اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدIdentification of Structured LTI MIMO State-Space Models
62
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The identification of structured state-space model has been intensively studied for a long time but still has not been adequately addressed. The main challenge is that the involved estimation problem is a non-convex (or bilinear) optimization problem. This paper is devoted to developing an identification method which aims to find the global optimal solution under mild computational burden. Key to the developed identification algorithm is to transform a bilinear estimation to a rank constrained optimization problem and further a difference of convex programming (DCP) problem. The initial condition for the DCP problem is obtained by solving its convex part of the optimization problem which happens to be a nuclear norm regularized optimization problem. Since the nuclear norm regularized optimization is the closest convex form of the low-rank constrained estimation problem, the obtained initial condition is always of high quality which provides the DCP problem a good starting point. The DCP problem is then solved by the sequential convex programming method. Finally, numerical examples are included to show the effectiveness of the developed identification algorithm.
قيم البحث
اقرأ أيضاً
Designing a static state-feedback controller subject to structural constraint achieving asymptotic stability is a relevant problem with many applications, including network decentralized control, coordinated control, and sparse feedback design. Lever
aging on the Projection Lemma, this work presents a new solution to a class of state-feedback control problems, in which the controller is constrained to belong to a given linear space. We show through extensive discussion and numerical examples that our approach leads to several advantages with respect to existing methods: first, it is computationally efficient; second, it is less conservative than previous methods, since it relaxes the requirement of restricting the Lyapunov matrix to a block-diagonal form.
In this paper, we introduce a definition of phase response for a class of multi-input multi-output (MIMO) linear time-invariant (LTI) systems whose frequency responses are (semi-)sectorial at all frequencies. The newly defined phase concept subsumes
the well-known notions of positive real systems and negative imaginary systems. We formulate a small phase theorem for feedback stability, which complements the celebrated small gain theorem. The small phase theorem lays the foundation of a phase theory of MIMO systems. We also discuss time-domain interpretations of phase-bounded systems via both energy signal analysis and power signal analysis. In addition, a sectored real lemma is derived for the computation of MIMO phases, which serves as a natural counterpart of the bounded real lemma.
A new framework for nonlinear system identification is presented in terms of optimal fitting of stable nonlinear state space equations to input/output/state data, with a performance objective defined as a measure of robustness of the simulation error
with respect to equation errors. Basic definitions and analytical results are presented. The utility of the method is illustrated on a simple simulation example as well as experimental recordings from a live neuron.
Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified algorithm to ef
ficiently learn a broad class of linear and non-linear state space models, including variants where the emission and transition distributions are modeled by deep neural networks. Our learning algorithm simultaneously learns a compiled inference network and the generative model, leveraging a structured variational approximation parameterized by recurrent neural networks to mimic the posterior distribution. We apply the learning algorithm to both synthetic and real-world datasets, demonstrating its scalability and versatility. We find that using the structured approximation to the posterior results in models with significantly higher held-out likelihood.
In this paper, we derive sufficient conditions on drift matrices under which block-diagonal solutions to Lyapunov inequalities exist. The motivation for the problem comes from a recently proposed basis pursuit algorithm. In particular, this algorithm
can provide approximate solutions to optimisation programmes with constraints involving Lyapunov inequalities using linear or second order cone programming. This algorithm requires an initial feasible point, which we aim to provide in this paper. Our existence conditions are based on the so-called $mathcal{H}$ matrices. We also establish a link between $mathcal{H}$ matrices and an application of a small gain theorem to the drift matrix. We finally show how to construct these solutions in some cases without solving the full Lyapunov inequality.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
