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Control Barrier Functions for Abstraction-Free Control Synthesis under Temporal Logic Constraints

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Document pages: 9 pages

Abstract: Temporal logic has been widely used to express complex task specificationsfor cyber-physical systems (CPSs). One way to synthesize a controller for CPSunder temporal logic constraints is to first abstract the CPS as a discretetransition system, and then apply formal methods. This approach, however, iscomputationally demanding and its scalability suffers due to the curse ofdimensionality. In this paper, we propose a control barrier function (CBF)approach to abstraction-free control synthesis under a linear temporal logic(LTL) constraint. We first construct the deterministic Rabin automaton of thespecification and compute an accepting run. We then compute a sequence of LTLformulae, each of which must be satisfied during a particular time interval,and prove that satisfying the sequence of formulae is sufficient to satisfy theLTL specification. Finally, we compute a control policy for satisfying eachformula by constructing an appropriate CBF. We present a quadratic program tocompute the controllers, and show the controllers synthesized using theproposed approach guarantees the system to satisfy the LTL specification,provided the quadratic program is feasible at each time step. A numerical casestudy is presented to demonstrate the proposed approach.

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