Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and bio-sequence analysis, and KFMs have been used for problems ranging from tracking planes and missiles to predicting the economy. However, HMMs and KFMs are limited in their “expressive power”. Dynamic Bayesian Networks (DBNs) generalize HMMs by allowing the state space to be represented in factored form, instead of as a single discrete random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linear-Gaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from sequential data. In particular, the main novel technical contributions of this thesis are as follows: a way of representing Hierarchical HMMs as DBNs, which enables inference to be done in O(T) time instead of O(T 3), where T is the length of the sequence; an exact smoothing algorithm that takes O(log T) space instead of O(T); a simple way of using the junction tree algorithm for online inference in DBNs; new complexity bounds on exact online inference in DBNs; a new deterministic approximate inference algorithm called factored frontier; an analysis of the relationship between the BK algorithm and loopy belief propagation; a way of applying Rao-Blackwellised particle filtering to DBNs in general, and the SLAM (simultaneous localization and mapping) problem in particular; a way of extending the structural EM algorithm to DBNs; and a variety of different applications of DBNs. However, perhaps the main value of the thesis is its catholic presentation of the field of sequential data modelling.

The problem of systematically synthesizing hybrid controllers which satisfy multiple control objectives is considered. We present a technique, based on the principles of optimal control, for determining the class of least restrictive controllers that satisfies the most important objective (which we refer to as safety). The system performance with respect to lower priority objectives (which we refer to as efficiency) can then be optimized within this class. We motivate our approach by showing how the proposed synthesis technique simplifies to well known results from supervisory control and pursuit evasion games when restricted to purely discrete and purely continuous systems respectively. We then illustrate the application of this technique to two examples, one hybrid (the steam boiler benchmark problem), and one primarily continuous (a flight vehicle management system with discrete flight modes). 1 Introduction Hybrid systems, or systems that involve the interaction of discrete and co...

This paper offers a synthetic overview of, and original contributions to, the use of logics and formal methods in the analysis of hybrid systems

Proof rules for program verification rely on auxiliary assertions. We propose a (sound and relatively complete) proof rule whose auxiliary assertions are transition invariants. A transition invariant of a program is a binary relation over program states that contains the transitive closure of the transition relation of the program. A relation is disjunctively well-founded if it is a finite union of well-founded relations. We characterize the validity of termination or another liveness property by the existence of a disjunctively well-founded transition invariant. The main contribution of

In this work we suggest a novel methodology for synthesizing switching controllers for continuous and hybrid systems whose dynamics are defined by linear differential equations. We formulate the synthesis problem as finding the conditions upon which a controller should switch the behavior of the system from one "mode" to another in order to avoid a set of bad states, and propose an abstract algorithm which solves the problem by an iterative computation of reachable states. We have implemented a concrete version of the algorithm, which uses a new approximation scheme for reachability analysis of linear systems.

Abstract not found

Intelligent agents have an agenda that is monitored continuously to decide what action is to be performed. Formally, an agenda is a set of deontic temporal constraints. Deontic, since the agenda specifies what the agent should do. Temporal, since the obligation is usually to be performed before a certain deadline, or as soon as possible. In this paper, we investigate the concepts necessary to describe deadlines. We describe a temporal deontic logic that facilitates reasoning about obligations and deadlines. The logic is a combination of temporal logic and deontic dynamic logic. We describe extensively which choices have to be made in combining temporal and dynamic aspects into one system. In the new logic, we can uniformally specify that an obligation starts at a certain time or event, that it must be done immediately, as soon as possible, before a deadline, or periodically. 1 Introduction It is not very difficult to develop a program that checks whether deadlines are met. The main id...

Abstract. Verification and compliance testing are required if agents are to be delegated responsibility for legally binding contracts, for example in electronic markets. This paper describes a general agent communication framework which allows several different notions of verification and compliance testing to be described. In particular we consider what type of verification or testing may be possible depending on the information which may be available (agent internals, observable behaviour, normative specifications) and the semantic definition of the communication language. We use this framework to identify the types of languages which will permit verification and testing in open systems where agents’ internals are kept private. This analysis gives some ideas about how compliance might be enforced in an open system. 1

This paper considers the problem of representing complex systems that evolve stochastically over time. Dynamic Bayesian networks provide a compact representation for stochastic processes. Unfortunately, they are often unwieldy since they cannot explicitly model the complex organizational structure of many real life systems: the fact that processes are typically composed of several interacting subprocesses, each of which can, in turn, be further decomposed. We propose a hierarchically structured representation language which extends both dynamic Bayesian networks and the object-oriented Bayesian network framework of [9], and show that our language allows us to describe such systems in a natural and modular way. Our language supports a natural representation for certain system characteristics that are hard to capture using more traditional frameworks. For example, it allows us to represent systems where some processes evolve at a different rate than others, or systems whe...

. I describe a systematic method for deductive verification of safety properties of concurrent programs. The method has much in common with the "verification diagrams" of Manna and Pnueli [17], but derives from different intuitions. It is based on the idea of strengthening a putative safety property into a disjunction of "configurations" that can easily be proved to be inductive. Transitions among the configurations have a natural diagrammatic representation that conveys insight into the operation of the program. The method lends itself to mechanization and is illustrated using a simplified version of an example that had defeated previous attempts at deductive verification. 1 Introduction In 1997, Shmuel Katz, Patrick Lincoln and I presented an algorithm for Group Membership together with a detailed, but informal proof of its correctness [14]. Shortly thereafter, our colleague Shankar and, independently, Sadie Creese and Bill Roscoe of Oxford University, noted that the algori...