P. Caines, V. Gupta, and G. Shen. The hierarchical control of ST-finite-state machines. Systems and Control Letters, 32:185--192, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....[5] We present here a relatively direct and intelligible theory within this overall area using a state aggregation formulation. The elements that permit this state dependent analysis are the Dynamical Consistency (DC) notions developed in the context of forced event (positive imperative) control [1, 3]. The preliminary notions presented here show that state aggregation in supervisory control leads to consistent, hierarchical control. Current work includes avoidance of bad state sets, applications to transfer lines and extensions of the consistency results to the case of dynamic ....

....0 ; Qm ) where X is the state set, Sigma u the uncontrollable transition set and Sigma c the controllable transition set. ffi : X Theta Sigma Gamma X is the (partially defined) transition function. Q 0 is the start state set and Qm is the marked goal state set. Motivated by the analysis in [1], for a partition of the state space we make the following definitions in order to describe the connections between aggregated blocks. 1 Work partially supported by NSERC grant number OGP 0001329, NSERC FCAR Nortel grant number CRD 180190 and NASA Ames Research Center grant number NAG 2 1040. ....

P.E. Caines, V. Gupta, and G. Shen. The hierarchical control of ST-finite state machines. To appear Systems and Control Letters, 1998.

....complexity of solving any given DP problem. The work in this paper is based upon that in (Caines and Wei, 1995) where hierarchical control systems are formulated in terms of the construction of partition machines via the notion of dynamically consistent (DC) state aggregation, and on that in (Caines et al. 1997), where the generalisation of the previous results to source target systems was presented. The HADP methodology proceeds by first decomposing a finite state dynamical system into hierarchical layers of partition machines. It is within this framework, that the set of trajectory optimisation ....

....to ensure that the procedure yields optimal, or near optimal, solutions to the original base level trajectory optimisation problem. 2. HIERARCHICAL CONTROL AND CONTROL CONSISTENCY In this section, we give formal definitions of the notions of dynamical consistency ( Caines and Wei, 1995) (Caines et al. 1997)) and control consistency (analogous to that defined in (Wong and Wonham, 1992) and (Zhong and Wonham, 1990) A hierarchical control structure consists of a finite state machine M and its abstractions which are called high level machines. A partition of the state space X of M is a collection of ....

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Caines, P.E., V. Gupta and G. Shen (1997). The hierarchical control of ST finite state machines.

....framework for multi agent systems and to introduce tractable methods for their analysis, control and optimisation. Work partially supported by NSERC grant number OGP 0001329 and NASA Ames Research Centre grant number NAG 2 1040. Email: shg, peterc cim.mcgill.ca. CDC99 REG0663 2 In [5] [2], 9] 10] and [7] a hierarchical control theory is developed for, respectively, supervisory (automata) control systems, finite state (forced event) machines, and hybrid systems; this work employs the basic notions of state space partitions (consisting of aggregated state sets) and dynamical ....

....the original model into an aggregated model; 2) solve the aggregated problem; 3) disaggregate to obtain a solution to the original problem. The algorithms in [1] and [9] are of this general type. In this section, we give a brief review of the hierarchical control theory developed in [4] and [2] upon which the procedure and theory of [9] rests. Partition machines are used to create aggregated models for finite state machines. A partition of the state space X of M is a collection of subsets of X, namely, fX 1 ; X 2 ; X n g satisfies (1) X = S i=n i=1 X i ; 2) X i X j = ....

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P.E. Caines, V. Gupta, and G. Shen. The hierarchical control of ST finite state machines. Systems and Control Letters, 32:pp185--192, 1997.

.... control in the supervisory framework has been considered previously in [20, 19] The distinct characteristic of the present work is that the state aggregation is based upon the Dynamical Consistency (DC) This is a notion developed in the context of forced event (positive imperative) control in [10, 6], generalised to differential control systems in [9] and which, further, are related to notions in a purely graph theoretic setting (see [13] and in computer science (see [4, 14] An aggregated modular approach to controller reduction also appeared in [27] An analysis of Petri Nets based on ....

....given sample run of the system, it is assumed the start state at the low level is known. Also, at present we only consider fully state observable systems at each level. In what follows, we develop a description of the dynamics between partition blocks and therefore, motivated by the analysis in [6], we make the following definitions. Definition 2.1 I(X i ; Q 0 ) The In set I(X i ; Q 0 ) of a partition block X i is the set of states in X i that are either in the initial state set or directly accessible (i.e. one step accessible) from the complement of the block, i.e. x 2 I(X i ; Q 0 ) ....

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P.E. Caines, V. Gupta, and G. Shen. The hierarchical control of ST-finite state machines. Systems and Control Letters, 32:185--192, December 1997.

....that given in [8] for supervisory control. It is shown that, when CC holds, the dynamics of M hi are given by the dynamical consistency (DC) relation associated with a partition of the states of M = M lo (see [2] Conversely, subject to the In Block Controllability (IBC) condition (see [2] [1]) if the dynamics of M hi are given by the DC relation, then CC holds. For a hierarchy with a given low level cost function d on transition events in M , we introduce the so called Hierarchically Accelerated Dynamic Programming (HADP) procedure for DP problems posed in M : for a two level ....

.... convexity does not imply optimality consistency as shown by an example in [7] We note that if all blocks of a partition are SISO, i.e. each block of the partition machine M has only one local entry (i.e. a state in that block which is one low level step accessible from the outside, see [1]) and one local exit (i.e. a state in that block which is one low level step reachable to the outside) then the hierarchy hM; M i (assumed to be CC and IBC) is OC. 4 Bounds Ensuring Optimality Consistency From the development in the last section, it is clear that the optimality consistency ....

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P.E. Caines, V. Gupta, and G. Shen. The hierarchical control of ST finite state machines. Systems and Control Letters, 32:185--192, December, 1997.

....space of a finite machine M corresponds to the existence, for every state x in X i , of some (x dependent) control sequence which takes that state into X j without excursions into other blocks. This idea, and its consequent properties, were generalized to so called ST finite state machines in [1] and to hybrid systems in [2] In the hybrid systems case, the state space of any given continuous base control system S may be arbitrarily partitioned into a finite set of blocks; for any such S and a high level finite Work partially supported by NSERC grant number OGP 0001329, ....

P.E Caines, V. Gupta, and G. Shen. The hierarchical control of st-finite state machines. Systems and Control Letter, To appear, 1998.

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P. Caines, V. Gupta, and G. Shen. The hierarchical control of ST-finite-state machines. Systems and Control Letters, 32:185--192, 1997.

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P. Caines, V. Gupta, and G. Shen. The hierarchical control of ST-Finite State Machines. Systems & Control Letters, 1997.

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