TY - GEN

T1 - Optimal parametric discrete event control

T2 - 2008 American Control Conference, ACC

AU - Griffin, Christopher

PY - 2008

Y1 - 2008

N2 - We present a novel optimization problem for discrete event control, similar in spirit to the optimal parametric control problem common in statistical process control. In our problem, we assume a known finite state machine plant model G defined over an event alphabet Σ- so that the plant model language L = ℒM(G) is prefix closed. We further assume the existence of a base control structure MK, which may be either a finite state machine or a deterministic pushdown machine. If K = ℒM(M K), we assume K is prefix closed and that K ⊆ L. We associate each controllable transition of MK with a binary variable X 1,...,Xn indicating whether the transition is enabled or not. This leads to a function MK(X1,...,Xn), that returns a new control specification depending upon the values of X 1,...,Xn. We exhibit a branch-and-bound algorithm to solve the optimization problem minX1,...,Xn maxw∈K C(w) such that MK(X1,...,Xn) |= Π and ℒM(MK(X1,...,Xn)) ∈ C(L). Here Π is a set of logical assertions on the structure of M K(X1,...,Xn), and MK(X 1,...,Xn) |= Π indicates that MK(X 1,...,Xn) satisfies the logical assertions; and, C(L) is the set of controllable sublanguages of L1.

AB - We present a novel optimization problem for discrete event control, similar in spirit to the optimal parametric control problem common in statistical process control. In our problem, we assume a known finite state machine plant model G defined over an event alphabet Σ- so that the plant model language L = ℒM(G) is prefix closed. We further assume the existence of a base control structure MK, which may be either a finite state machine or a deterministic pushdown machine. If K = ℒM(M K), we assume K is prefix closed and that K ⊆ L. We associate each controllable transition of MK with a binary variable X 1,...,Xn indicating whether the transition is enabled or not. This leads to a function MK(X1,...,Xn), that returns a new control specification depending upon the values of X 1,...,Xn. We exhibit a branch-and-bound algorithm to solve the optimization problem minX1,...,Xn maxw∈K C(w) such that MK(X1,...,Xn) |= Π and ℒM(MK(X1,...,Xn)) ∈ C(L). Here Π is a set of logical assertions on the structure of M K(X1,...,Xn), and MK(X 1,...,Xn) |= Π indicates that MK(X 1,...,Xn) satisfies the logical assertions; and, C(L) is the set of controllable sublanguages of L1.

UR - http://www.scopus.com/inward/record.url?scp=52449090855&partnerID=8YFLogxK

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U2 - 10.1109/ACC.2008.4586650

DO - 10.1109/ACC.2008.4586650

M3 - Conference contribution

AN - SCOPUS:52449090855

SN - 9781424420797

T3 - Proceedings of the American Control Conference

SP - 1166

EP - 1171

BT - 2008 American Control Conference, ACC

Y2 - 11 June 2008 through 13 June 2008

ER -