Eventuality synthesis for controlled linear automata

Xia, Hao; Pang, Yan; Trontis, A.; Spathopoulos, M.P.

doi:10.1109/acc.2002.1024797

Cited by 5 publications

(5 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A backward reachability computation starting from the target set F t is necessary to guarantee the optimal cost is finite. 15 The optimal cost is finite when the starting state (q 0 , x 0 ) is chosen from the reachable set. The procedure of finding an optimal trajectory j Ã minimizing equation 3can be summarized as the following steps.…”

Section: The Weighted Scheduling Problemmentioning

confidence: 99%

See 1 more Smart Citation

A hybrid modeling and optimization approach for scheduling problems of assembly automation processes

Pang

Xia

2016

Proceedings of the Institution of Mechanical Engineers, Part I:

View full text Add to dashboard Cite

Dynamics of assembly automation systems involve the interaction of discrete-event and continuous-variable dynamics. Hence, a hybrid model is a natural framework for scheduling tasks in assembly automation processes. This study indicates that a weighted scheduling problem can be transformed into a weighted time-optimal problem for hybrid systems. In particular, it shows that the problem can be cast as a constrained optimization problem with inequalities quantifiers. In order to obtain quantifier-free inequalities, quantifier elimination techniques are used. Based on the quantifier-free inequalities, the scheduling problem of the assembly manufacturing process can be solved using linear programming methods. Applicability and simulation results are provided to illustrate the performance of the developed algorithms.

show abstract

Section: The Weighted Scheduling Problemmentioning

confidence: 99%

“…The QE procedure in Xia et al was adopted, where it was proven that the quantifier-free formula f is made up of linear inequalities whose closure is convex. 15 In brief, the procedure includes getting formula f(t), which is the feasible region of the LP problem, from u(t) by eliminating quantifiers u l(p)n . .…”

Section: Quantifier Eliminationmentioning

confidence: 99%

A hybrid modeling and optimization approach for scheduling problems of assembly automation processes

Pang

Xia

2016

Proceedings of the Institution of Mechanical Engineers, Part I:

View full text Add to dashboard Cite

show abstract

“…In order to guarantee that the optimal cost is finite, a backward reachability analysis (Xia et al, 2002) is performed starting from the target set F . If the target is reachable from (q 0 ,x 0 ), then the optimal cost is finite.…”

Section: Problem Statementmentioning

confidence: 99%

“…An important subclass of hybrid systems is the so called rectangular hybrid automata (Preußĩg et al, 1998), where in each mode the continuous dynamics are given as constant differential inclusions. When linear continuous dynamics with both control and d isturbance inputs are considered the so called linear hybrid automata (Xia et al, 2002) are derived.…”

Section: Introductionmentioning

confidence: 99%

On weighted time-optimal control for linear hybrid automata using quantifier elimination

Pang¹,

Spathopoulos²

2004

IFAC Proceedings Volumes

View full text Add to dashboard Cite

This paper considers the optimal control problem for linear hybrid automata. In particular, it is shown that the problem can be transformed into a constrained optimization problem whose constraints are a set of inequalities with quantifiers. Quantifier Elimination (QE) techniques are employed in order to derive quantifier free inequalities that are linear. The optimal cost is obtained using linear programming. The optimal switching times and optimal continuous control inputs are computed and used in order to derive the optimal hybrid controller. Our results are applied to an air traffic management example. Copyright c 2004 IFAC

show abstract

“…Research on hybrid systems (HSs) has led to a variety of methods for verification of properties, such as safety or liveness (e.g., [1][2][3][4]), and controller synthesis (e.g., [5][6][7][8][9][10]). For the vast majority of these methods, a common step is to compute approximations for the set of reachable states in the continuous state space.…”

Section: Introductionmentioning

confidence: 99%

Efficient Representation and Computation of Reachable Sets for Hybrid Systems

Stursberg

Krogh

2003

Hybrid Systems: Computation and Control

116

View full text Add to dashboard Cite

Abstract. Computing reachable sets is an essential step in most analysis and synthesis techniques for hybrid systems. The representation of these sets has a deciding impact on the computational complexity and thus the applicability of these techniques. This paper presents a new approach for approximating reachable sets using oriented rectangular hulls (ORHs), the orientations of which are determined by singular value decompositions of sample covariance matrices for sets of reachable states. The orientations keep the over-approximation of the reachable sets small in most cases with a complexity of low polynomial order with respect to the dimension of the continuous state space. We show how the use of ORHs can improve the efficiency of reachable set computation significantly for hybrid systems with nonlinear continuous dynamics.

show abstract

Eventuality synthesis for controlled linear automata

Cited by 5 publications

References 10 publications

A hybrid modeling and optimization approach for scheduling problems of assembly automation processes

A hybrid modeling and optimization approach for scheduling problems of assembly automation processes

On weighted time-optimal control for linear hybrid automata using quantifier elimination

Efficient Representation and Computation of Reachable Sets for Hybrid Systems

Contact Info

Product

Resources

About