This paper considers the application of Kalman estimation theory to the problem of estimating two-dimensional isotropic random fields, whose equations are expressed in terms of the Laplacian, given some noisy observat...
详细信息
This paper considers the application of Kalman estimation theory to the problem of estimating two-dimensional isotropic random fields, whose equations are expressed in terms of the Laplacian, given some noisy observations on a finite disk. It is shown that this problem is equivalent to that of solving a countably infinite number of one-dimensional estimation problems. Markovian models for the one-dimensional processes are developed and the associated Kalman filters are shown to be asymptotically stable. The desired field estimate is then obtained by combining the smoothed estimates resulting from each of the one-dimensional problems weighted in an appropriate fashion.
Recent two-time scale results can be derived from a geometric framework which allows further extensions and computational improvements. In this paper the two-time scale behavior of singularly perturbed systems is expl...
详细信息
Recent two-time scale results can be derived from a geometric framework which allows further extensions and computational improvements. In this paper the two-time scale behavior of singularly perturbed systems is exploited to design slow and fast controls and to combine them into a composite control. As an illustration we present a corrective design to compensate for fast actuator dynamics modeled as singular perturbations.
Simulated annealing is a popular Monte Carlo algorithm for combinatorial optimization. The annealing algorithm simulates a nonstationary finite state Markov chain whose state space Ω is the domain of the cost functio...
详细信息
Simulated annealing is a popular Monte Carlo algorithm for combinatorial optimization. The annealing algorithm simulates a nonstationary finite state Markov chain whose state space Ω is the domain of the cost function to be minimized. We analyze this chain focusing on those issues most important for optimization. In all of our results we consider an arbitrary partition optimization {I, J} of Ω; important special cases are when I is the set of minimum cost states or a set of all states with sufficiently small cost. We give a lower bound on the probability that the chain visits I at some time less than or equal to k, for k = 1,2, .... This bound may be useful even when the algorithm does not converge. We give conditions under which the chain converges to I in probability and obtain an estimate of the rate of convergence as well. We also give conditions under which the chain visits I infinitely often, visits I almost always, or does not converge to I, with probability 1.
In this paper we consider a stochastic incentive decision problem with N > 1 followers and decentralized static information, where the leader's dynamic information comprises only a linear combination of the fol...
详细信息
In this paper we consider a stochastic incentive decision problem with N > 1 followers and decentralized static information, where the leader's dynamic information comprises only a linear combination of the followers' actions. We obtain an incentive policy, affine in this dynamic information, which yields the same overall performance as the one the leader would obtain if he had observed the followers' actions separately. The existence conditions involved have been obtained explicitly for the case of finite probability spaces, and some challenging issues have been identified when the random variables are infinite valued.
We explore the fusion of expert control system analysis and design tools into a prototype computer environment. The use of expert systems technology allows the transfer of recent developments in control system design ...
详细信息
We explore the fusion of expert control system analysis and design tools into a prototype computer environment. The use of expert systems technology allows the transfer of recent developments in control system design to users who may not be experts in either theoretical developments or computer technology, in a vehicle which provides considerable design flexibility. The technology does not provide as general a framework as, for example, a command language based environment; however, in specific applications, such as system modeling and linear controlsystems, it is useful and appropriate. Criteria for such applications is that they have a mature theoretical basis, and that the user interaction influence the sequence of the design process.
In this paper, two theorems are quoted which, when applied together, provide much information about the robustness of adaptive control schemes. From these two theorems, another theorem is developed which can explain w...
详细信息
In this paper, two theorems are quoted which, when applied together, provide much information about the robustness of adaptive control schemes. From these two theorems, another theorem is developed which can explain why adaptive controllers can perform robustly in certain practical situations, while possibly failing in other situations. In particular, if the bandwidth constraints on a controlsystems are lenient enough to allow the use of a sampling frequency which is smaller than the frequency at which unstructured uncertainty becomes significant, an adaptive controller can behave robustly. Many, if not all, of the applications of adaptive control which have been successful employ relatively slow sampling of the process. Thus, the results of this paper provide a theoretical explanation of how certain adaptive controllers are performing robustly in practice. In addition, the final theorem is of a form which provides insight into what a priori knowledge is required to achieve robust adaptive control and how this knowledge say be used.
作者：
TSITSIKLIS, JNDoctoral Student
Laboratory for Information and Decision Systems Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology Cambridge Massachusetts
An infinite horizon, expected average cost, dynamic routing problem is formulated for a simple failure-prone queueing system, modelled as a continuous time, continuous state controlled stochastic process. We prove tha...
详细信息
An infinite horizon, expected average cost, dynamic routing problem is formulated for a simple failure-prone queueing system, modelled as a continuous time, continuous state controlled stochastic process. We prove that the optimal average cost is independent of the initial state and that the cost-to-go functions of dynamic programming are convex. These results, together with a set of optimality conditions, lead to the conclusion that optimal policies are switching policies, characterized by a set of switching curves (or regions), each curve corresponding to a particular state of the nodes (servers).
The Schur algorithm is a signal processing algorithm which works on a layer‐stripping principle. Its time‐domain version, the fast Cholesky recursion, is a fast and efficient algorithm well‐suited for high‐speed d...
详细信息
The Schur algorithm is a signal processing algorithm which works on a layer‐stripping principle. Its time‐domain version, the fast Cholesky recursion, is a fast and efficient algorithm well‐suited for high‐speed data processing. In this paper, these algorithms are applied to the inverse problem for a continuous layered acoustic medium. Three different excitations of the medium are considered: impulsive plane waves at normal incidence, impulsive plane waves at oblique incidence, and spherical waves emanating from an impulsive point source. The fast algorithms obtained for each of these problems seem to be computationally superior to past work done on these problems that employed Gelfand–Levitan theory to reconstruct the potential of a Schr?dinger equation.
This paper presents a new inverse scattering method for reconstructing the reflectivity function of symmetric two-component wave equations, or the potential of a Schrodinger equation, when the reflection coefficient i...
详细信息
This paper presents a new inverse scattering method for reconstructing the reflectivity function of symmetric two-component wave equations, or the potential of a Schrodinger equation, when the reflection coefficient is rational. This method relies on the so-called Chandrasekhar equations which implement the Kalman filter associated to a stationary state-space model. These equations are derived by using first a general layer stripping principle to obtain some differential equations for reconstructing a general scattering medium, and by specializing these recursions to the case when the probing waves have a state-space model.
暂无评论