A Logic-Based Approach to Model Supervisory Control Systems Pierangelo Dell’Acqua Anna Lombardi Dept. of Science and Technology - ITN Linköping University, Sweden Luís Moniz Pereira Centro de Inteligência Artificial - CENTRIA Universidade Nova de Lisboa, Portugal ISMIS’06 - Bari, Italy September, 2005 September, 2006

Controller: discrete-time system Interface ( in dashed red) Plant: time-continuous system to be controlled Hybrid control systems Generator Actuator Plant Controller x(t) x(t k )r(t k ) r(t) Closed-loop configuration

Supervisory control systems hybrid control system system (Controller+Plant) consists of a family of subsystems that can be activated supervisor selects which candidate controller to activate activated controller will steer the Plant abstraction obtained by separating logics from control Plant Supervisor Control module

Behaviour networks Introduced by P. Maes in ’89 for action selection in dynamic and complex environments, where the system has limited computational and time resources. A behaviour network is a network composed of specific competence modules (rules) which activate and inhibit one another along the links of the network: The activation/inhibition dynamics of the network is guided by global parameters. Competence modules cooperate so that the network as a whole functions properly. This architecture is distributed, modular, robust and has an emergent global functionality.

Extended behaviour networks To model hybrid control systems, we extended behaviour networks to allow for: rules containing variables internal actions integrity constraints modules (sets of atoms and rules)

An extended behaviour network consists of 5 modules: R - set of rules formalizing the behaviour of the network P - set of global parameters H - internal memory C - set of integrity constraints G - set of goals The tuple S = (R, P, H, C, G) defines the state of the network. We employ E to indicate the input coming from the Plant.

Logic-based supervisor Plant Supervisor eBNs Control module Logic-based supervisor modelled via eBNs Declarative control E

Atom takes the form: m:X meaning that X belongs to module M whose name is m m÷X meaning that X does not belong to M Sequence of atoms: Atom 1, Atom 2,..., Atom n (n  0) # denotes the empty sequence Goal is a sequence of atoms It expresses a condition to be achieved Integrity constraint is a sequence of atoms It expresses a condition that must not hold Language (simplified)

Rule is a tuple of the form: prec - preconditions del, add - represent the internal effect of the rule action - atom representing the external effect of the rule  - level of strength of the rule Variables in rules are universally quantified:

At every state S, a rule in R must be selected for execution  find all the rules that are executable and select one A framework of rule selection for behaviour network is presented in: P. Dell'Acqua, A. Lombardi, and L. M. Pereira Modelling Hybrid Control Systems with Behaviour Networks 2 nd Int. Conf. on Informatics in Control, Automation and Robotics (ICINCO’05)

Consider a virtual marine world inhabited by a variety of fish: Fish are situated in the environment, and sense and act over it. The behaviour of a fish consists of searching and eating food, escaping, etc. Actions of the fish: search, eat, escape, etc. Example: modelling an artificial fish

Artificial fish: Supervisor Describes the behaviour of the fish. Receives information from the plant (state of the fish) at every time instant. Selects an action satisfying the constraints in C and activates the corresponding controller: C = { e:fear(x), x>0.5, h:search(food)} G = { h:safe, h:satiated } R contains: 0.5, h:flocking | h:safe, h:flocking | h:fleeing | flee(x  2) | x  3 >

Artificial fish: Control Module Contains all the controllers. Each controller implements an action of the fish, like

Artificial fish: Plant Contains several state variables representing the stimuli of the fish, like hunger(t) = min {  t  , 1} fear(t) = min { D 0 / d(t), 1 } At any time instant the plant receives the new velocity of the fish from the activated controller and calculates the new position of the fish

Conclusions - 1 Separating logic from control makes the overall architecture modular, and therefore easily changeable and extensible. Exploiting eBNs for modelling supervisory control leads to a distributed system architecture that has an global emergent functionality. eBNs having a formal semantics allows one to formally prove properties of the system. - model checking

AI techniques can be integrated at the supervisory level: - learning - update and preference reasoning - prospective programming (i.e. anticipatory control by look-ahead) BNs permit a more reactive or a more deliberative form of control, depending on the relative strength combination of bottom-up and top- down energy propagation: - meta-rules for updating the control rules become possible Conclusions - 2