1,261 research outputs found
Recommended from our members
The numerical solution of stefan problems with front-tracking and smoothing methods
Network Reconstruction from Intrinsic Noise
This paper considers the problem of inferring an unknown network of dynamical
systems driven by unknown, intrinsic, noise inputs. Equivalently we seek to
identify direct causal dependencies among manifest variables only from
observations of these variables. For linear, time-invariant systems of minimal
order, we characterise under what conditions this problem is well posed. We
first show that if the transfer matrix from the inputs to manifest states is
minimum phase, this problem has a unique solution irrespective of the network
topology. This is equivalent to there being only one valid spectral factor (up
to a choice of signs of the inputs) of the output spectral density.
If the assumption of phase-minimality is relaxed, we show that the problem is
characterised by a single Algebraic Riccati Equation (ARE), of dimension
determined by the number of latent states. The number of solutions to this ARE
is an upper bound on the number of solutions for the network. We give necessary
and sufficient conditions for any two dynamical networks to have equal output
spectral density, which can be used to construct all equivalent networks.
Extensive simulations quantify the number of solutions for a range of problem
sizes. For a slightly simpler case, we also provide an algorithm to construct
all equivalent networks from the output spectral density.Comment: 11 pages, submitted to IEEE Transactions on Automatic Contro
Non-linear predictive control for manufacturing and robotic applications
The paper discusses predictive control algorithms in the context of applications to robotics and manufacturing systems. Special features of such systems, as compared to traditional process control applications, require that the algorithms are capable of dealing with faster dynamics, more significant unstabilities and more significant contribution of non-linearities to the system performance. The paper presents the general framework for state-space design of predictive algorithms. Linear algorithms are introduced first, then, the attention moves to non-linear systems. Methods of predictive control are presented which are based on the state-dependent state space system description. Those are illustrated on examples of rather difficult mechanical systems
A new design approach for solving linear quadratic Nash games of multiparameter singularly perturbed systems
In this paper, the linear quadratic Nash games for infinite horizon nonstandard multiparameter singularly perturbed systems (MSPS) without the nonsingularity assumption that is needed for the existing result are discussed. The new strategies are obtained by solving the generalized cross-coupled multiparameter algebraic Riccati equations (GCMARE). Firstly, the asymptotic expansions for the GCMARE are newly established. The main result in this paper is that the proposed algorithm which is based on the Newton's method for solving the GCMARE guarantees the quadratic convergence. In fact, the simulation results show that the proposed algorithm succeed in improving the convergence rate dramatically compared with the previous results. It is also shown that the resulting controller achieves O(∥μ∥2n) approximation of the optimal cost
Iterative Algorithm for Solving a System of Nonlinear Matrix Equations
We discuss the positive definite solutions for the system of nonlinear matrix equations and , where , are two positive integers. Some properties of solutions are studied, and the necessary and sufficient conditions for the existence of positive definite solutions are given. An iterative algorithm for obtaining positive definite solutions of the system is proposed. Moreover, the error estimations are found. Finally, some numerical examples are given to show the efficiency of the proposed iterative algorithm
On the Iterative Method for the System of Nonlinear Matrix Equations
The positive definite solutions for the system of nonlinear matrix equations are considered, where are two positive integers and A, B are nonsingular complex matrices. Some sufficient conditions for the existence of positive definite solutions for the system are derived. Under some conditions, an iterative algorithm for computing the positive definite solutions for the system is proposed.
Also, the estimation of the error is obtained. Finally, some numerical examples are given to
show the efficiency of the proposed iterative algorithm
Reinforcement Learning in Deep Structured Teams: Initial Results with Finite and Infinite Valued Features
In this paper, we consider Markov chain and linear quadratic models for deep
structured teams with discounted and time-average cost functions under two
non-classical information structures, namely, deep state sharing and no
sharing. In deep structured teams, agents are coupled in dynamics and cost
functions through deep state, where deep state refers to a set of orthogonal
linear regressions of the states. In this article, we consider a homogeneous
linear regression for Markov chain models (i.e., empirical distribution of
states) and a few orthonormal linear regressions for linear quadratic models
(i.e., weighted average of states). Some planning algorithms are developed for
the case when the model is known, and some reinforcement learning algorithms
are proposed for the case when the model is not known completely. The
convergence of two model-free (reinforcement learning) algorithms, one for
Markov chain models and one for linear quadratic models, is established. The
results are then applied to a smart grid.Comment: This version corrects some typographical error
- …