by constructing automat-ically, sub-optimal controllers with improving optimal costs. I.