349 research outputs found
Learning First-Order Definitions of Functions
First-order learning involves finding a clause-form definition of a relation
from examples of the relation and relevant background information. In this
paper, a particular first-order learning system is modified to customize it for
finding definitions of functional relations. This restriction leads to faster
learning times and, in some cases, to definitions that have higher predictive
accuracy. Other first-order learning systems might benefit from similar
specialization.Comment: See http://www.jair.org/ for any accompanying file
Equational binary decision diagrams
We incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and tautology checking can be done in constant time. Several procedures to eliminate equality from BDDs have been reported in the literature. Typical for our approach is that we keep equalities, and as a consequence do not employ the finite domain property. Furthermore, our setting does not strictly require Ackermann's elimination of function symbols. This makes our setting much more amenable to combinations with other techniques in the realm of automatic theorem proving, such as term rewriting. We introduce an algorithm, which for any propositional formula with equations finds an EQ-OBDD that is equivalent to it. The algorithm is proved to be correct and terminating, by means of recursive path ordering. The algorithm has been implemented, and applied to benchmarks known from literature. The performance of a prototype implementation is comparable to existing proposals
DYNAMIC MODELING AND CLOSED-LOOP CONTROL OF A TWIN ROTOR MIMO SYSTEM
The Twin rotor MIMO system (TRMS) is an aero-dynamical model of helicopter
with significant cross-couplings between longitudinal and lateral directional motions.
Its behavior in certain aspects resembles the real of a helicopter. Firstly, open loop
control is implemented both for tail and main rotor to get the relationship of input and
output of the system. Open-loop control is often the preliminary step for development
of more complex feedback control laws. Next step was model identification as it is a
well established technique for modeling of complex systems whose dynamics are not
well understood or difficult to model from the first principles. State feedback
controllers were designed by pole placement method for both rotors independently.
The model then can be implemented in real-time experiments of the Twin Rotor
MIMO System
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Non-linear discrete-time observer design by sliding mode
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University, 09/02/2007.Research into observer design for non-linear discrete-time systems has produced many design methods. There is no general design method however and that provides the motivation to search for a new simple and realizable design method. In this thesis, an observer for non-linear discrete-time systems is designed using the sliding mode technique. The equation of the observer error is split into two parts; the first part being a linearized model of the system and the second part an uncertain vector. The sliding mode technique is introduced to eliminate the uncertainty caused by the uncertain vector in the observer error equation. By choosing the sliding surface and the boundary layer, the observer error is attracted to the sliding surface and stays within the sliding manifold. Therefore, the observer error converges to zero. The proposed technique is applied to two cases of observers for nonlinear discrete-time systems. The second case is chosen to be a particular practical system, namely the non-linear discrete-time ball and beam system. The simulations show that the sliding mode technique guarantees the convergence of the observer error for both systems
Metalevel and reflexive extension in mechanical theorem proving
In spite of many years of research into mechanical assistance for mathematics
it is still much more difficult to construct a proof on a machine than on
paper. Of course this is partly because, unlike a proof on paper, a machine
checked proof must be formal in the strictest sense of that word, but it is
also because usually the ways of going about building proofs on a machine
are limited compared to what a mathematician is used to. This thesis looks
at some possible extensions to the range of tools available on a machine
that might lend a user more flexibility in proving theorems, complementing
whatever is already available.In particular, it examines what is possible in a framework theorem
prover. Such a system, if it is configured to prove theorems in a particular
logic T, must have a formal description of the proof theory of T written
in the framework theory F of the system. So it should be possible to use
whatever facilities are available in F not only to prove theorems of T, but
also theorems about T that can then be used in their turn to aid the user
in building theorems of T.The thesis is divided into three parts. The first describes the theory
FSā, which has been suggested by Feferman as a candidate for a framework
theory suitable for doing meta-theory. The second describes some experiments with FSā, proving meta-theorems. The third describes an experiment
in extending the theory PRA, declared in FSā, with a reflection facility.More precisely, in the second section three theories are formalised:
propositional logic, sorted predicate logic, and the lambda calculus (with
a deBruijn style binding). For the first two the deduction theorem and
the prenex normal form theorem are respectively proven. For the third, a
relational definition of beta-reduction is replaced with an explicit function.In the third section, a method is proposed for avoiding the work involved
in building a full Godel style proof predicate for a theory. It is suggested
that the language be extended with quotation and substitution facilities directly, instead of providing them as definitional extensions. With this, it
is possible to exploit an observation of Solovay's that the Lob derivability
conditions are sufficient to capture the schematic behaviour of a proof
predicate. Combining this with a reflection schema is enough to produce
a non-conservative extension of PRA, and this is demonstrated by some
experiments
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