ABSTRACT
Basic dynamical features of hybrid systems are reviewed in this paper. Some results on existence and uniqueness of executions for hybrid automata are obtained. Continuous dependence on initial states are shown for a class of hybrid automata. Zeno hybrid automata, i.e., hybrid automata that exhibit infinitely many discrete transitions in finite time, are also discussed.
ABSTRACT
We consider a multi-stage manufacturing process where each job has a physical state characterized by time-driven dynamics and a temporal state by event-driven dynamics, thus giving rise to a hybrid system model. A common problem is to derive an optimal control strategy to trade othe conflicting objectives of minimizing job completion times (satisfaction of customer demand) against the quality of the completed jobs. Extending our past work, in this paper we derive necessary conditions for optimality for a multi-stage system where the control inputs are bounded. The issue of nondifferentiability due to the nature of the event-driven state dynamics creates serious analytical diculties which we can no longer eectively resolve using nonsmooth optimization methods. Instead, we establish some properties of the optimal control sequence that have interesting implications in terms of designing control policies for this class of hybrid systems.
Key Words. Hybrid Systems, Optimal Control
ABSTRACT
The design of engine control systems has been traditionally carried out using heuristic techniques validated by simulation and prototyping using approximate average-value models. Increasing demands on controllers performance call for more robust techniques and the use of cycle{accurate models. In this paper we present a hybrid model of the engine and powertrain in which both continuous and discrete time{domain as well as event-based phenomena are modeled in a separate but integrated manner.
ABSTRACT
In this paper paper we discuss a two-person zero- sum differential game of finite horizon with graph- constrained control strategies. Both players are constrained to use piecewise constant controls, where the control switches are selected from a finite control graph. The control graph is a directed graph where the vertices define pairs of control values for both players, and the edges define the allowable control switches. Each edge represents a positive switching cost. The payoff function includes the sum of the switching costs associated with each player. We prove the existence of value and state optimality conditions in terms of value functions that solve a coupled system of quasi-variational inequalities. Optimal strategies are then derived in terms of these value functions.
Keywords: Hybrid systems, graph games, dier- ential games, switching strategies, non-smooth anal- ysis and control.
ABSTRACT
In this work we propose an approach to the problem of failure diagnosis for Hybrid Systems (HS). This approach is applicable to a wide rage of systems since hybrid systems involve both continuous and discrete dynamics. The states of the HS model reflect the normal and the failed status of the system components. The faults in our setting are modeled as either discrete or continuous (detrimental) state changes.
Key Words. Fault diagnosis, failure detection, hybrid systems.