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The control of manufacturing systems consisting of a certain number of parallel machines processing a given number of jobs is addressed in this work. A decentralized scheme is defined in which at a local level, the optimal control of each single machine is considered, whereas, at a higher level, the optimal splitting of jobs on parallel machines is taken into account. At the local level, an optimization problem with quadratic cost function and nonlinear constraints is stated as a multistage control problem and solved by means of dynamic programming techniques.

Signalized urban areas are considered in order to improve the performances of traffic systems by means of real-time actions having the purpose of varying the length of traffic lights phases with respect to predefined durations. In this connection, a macroscopic traffic model and an optimization problem are presented in this paper. The proposed model allows the representation of all possible traffic conditions (congested as well as non-congested). The optimization problem is stated with the objective of minimizing the number of vehicles in the overall system, over the whole optimization horizon, by suitably choosing the duration of the phases in each semaphoric cycle.

The problem of optimally defining and controlling the behaviour of a single machine processing a certain number of jobs and modelled as a discrete event dynamic system is addressed. The number of jobs, their sizes, and their service sequence are fixed, whereas their timing is the matter of the optimisation problem. The objective function to be optimised is a weighted sum of the inventory cost of the quadratic deviations from the due-dates of jobs and their completion times, and the quadratic deviations between the unitary processing times of jobs and those specified by the regular system functioning. An optimisation problem with quadratic cost function and nonlinear constraints is stated and formalised as a multi-stage optimal control problem. The control problem is solved by a procedure making use of dynamic programming techniques; the optimal closed-loop control laws at each stage are thus obtained.

This paper formalizes a unique decisional framework to state different problems relevant to automated manufacturing systems, such as production planning, material requirements planning, and online management. Since the manufacturing systems are modelled as discrete-event systems, the (timed) Petri net formalism can be adopted to represent their dynamics. Moreover, in order to make the decisional problems addressed computationally tractable, it is assumed that the manufacturing systems can be represented by means of a particular class of timed Petri nets-the timed event graphs. Two particular optimization problems are discussed in the paper: the first one is relevant to the minimization of production and inventory costs, while satisfying a pre-specified production demand; and the second one refers to an online management problem in which the deviations between the actual system behaviour and a pre-defined nominal behaviour are sought to be minimized.

The optimal control of a production facility consisting of a single machine processing a certain number of jobs with a fixed service sequence is considered. The objective of the problem is that of determining the optimal timing and lot-sizing of the considered jobs. Necessary conditions for optimality are derived which allow the determination of an optimal solution for the control problem.

Timed Event Graphs can be applied successfully to the modelling, the analysis and the optimization of manufacturing systems. The choice of using such a particular class of Petri Nets allows to apply a set of related algebraic results to determine some performance measures as functions of a set of decision parameters. On this basis, performance optimization problems can be posed and solved as mathematical programming problems. In this paper, the problem consisting in the maximization of the weighted system throughput, while keeping the steady-state flow time of each product limited by an a-priori upper bound, is considered. This problem turns out to be a linear fractional programming one, which can be solved by means of standard techniques and software tools.

The hydrometeorological and conceptual bases and guidelines for the implementation of a Decision Support System (DSS) able to provide policy makers and local civil protection authorities with suitable procedures in order to issue flash flood warnings in the southern European regions are presented in this paper. The research was undertaken within the EU Environment project STORM'93, aiming at the optimum use of multisensor monitoring tools in supporting flood forecasting applications. The proposed DSS is designed to improve cross‐fertilizing interactions and proper interpretation of data coming from different monitoring tools, addressing in particular radar and satellite derived rainfall estimates together with the traditional use of rain‐gauge networks and weather map forecasts. The structure of the system is oriented to a suitable non‐traditional approach, based on distributed warnings, to the assessment of flood hazard at the regional scale.

This chapter presents a general theory that is viewed as a basis for the proper use of ARX implicit models in adaptive control schemes. Necessary and sufficient conditions for the existence of such models have been given. The possible use of such models has been discussed to design adaptive algorithms based on finite and infinite horizon quadratic criteria. A particular way of exploiting the information provided by an implicit model has been considered. The main feature of this approach is that of obtaining, at every iteration of the algorithm, the new regulator not on the basis of the identified prediction model only, but also making use of the equation of the previously acting regulator. This is accomplished by solving a variational control problem and allows developing adaptive control algorithms based on either finite or infinite horizon quadratic optimization. Some theoretical results have been reported showing that the developed algorithm admits the optimal control law as an equilibrium point, and that a proper structuring of such algorithm assures that it admits a unique whitening equilibrium point coinciding with the optimal regulator. Furthermore, a technical way to test whether a generic convergence point coincides with this unique whitening equilibrium point has been indicated. Based on such a result, a modification to the basic algorithm has been described that ensures the enjoyment of the self-tuning property. Some simulation results show the effectiveness of the proposed approach.

The problem of building train schedules for an underground railway line to improve the quality of the service offered to passengers, taking into account safety constraints, is considered. To this end, a mathematical optimization problem is defined and solved. However, the proposed solution methodology, as others provided in the literature, is not suitable in the case of nonsmooth passenger arrival rates. Then, a new heuristic capable of generating train schedules even in such a situation is developed, and some experimental results are shown.

An approach for the automatic generation of Petri net models for a particular class of manufacturing systems is described. Our tool, starting from a system description in terms of precedence-relation graphs, is able to build Petri net models which can be subject of subsequent analysis and simulation. The paper particularly focuses on the definition of the manufacturing system model and on the procedures for the automatic generation of the Petri net. >

The event of November 23–25th, 1987 on the Arno basin was observed by ground raingauges and a hydrometric reporting network, the Meteosat geosyncronous satellite, and the Special Sensor Microwave/Imager (SSM/I) aboard a polar orbiting satellite. In the present paper the three data sets derived from the different information sources are used as an input to a coherence assessment analysis; information provided by raingauges, geosyncronous and polar satellites are indeed intrinsecally different as far as space and time scales and reliability are concerned. The proposed approach has two main purposes: i) to integrate effectively different data sources to obtain a rain rate estimate which minimises the overall deviation from the set of available measurements; ii) to assess the relative reliability of a source with respect to the others. Hydrographs in Florence at Uffizi, simulated by a distributed model using the Meteosat information and raingauge data, have been compared to the observed one in order to assess the use of multisensor observations to predict rainfall ground effects during the considered extreme meteorological event.

In the paper, a discrete event system has been considered, consisting of a set of tasks, organized in precedence-relation graphs, to be executed by a set of machines, in the fulfilment of a certain set of constraints. It has been shown that, using minimax algebra formalism, one is able to: i) express the task completion times as analytic functions of the binary decision variables relevant to the alternative choices and of the continuous variables representing the task activation delays with respect to the earliest activation times; ii) represent analytically all the constraints affecting the decision variables and resulting from the structure of the model considered. Thus, we are able to determine the structure, which means, the cost functional plus the constraints imposed, of a mathematical programming problem having the objective of optimizing a cost functional related to task completion times. The resulting optimization problems are of the mixed-integer type. To write the optimization problem, i.e., the cost functional and the relevant constraints, in terms of the decision variables it is not necessary to list explicitly all the possible perturbed semi-schedules.

The authors present the basic concepts of a new approach for the analysis and the optimization of a certain class of discrete event systems modeling manufacturing processes. Performance analysis of discrete event dynamic systems is performed with respect to a set of possible assignment/sequencing or delay perturbations. A model of a discrete event system is considered where some decisions are fixed and others are to be taken regarding the assignment of the tasks to the machines and the sequencing of such tasks on the machines. The approach described is based on the analytic tools peculiar to minimax algebra, which provide an effective way to write the performance indexes, and the relevant constraints of the analysis/optimization problems considered. >

In this paper, a new class of adaptive schemes, called “direct variational adaptive control schemes”, is presented, which introduces an alternative way to make use of the information provided by the identification of the prediction model, with respect to “conventional” self-tuning control schemes. Adaptive control algorithms, related to quadratic optimization criteria, are derived which admit a unique “whitening” equilibrium point, corresponding to the optimal control law. Finally, a theoretical analysis of the stability properties of this equilibrium point, for a particular quadratic optimization criterion, is provided.

A communication network with stochastic input flows is considered. The nodes which route the traffic are required: i) to react instantaneously to the variations of their incoming flows so as to minimize an aggregate cost function, ii) to compute or adapt their routing strategies on line on the basis of the measured values of the incoming flows and of some local information (e.g., the characteristics, possibly time-varying, of the links connecting each node with the upstream and the downstream neighbours). Due to the first requirement, the routing nodes must be considered as the cooperating members of a team organization. The second requirement calls for a computationally distributed algorithm. This fact and the intractability, under general conditions, of team functional optimization problems lead us to structure the routing nodes as multi-layer feed-forward neural networks, for which the stochastic input flows play the role of training patterns. The weights of the routing neural networks are then adjusted by means of an efficient algorithm based on back-propagation and stochastic approximation.

In the emergency management related to either natural or anthropogenic disasters, transport and communication infrastructures play a key role for a good realisation of the emergency plans. Communication in this phase is essential both from a bottom-up (information related to the actual state of a catastrophic event), and from a top-down point of view (information related to the policy of the decision makers relevant to resources management). On the other hand, the importance of transport infrastructures is fundamental, as it is an essential instrument for emergency resource intervention, as well as for population evacuation. Thus, an effort should be made in order to define instruments capable of aiding decision makers in using infrastructures during emergency management. In this paper, a Decision Support System (DSS) for resource intervention in real-time emergency management is proposed. The general methodological framework and the mathematical formulation of one of the problems solved by the DSS are described.

A team control problem is considered whose information structure is partially nested and is characterized by the existence of a common past information set shared by the team members after a finite delay. Under LQG assumptions, it is shown that the optimal control strategy can take on a time-invariant recursive form based on suitable sufficient statistics.

The concept of extended implicit model is introduced and thoroughly used in the paper. The term extended implicit model is used to designate a model of a system acting in closed-loop, which is structurally different from the true model of the system, but yet capable of correctly predicting the output. In particular, interest is focused on extended implicit models which can be identified via the use of simple Least Squares techniques. The possible presence of an external dither signal is taken into account. The main part of the paper deals with the possibility of using extended implicit models in adaptive control algorithms based on finite or infinite-horizon quadratic cost functionals.

Decentralized dynamic routing in networks is considered in the paper. Finite buffers at nodes, stochastic inputs, discrete control and state variables characterize the problem. An information structure of the decision makers is introduced which allows to solve the problem via a static team optimization. Then, on the basis of the existence of a common past information set, the structure of the optimal control strategy is studied and the possibility of using a receding-horizon control scheme is discussed. Finally, stationary infinite-horizon optimal decentralized solutions are sought. A possible procedure to find such solutions is discussed, which is simply based on standard Markov chains properties.

An approach to the solution of the dynamic routing problem in a queueing network is presented in the paper, based on Lagrangian duality and decomposition techniques. A numerical solution can be obtained by a multilevel off-line computational procedure. The considered network has deterministic inputs and initial state, and the optimization problem is in discrete time. Link capacity and queue length constraints are taken into account.

The routing problem in computer communication networks which is considered in the paper is characterized by the following features: i) routing decisions are taken only at the input nodes to the network; ii) the input nodes act as decentralized decision makers, without any information exchange; iii) the objective of the routing problem is that of minimizing over the entire network an aggregate cost made up with single link costs which are quadratic in the link flow. The single node strategy is a function of the node information, which is simply the level of the incoming flow. Since no information exchange is supposed to take place in the network among the decision nodes, the considered routing problem induces a static team decision problem. In the paper it is shown how the strategies of the decision makers are actually coupled only through a finite set of parameters, due to the particular structure of the problem considered. These parameters correspond to the average flows assigned to the various paths and they can be found by solving a set of equations which take into account the solution of each decision maker's personal problem and the a-priori distribution of the incoming flows.

The theory of implicit models. developed in previous papers. is here used in order to define a class of adaptive algorithms based on m-step ahead.or infinite horizon. quadratic optimization. and on Recursive Least Squares identification. even in presence of systems having an ARMAX structure. This can be possible due to the fact that not the true system model but an implicit model is actually sought by the identification procedure. the latter being a model of the system which is correct only in certain closed-loop conditions. In the paper. it is shown that. via the identification of a single extended implicit model (which takes into account the presence of an external dither noise in the control law). and basing on almost no a-priori knowledge about the true system. it is possible to structure the adaptive algorithms in such a way that a single equilibrium point is allowed. coinciding with the optimum control situation

Two problems related with the dynamic control of the information flow within packet switched data communication networks, namely routing and multiple access, are considered. While addressing different aspects of network control, the two topics exhibit some common features which allow embedding them within the framework of a team theoretical approach to decentralized control. In both cases, finding the optimal solution would involve heavy analytical and computational difficulties. However, the peculiarities of the problems considered allow the development of suboptimal approaches for the multiple access case, and the definition of a possible operating procedure to obtain optimal routing decision.

The solution of a particular synthesis problem is dealt with in this paper. With reference to a multiclass closed queueing network with deterministic service times, we consider the problem of determining the populations in the network in order to achieve a fixed set of production rates. The general expression of the required workpiece populations is found by making use of the relationships characterizing the equilibrium point of an approximate performance analysis method called QNA (Queueing Network Analyzer).

A software package for adaptive control of multivariable plants is presented in the paper. The adaptive control algorithms are of the certainty equivalence class and include, among others, efficient adaptive schemes whose control strategy is the infinite horizon LQG one. The package is presented as a tool for the design of control algorithms for unknown or complex plants. The algorithms which the program is based upon are summarized and the various features of the package are outlined. Simulation examples are provided to show the effectiveness of the techniques that are proposed and the use of the programs.

The implementation of various control algorithms by means of microcomputers is discussed. Considering a two-level computer structure, it is pointed out that microprocessor-based devices can not only realize simple control algorithms, but, in certain cases, also perform some more complex tasks, like parameter estimation and controller synthesis. The problems of computing times and numerical accuracy are both considered. Simulation results are provided concerning the implementation of an adaptive control scheme by means of a microcomputer.

The problem of dynamic routing in data communication networks is considered. A model is introduced which takes into proper account the decentralization of the information about the network status. The problem is thus considered in a team-theory framework and the structure of the optimal strategies is derived.

A software package for adaptive control of multivariable plants is presented in the paper. The adaptive control algorithms are of the certainty equivalence class and include, among others, efficient adaptive schemes whose control strategy is the infinite horizon LQG one. The package is presented as a tool for the design of control algorithms for unknown or complex plants. The algorithms which the program is based upon are summarized and the various features of the package are outlined. Simulation examples are provided to show the effectiveness of the techniques that are proposed and the use of the programs.

In the field of decentralized stochastic (team) control, the search for stationary strategies over an infinite time horizon has always represented a challenging and still unsolved problem. For this reason, one is led to consider the application of a receding horizon control scheme. In this case, one must solve at each time instant an optimization problem with constant structure, conditioned to what has taken place in the past. More specifically, the information structure of the team which will be considered in the paper is characterized by two important properties: i) partial nestedness; ii) existence of a common past information set. With these hypotheses, and with reference to a LQG setting of the problem, it has been proven that the receding horizon control scheme yields a linear strategy of constant structure, but with time-varying parameters. This fact is due to the dependence of the solution of the optimization problem from a set of past strategies. The purpose of the paper is to determine necessary conditions for the existence of a decentralized optimal receding horizon stationary strategy.

Decentralized dynamic (closed-loop) optimal control strategies are sought for a class of finite state Markov decision processes, characterized by the sharing of a common past after k steps of delay. The control is considered over a finite time horizon, and it is shown that a nonclassical dynamic programming procedure can be applied, based on the existence of a sufficient statistic of constant dimension. Finally, the infinite horizon case is briefly discussed, in view of an extention of existing results on the minimization of average expected cost for the centralized and decentralized control of Markov chains.

Two classes of algorithms for microprocessor-based controllers are investigated: Algorithms based on discrete-time transfer functions and algorithms derived from state space methods. Block-floating-point arithmetic is proposed, and two basic characteristics are examined: Minimum time to generate control actions and round-off errors. Analyses are carried out for 8 and 16-bit microprocessor configurations.

Basic aggregation schemes are introduced for multiperson multi-criterion decision processes. The possibility of introducing an intermediate step in such processes is also considered, which has the scope of fixing the structure of the final decision phase. In this connection, some possible models are discussed.

Decentralized dynamic routing in communication networks is dealt with in the paper. A procedure to find the optimal solution over a finite control horizon is given and then the structure of the optimal control law is investigated. Finally, a receding horizon control scheme is proposed whose application is made possible by the existence of a sufficient statistic.

The routing of customers in a network of queues (e.g., packets in a communication network) is considered as a decentralized (team) control problem. By a suitable information exchange among the network nodes, a partially nested information structure with a common past is obtained, which allows the existence of a sufficient statistic and the exploitation of a non-classical dynamic programming decomposition. Based on these, an infinite horizon optimization problem can be defined, and some existing results in the centralized control of Markov chains can be extended in order to seek stationary decentralized strategies. Some implications arising in this respect, due to the peculiar nature of the sufficient statistic, are discussed.

A new heuristic algorithm called QNA (Queueing Network Analyzer), has been proposed by the authors for the evaluation of the average performance measures in a queueing network, This algorithm iteratively computes mean queue lengths, throughputs and machine utilizations by means of heuristically derived formulas. The same approach is extended to the computation of the partial derivatives of the same quantities with respect to the parameters of the routing policies. This can be accomplished by considering aside to the basic algorithm an additional set of equations which give, at convergence, the desired sensitivity coefficients.

The problem dealt with in the paper refers to the decomposition of a geographical region into an unspecified number of non-overlapping regional partitions. Each partition is given by a connected aggregation of indivisible elementary areas and must contain at least one source of a certain social service characterized by assigned capacity and location. Each area is characterized by a service demand and by a measure quantifying its dimension. Two heuristic methods are proposed to obtain a preliminary aggregation of the elementary areas, in order to reduce the computational effort involved in generating the feasible partitions. A fuzzy sets approach is presented for rating and ranking the regional partitions. This approach seems to be particularly suited to planning problems, when some kind of compromise between qualitative and quantitative issues must be sought. A health-care districting problem is then discussed as a case study.

A decision support system for forest biomass exploitation for energy supply is presented. The system allows supporting decisions on a finite time horizon, concerning the localization, sizing, and setting of a number of biomass-to-energy conversion plants in a small-medium region. The system is based on the formalization of an optimal decision problem stated with reference to a dynamic biomass model. In the proposed approach, geographic information system based techniques are integrated with mathematical programming methods yielding a comprehensive system which allows formalizing the problem, taking decisions, and evaluating their effects. The application to a real case study is considered.

A shortened list of the basic results about implicit modelling theory and its application for adaptive control is provided. This theory deals with the possibility of representing systems driven by proper feedback laws by means of models which are structurally different from the true model, and simpler to be identified. The relevance of this subject derives from the possibility of devising adaptive control algorithms based on the identification of relatively simple models, which admit the optimum control situation as an equilibrium point.

A class of manufacturing systems that can be modelled by use of timed event graphs is considered in this paper. The interest for considering such a subclass of timed Petri nets is due to the possibility of applying a set of mathematical results, mainly based on the use of max-plus algebra, for performance analysis. Basing on these results, some significant performance indexes can be computed as functions of a certain set of decision parameters. Then, the system throughput optimization problem can be stated as a linear fractional programming problem. >

The class of Petri nets denoted as timed event graphs can be used to represent a wide class of manufacturing systems. This fact allows one to apply analytical techniques for performance evaluation of such Petri nets. This, in turn, permits to state mathematical programming problems whose objective is the optimization of manufacturing system performances. In this paper, the optimization of the system throughput is considered, with respect to the definition of the lot sizes in a cyclic manufacturing process. As a secondary optimization objective, the minimization of the work-in-progress, while keeping the system working at its maximum productivity, is considered. >

In this paper, the proposed Hybrid Inventory-Production model represents a manufacturing center with two inventories (the input one for raw parts and the output one for processed parts) and a production resource which moves parts from the input to the output inventory, at a certain rate. In the considered modelling framework, time-driven and event-driven dynamics coexist, yielding to a hybrid system. An optimization problem is defined where decisions concern the production process (piece-wise constant function changing its value at asynchronous time instants) and the arrival process. Then, an optimal control problem is stated in order to find the closed-loop solutions as functions of the system state. In particular, a multi-stage optimal control problem is defined and it is solved by applying dynamic programming techniques.

An optimization problem concerning deterministic queuing networks is considered. The optimization problem examined is relevant to the routing policy of incoming customers which have to flow through the network. The cost functional is the customer mean flow time. The authors survey all the results previously obtained for the simplest case, and propose further results concerning more complex queuing networks. >

We provide a formal approach to obtain a discrete event system (DES) representation of a flexible manufacturing system (FMS). The complexity of real FMSs typically yields formidable problems in modeling such systems and in their representation by means of any predefined formalism, for instance Petri nets (PNs). A technique which allows one to obtain the PN from a description of a system is called a synthesis procedure. A synthesis procedure is presented which is based on a modular conception: a generic FMS can be easily divided, from a physical point of view, into a set of connected resources totally independent one from the other. Once such resources have been identified, we represent them by means of a set of independent subnets, the Petri net modules (PNMs), and then we can apply the synthesis procedure. For this reason, the proposed procedure has been called modular structural synthesis.