Robust set stabilization of Boolean control networks with impulsive effects

This paper addresses the robust set stabilization problem of Boolean control networks (BCNs) with impulsive effects via the semi-tensor product method. Firstly, the closed-loop system consisting of a BCN with impulsive effects and a given state feedback control is converted into an algebraic form. Secondly, based on the algebraic form, some necessary and sufficient conditions are presented for the robust set stabilization of BCNs with impulsive effects under a given state feedback control and a free-form control sequence, respectively. Thirdly, as applications, some necessary and sufficient conditions are presented for robust partial stabilization and robust output tracking of BCNs with impulsive effects, respectively. The study of two illustrative examples shows that the obtained new results are effective

Modelling & analysis of hybrid dynamic systems using a bond graph approach

Hybrid models are those containing continuous and discontinuous behaviour. In constructing dynamic systems models, it is frequently desirable to abstract rapidly changing, highly nonlinear behaviour to a discontinuity. Bond graphs lend themselves to systems modelling by being multi-disciplinary and reflecting the physics of the system. One advantage is that they can produce a mathematical model in a form that simulates quickly and efficiently. Hybrid bond graphs are a logical development which could further improve speed and efficiency. A range of hybrid bond graph forms have been proposed which are suitable for either simulation or further analysis, but not both. None have reached common usage. A Hybrid bond graph method is proposed here which is suitable for simulation as well as providing engineering insight through analysis. This new method features a distinction between structural and parametric switching. The controlled junction is used for the former, and gives rise to dynamic causality. A controlled element is developed for the latter. Dynamic causality is unconstrained so as to aid insight, and a new notation is proposed. The junction structure matrix for the hybrid bond graph features Boolean terms to reflect the controlled junctions in the graph structure. This hybrid JSM is used to generate a mixed-Boolean state equation. When storage elements are in dynamic causality, the resulting system equation is implicit. The focus of this thesis is the exploitation of the model. The implicit form enables application of matrix-rank criteria from control theory, and control properties can be seen in the structure and causal assignment. An impulsive mode may occur when storage elements are in dynamic causality, but otherwise there are no energy losses associated with commutation because this method dictates the way discontinuities are abstracted. The main contribution is therefore a Hybrid Bond Graph which reflects the physics of commutating systems and offers engineering insight through the choice of controlled elements and dynamic causality. It generates a unique, implicit, mixed-Boolean system equation, describing all modes of operation. This form is suitable for both simulation and analysis

RULES BASED MODELING OF DISCRETE EVENT SYSTEMS WITH FAULTS AND THEIR DIAGNOSIS

Failure diagnosis in large and complex systems is a critical task. In the realm of discrete event systems, Sampath et al. proposed a language based failure diagnosis approach. They introduced the diagnosability for discrete event systems and gave a method for testing the diagnosability by first constructing a diagnoser for the system. The complexity of this method of testing diagnosability is exponential in the number of states of the system and doubly exponential in the number of failure types. In this thesis, we give an algorithm for testing diagnosability that does not construct a diagnoser for the system, and its complexity is of 4th order in the number of states of the system and linear in the number of the failure types. In this dissertation we also study diagnosis of discrete event systems (DESs) modeled in the rule-based modeling formalism introduced in [12] to model failure-prone systems. The results have been represented in [43]. An attractive feature of rule-based model is it\u27s compactness (size is polynomial in number of signals). A motivation for the work presented is to develop failure diagnosis techniques that are able to exploit this compactness. In this regard, we develop symbolic techniques for testing diagnosability and computing a diagnoser. Diagnosability test is shown to be an instance of 1st order temporal logic model-checking. An on-line algorithm for diagnosersynthesis is obtained by using predicates and predicate transformers. We demonstrate our approach by applying it to modeling and diagnosis of a part of the assembly-line. When the system is found to be not diagnosable, we use sensor refinement and sensor augmentation to make the system diagnosable. In this dissertation, a controller is also extracted from the maximally permissive supervisor for the purpose of implementing the control by selecting, when possible, only one controllable event from among the ones allowed by the supervisor for the assembly line in automaton models