1,963,858 research outputs found
Using Student Knowledge of Linear Systems Theory to Facilitate the Learning of Optical Engineering
For students learning a new topic, being able to use existing knowledge and mental models in the context of the new topic leads to faster learning and a deeper understanding of the new concepts. This paper describes how teaching a graduate-level course providing an introduction to optical engineering for students from multiple engineering majors can be facilitated by using existing concepts and knowledge of linear systems theory, which are common to them all
Bisimulation theory for switching linear systems
A general notion of hybrid bisimulation is proposed and related to the notions of algebraic, state-space and input-output equivalences for the class of switching linear systems. An algebraic characterization of hybrid bisimulations and a procedure converging in a finite number of steps to the maximal hybrid bisimulation are derived. Bisimulation-based reduction and simulation-based abstraction are defined and characterized. Connections with observability are investigated
Perturbation theory of observable linear systems
The present work is motivated by the asymptotic control theory for a system
of linear oscillators: the problem is to design a common bounded scalar control
for damping all oscillators in asymptotically minimal time. The motion of the
system is described in terms of a canonical system similar to that of the
Pontryagin maximum principle. We consider the evolution equation for adjoint
variables as a perturbed observable linear system. Due to the perturbation, the
unobservable part of the state trajectory cannot be recovered exactly. We
estimate the recovering error via the -norm of perturbation. This allows
us to prove that the control makes the system approach the equilibrium state
with a strictly positive speed.Comment: 7 pages; the subject of the present paper has grown out of study
arXiv:1308.6090 (see Appendix V); published versio
Linear Invariant Systems Theory for Signal Enhancement
This paper discusses a linear time invariant (LTI) systems approach to signal enhancement via projective subspace techniques. It provides closed form expressions for the frequency response of data adaptive finite impulse response eigenfilters. An illustrative example using speech enhancement is also presented.Este artigo apresenta a aplicação da teoria de sistemas lineares invariantes no tempo (LTI) na anĂĄlise de tĂ©cnicas de sub-espaço. A resposta em frequĂȘncia dos filtros resultantes da decomposição em valores singulares Ă© obtida aplicando as propriedades dos sistemas LTI
A linear theory for control of non-linear stochastic systems
We address the role of noise and the issue of efficient computation in
stochastic optimal control problems. We consider a class of non-linear control
problems that can be formulated as a path integral and where the noise plays
the role of temperature. The path integral displays symmetry breaking and there
exist a critical noise value that separates regimes where optimal control
yields qualitatively different solutions. The path integral can be computed
efficiently by Monte Carlo integration or by Laplace approximation, and can
therefore be used to solve high dimensional stochastic control problems.Comment: 5 pages, 3 figures. Accepted to PR
Team decision theory for linear continuous-time systems
This paper develops a team decision theory for linear-quadratic (LQ) continuous-time systems. First, a counterpart of the well-known result of Radner on quadratic static teams is obtained for two-member continuous-time LQ static team problems when the statistics of the random variables involved are not necessarily Gaussian. An iterative convergent scheme is developed, which in the limit yields the optimal team strategies. For the special case of Gaussian distributions, the team-optimal solution is affine in the information available to each DM, and for the further special case when the team cost function does not penalize the intermediate values of state, the optimal strategies can be obtained by solving a Liapunov type time-invariant matrix equation. This static theory is then extended to LQG continuous-time dynamic teams with sampled observations under the one-step-delay observation sharing pattern. The unique solution is again affine in the information available to each DM, and further, it features a certainty-equivalence property
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