Abstract not found

Local Local Control input State Meas.

The hybrid systems of interest contain two distinct types of components, subsystems with continuous dynamics and subsystems with discrete dynamics that interact with each other. Such hybrid systems arise in varied contexts in manufacturing, communication networks, auto-pilot design, automotive engine

In this paper, a novel methodology for analysis of piecewise linear hybrid systems based on discrete abstractions of the continuous dynamics is presented. An important characteristic of the approach is that the available control inputs are taken into consideration in order to simplify the continuous dynamics. Control specifications such as safety and reachability specifications are formulated in terms of partitions of the state space of the system. The approach provides a convenient general framework not only for analysis, but also for controller synthesis of hybrid systems. The research contributions of this paper impact the areas of analysis, verification, and synthesis of piecewise linear hybrid systems. 1

In this paper, a novel methodology for analysis of piecewise linear hybrid systems based on discrete abstractions of the continuous dynamics is presented. An important characteristic of the approach is that the available control inputs are taken into consideration in order to simplify the continuous dynamics. Control specifications such as safety and reachability specifications are formulated in terms of partitions of the state space of the system. The approach provides a convenient general framework not only for analysis, but also for controller synthesis of hybrid systems. The research contributions of this paper impact the areas of analysis, verification, and synthesis of piecewise linear hybrid systems. 1 Introduction A great amount of research work has already been done in the hybrid systems area during the past decade; see for example [3] and the references there in. A survey of different models and methodologies can be found in [4]. The approach presented in this paper is...

Abstract. We consider networked transport systems defined on directed graphs: the dynamics on the edges correspond to solutions of transport equations with space dimension one. In addition to the graph setting, a major consideration is the introduction and propagation of discontinuities in the solutions when the system may discontinuously switch modes, naturally or as a hybrid control. This kind of switching has been extensively studied for ordinary differential equations, but not much so far for systems governed by partial differential equations. In particular, we give well-posedness results for switching as a control, both in finite horizon open loop operation and as feedback based on sensor measurements in the system.

Hybrid timed Petri nets (HTPNs) are derived to study random topology and complexity multioperational production systems where parts of one type follow the same route to produce a final product. Each production system is first decomposed into a fundamental multiproductive machine, multiassembly and multidisassembly modules, followed by derivation of their corresponding HTPN models. The overall system HTPN model is obtained via individual module synthesis, satisfying system constraints. Individual module and overall HTPN models nodes (places and transitions) are calculated. Individual module and overall system model invariants are derived mathematically. Performance and possible tradeoffs due to varying operational constraints (buffer capacity, work in process, machine utilization, backlog, etc.) are investigated through extensive simulations. Results show the applicability of the proposed methodology and

The design of an optimal control strategy for a hybrid system is a matter of growing interest in computational engineering. The solution of optimization problems in most engineering disciplines often requires efficient parallel optimization algorithms to solve these kinds of problems in reasonable time. Instead of introducing parallelism to selected components of an existing sequential algorithm, the algorithm proposed in this paper is aimed at utilizing the available computational resources efficiently throughout the course of the optimization. To assure a certain level of efficiency, the algorithm can be adapted to the available resources and the dimension of the problem to be solved. The features of this inherently parallel algorithm are described, and the parallel performance is analyzed by means of a scalability analysis. To demonstrate the use of the algorithm for the solution of optimization problems in computational engineering, two problems from groundwater engineering are solved.

Many practical optimal control problems include discrete decisions. These may be either time–independent parameters or time–dependent control functions as gears or valves that can only take discrete values at any given time. While great progress has been achieved in the solution of optimization problems involving integer variables, in particular mixed–integer linear programs, as well as in continuous optimal control problems, the combination of the two is yet an open field of research. We consider the question of lower bounds that can be obtained by a relaxation of the integer requirements. For general nonlinear mixed–integer programs such lower bounds typically suffer from a huge integer gap. We convexify (with respect to binary controls) and relax the original problem and prove that the optimal solution of this continuous control problem yields the best lower bound for the nonlinear integer problem. Building on this theoretical result we present a novel algorithm to solve mixed–integer optimal control problems, with a focus on discrete–valued control functions. Our algorithm is based on the direct multiple shooting method, an adaptive refinement of the underlying control discretization grid and tailored heuristic integer methods. Its applicability is shown by a challenging application, the energy optimal control of a subway train with discrete gears and velocity limits.