Wolf Kohn

Hybrid Systems II

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Hybrid Systems V

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Repair-control of enterprise systems using RFID sensory data

Abstract This paper presents an architecture for implementing real-time enterprise planning, scheduling and control processes based on information provided by radio frequency identification (RFID) sensing systems. It introduces a new paradigm, called repair, for modeling enterprise processes that is based on the idea of incremental performance improvements and disruption minimization. The proposed model is expressed using differential equations with discontinuous right-hand sides. The repair framework is suitable for implementing enterprise feedback control systems that can easily be interfaced with an existing enterprise resource planning infrastructure. RFID sensing systems have the potential to provide the real-time data needed to implement enterprise feedback functionality.

Hybrid Systems as Finsler Manifolds: Finite State Control as Approximation to Connections

Hybrid systems are networks of interacting digital devices and continuous plants reacting to a changing environment. Our multiple agent hybrid control architecture ([KN93b], [KN93c]) is based on the notion of hybrid system state. The latter incorporates evolution models using differential or difference equations, logic constraints, and geometric constraints. The set of hybrid states of a hybrid system can be construed in a variety of ways as a differentiable (or a C∞) manifold which we have called the carrier manifold ([KNRG95]). We have suggested that for control problems the coordinates of points of the carrier manifolds should be selected to incorporate all information about system state, control state, and environment needed to choose new values of control parameters.

The interacting-particle algorithm with dynamic heating and cooling

We consider an interacting-particle algorithm which is population-based like genetic algorithms and also has a temperature parameter analogous to simulated annealing. The temperature parameter of the interacting-particle algorithm has to cool down to zero in order to achieve convergence towards global optima. The way this temperature parameter is tuned affects the performance of the search process and we implement a meta-control methodology that adapts the temperature to the observed state of the samplings. The main idea is to solve an optimal control problem where the heating/cooling rate of the temperature parameter is the control variable. The criterion of the optimal control problem consists of user defined performance measures for the probability density function of the particles’ locations including expected objective function value of the particles and the spread of the particles’ locations. Our numerical results indicate that with this control methodology the temperature fluctuates (both heating and cooling) during the progress of the algorithm to meet our performance measures. In addition our numerical comparison of the meta-control methodology with classical cooling schedules demonstrate the benefits in employing the meta-control methodology.

Hybrid systems: chattering approximation to relaxed controls

We explain a main connection between relaxed control and hybrid systems. We summarize the non-multiple agent aspects of our research. We describe new algorithms for approximating relaxed optimal controls based on a generalized form of linear programming using convex analysis. Finally we use chattering to derive an analogue of the Hamilton-Jacobi-Bellman equation and dynamic programming in our hybrid systems model.

Enterprise Dynamics Via Non-Equilibrium Membrane Models

This paper describes a distributed dynamic model of enterprise systems via a network of elements which are abstractions of biological membranes. Membrane characteristics such as active sites controlling the flow of substances correspond to local feedback laws in the elements of the supply chain of the enterprise. Flow conservation and chemical reactions of substances across the membrane are abstracted to represent component flow interaction in the supply chain. The model characteristics are illustrated with a simulation example. This model methodology is completely encodable. It provides a blueprint for highly automated model generation of enterprise systems, and for on-line generation of continuous repair implementations of planning, scheduling and execution applications. The proposed embedded distributed control system allows for the realization of diverse optimization strategies because a given criterion is approximated by a generic criterion via the penalty method. The control system also satisfies network element constraints and inter-element synchronization requirements.

Optimization of Algorithmic Parameters using a Meta-Control Approach*

Optimization algorithms usually rely on the setting of parameters, such as barrier coefficients. We have developed a generic meta-control procedure to optimize the behavior of given iterative optimization algorithms. In this procedure, an optimal continuous control problem is defined to compute the parameters of an iterative algorithm as control variables to achieve a desired behavior of the algorithm (e.g., convergence time, memory resources, and quality of solution). The procedure is illustrated with an interior point algorithm to control barrier coefficients for constrained nonlinear optimization. Three numerical examples are included to demonstrate the enhanced performance of this method.

Rule-based control system design for smart grids

The growth of distributed generation or renewable generation resources and advanced information systems add uncertainties and complexity to the energy system and call for a “smart grid” solution. The mathematical models that are conventionally utilized in the energy management system usually take a long time to develop and execute and are not flexible enough to accommodate operational rules for generations (wind, solar and hydro) under varying conditions and loads. A rule-based system model would allow power system operators (who may lack experience in exploiting mathematical models and computer capabilities) to model their operations directly using their expertise, which enables the power system to make quick responses to real-time conditions. In this paper, a new rule-based system design methodology for power system automation and control is proposed. The methodology formulates the rule-based system as an optimal control problem in a feedback control architecture. The solution to the optimal control problem provides action rules for power system substation operations to achieve operator-configured preferences while minimizing cost. The proposed methodology, which integrates real-time information, optimal control, environmental constraints and humans expertise, provides a systematic tool for rule-based system design that gives more robust and realistic solutions.

Rule-based forecasting and production control system design utilizing a feedback control architecture

Forecasting and production control systems typically rely on operational rules that have been accumulated and refined from enterprise experts. Designing a rule-based system is a challenging task. In this article, a new rule-based system design methodology for forecasting and production control is proposed. The methodology first represents the rule-based system as a finite state automaton (a Moore machine) and then formulates an optimal control problem in a feedback control architecture. The solution to the optimal control problem provides action rules for forecasting and production that minimize cost over a given time horizon. The proposed methodology provides a systematic tool for rule-based system design that gives robust and realistic solutions.