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 -