Showing papers by "John B. Moore published in 1997"
Book•
01 Sep 1997TL;DR: Performance enhancement stabilizing controllers design environment off-line controller design iterated and nested (S, Q) design direct adaptive-Q control indirect adaptive control adaptive Q application to non-linear systems real-time implementation laboratory case studies.
Abstract: Performance enhancement stabilizing controllers design environment off-line controller design iterated and nested (S, Q) design direct adaptive-Q control indirect (S, Q) adaptive control adaptive-Q application to non-linear systems real-time implementation laboratory case studies.
196 citations
TL;DR: This paper addresses the risk-sensitive filtering problem which is minimizing the expectation of the exponential of the squared estimation error multiplied by a risk- sensitive parameter, and considers a class of discrete-time stochastic nonlinear state-space models.
Abstract: We address the risk-sensitive filtering problem which is minimizing the expectation of the exponential of the squared estimation error multiplied by a risk-sensitive parameter. Such filtering can be more robust to plant and noise uncertainty than minimum error variance filtering. Although optimizing a differently formulated performance index to that of the so-called H/sub /spl infin// filtering, risk-sensitive filtering leads to a worst case deterministic noise estimation problem given from the differential game associated with H/sub /spl infin// filtering. We consider a class of discrete-time stochastic nonlinear state-space models. We present linear recursions in the information state and the result for the filtered estimate that minimizes the risk-sensitive cost index. We also present fixed-interval smoothing results for each of these signal models. In addition, a brief discussion is included on relations of the risk-sensitive estimation problem to minimum variance estimation and a worst case estimation problem in a deterministic noise scenario related to minimax dynamic games. The technique used in this paper is the so-called reference probability method which defines a new probability measure where the observations are independent and translates the problem to the new measure. The optimization problem is solved using simple estimation theory in the new measure, and the results are interpreted as solutions in the original measure.
80 citations
01 Jan 1997
TL;DR: In this paper, the risk-sensitive nonlinear stochastic filtering problem is addressed in both continuous and discrete-time for quite general finite-dimensional signal models, including also discrete state hidden Markov models (HMMs).
Abstract: In this paper, the risk-sensitive nonlinear stochastic filtering problem is addressed in both continuous and discrete-time for quite general finite-dimensional signal models, including also discrete state hidden Markov models (HMMs). The risk sensitive estimates are expressed in terms of the so-called information state of the model given by the Zakai equation which is linear. In the linear Gaussian signal model case, the risk-sensitive (minimum exponential variance) estimates are identical to the minimum variance Kalman filter state estimates, and are thus given by a finite dimensional estimator. The estimates are also finite dimensional for discrete-state HMMs, but otherwise, in general, are infinite dimensional. In the small noise limit, these estimates (including the minimum variance estimates) have an interpretation in terms of a worst case deterministic noise estimation problem given from a differential game. The related control task, that is the risk-sensitive generalization of minimum-variance control is studied for the discrete-time models. This is motivated by the need for robustness in the widely used (risk neutral) minimum variance control, including adaptive control, of systems which are minimum phase, that is having stable inverses.
52 citations
20 Apr 1997
TL;DR: Two versions of strictly convex cost functions including a barrier term, one of them self-concordant, are considered and it is shown that the proposed algorithms guarantee convergence to the unique solution of the underlying semidefinite program.
Abstract: In dextrous robotic hand grasping the external object force needs to be balanced with contact forces maintaining grasp stability. Redundancy in the grasp yields the optimization problem to minimize the grasp effort subject to nonlinear friction stability constraints. We reformulate the optimization problem as a semidefinite program with affine constraints. In this paper, two versions of strictly convex cost functions including a barrier term, one of them self-concordant, are considered. For the general class of such cost functions Dikin-type algorithms are considered. It is shown that the proposed algorithms guarantee convergence to the unique solution of the underlying semidefinite program. Numerical examples demonstrate the simplicity of implementation and the good numerical properties of the approach.
21 citations
TL;DR: In this paper, an infinite-dimensional convex optimization problem with the linear quadratic cost function and linear-quadratic constraints is considered, and it is shown that for this problem the Newton step is basically reduced to the standard LQ problem.
Abstract: An infinite-dimensional convex optimization problem with the linear-quadratic cost function and linear-quadratic constraints is considered. We generalize the interior-point techniques of Nesterov-Nemirovsky to this infinite-dimensional situation. The complexity estimates obtained are similar to finite-dimensional ones. We apply our results to the linear-quadratic control problem with quadratic constraints. It is shown that for this problem the Newton step is basically reduced to the standard LQ problem.
19 citations
TL;DR: In this paper, the authors considered the problem of filtering and control in stochastic control and showed that the interdependence of these two problems is so superficial that in effect, they are problems which can be treated separately.
11 citations
21 Apr 1997
TL;DR: A rank preserving flow is used to accommodate the rank constraint and the associated gradient formulas are carefully developed, and the convergence of the resulting algorithm is guaranteed.
Abstract: This paper concerns quadratic programming problems subject to quadratic equality constraints such as arise in broadband antenna array signal processing and elsewhere. At first, such a problem is converted into a semidefinite programming problem with a rank constraint. Then, a rank preserving flow is used to accommodate the rank constraint. The associated gradient formulas are carefully developed. The convergence of the resulting algorithm is also guaranteed. Our approach is demonstrated by a numerical experiment.
7 citations
TL;DR: In this article, a continuous-time version of Kronecker's Lemma is established and used to give rates of convergence for parameter estimates in hidden Markov models, which is used in our work.
6 citations
TL;DR: In this article, a dynamic programming equation solution is given to an optimal risk-sensitive dual control problem penalizing outputs, rather than the states, for a reasonably general class of nonlinear signal models.
Abstract: In this paper, we develop new results concerning the risk-sensitive dual control problem for output feedback nonlinear systems, with unknown time-varying parameters. A dynamic programming equation solution is given to an optimal risk-sensitive dual control problem penalizing outputs, rather than the states, for a reasonably general class of nonlinear signal models. This equation, in contrast to earlier formulations in the literature, clearly shows the dual aspects of the risk-sensitive controller regarding control and estimation. The extensive computational burden for solving this equation motivates our study of risk-sensitive versions for one-step horizon cost indices and suboptimal risk-sensitive dual control. The idea of a more generalized optimal risk-sensitive dual controller is briefly introduced.
5 citations
10 Dec 1997
TL;DR: An approach for deinterleaving pulse trains and estimating their periods using an extended Kalman filter (EKF) is presented and a form of smoothing of the discontinuities is proposed so that the EKF approach becomes attractive.
Abstract: If more than one pulse train is transmitted over the same communication channel, a challenge is to separate them for source identification at the receiver. This is known as pulse train deinterleaving, and is clearly a fundamental problem in the study of discrete-event systems. We present an approach for deinterleaving pulse trains and estimating their periods using an extended Kalman filter (EKF). A form of smoothing of the discontinuities is proposed so that the EKF approach becomes attractive. The advantage of this EKF approach is that it is less computationally expensive than most previously proposed methods. The method proposed appears to give useful results for up to seven or so pulse trains, particularly when there is some a priori information on the pulse frequencies, which can be obtained using computations of order Nlog N.
4 citations
10 Dec 1997
TL;DR: In this paper, the authors consider the problem of optimal control with finitely many IQ (integral quadratic) constraints and show that the separation theorem does not hold, but a generalization which they call a quasi-separation theorem holds instead.
Abstract: We consider the deterministic, the full observation and the partial observation LQG optimal control problems with finitely many IQ (integral quadratic) constraints. We show that the separation theorem does not hold. However, a generalization which we call a quasi-separation theorem holds instead. We show how gradient-type optimization algorithms can be used to calculate the optimal control.
01 Jul 1997
TL;DR: In this article, a modified Zakai equation is obtained for the risk sensitive information state and an expression for the optimizing risk-sensitive estimate is given for a class of continuous-time nonlinear stochastic signal models.
Abstract: Risk-sensitive filtering results are obtained for a class of continuous-time nonlinear stochastic signal models. A modified Zakai equation is obtained for the risk-sensitive information state and an expression for the optimizing risk-sensitive estimate is given. It is shown that if the drift function in the state space model satisfies a certain partial differential equation involving the risk-sensitive cost-kernel, finite-dimensional risk-sensitive information states and filters can be obtained for quite general nonlinear drift functions. Brief discussions on small noise limit results and possible extensions are also included.
01 Jul 1997
TL;DR: In this paper, the authors considered a semi-infinite linear programming problem where the variables may belong to an infinite-dimensional Hilbert space and generalize a potential reduction method introduced by Ye so that it can be used to solve this problem.
Abstract: We consider a semi-infinite linear programming problem where the variables may belong to an infinite-dimensional Hilbert space We generalize a potential reduction method introduced by Ye so that it can be used to solve this problem Furthermore, convergence of the iterates produced by this algorithm to the optimal solution is proven As an example, we show how this algorithm can be used to solve continuous linear programming (CLP) problems
01 Jan 1997
TL;DR: Dynamical systems can be thought of as either non-linear continuous-time differential equations or difference equations, and at the heart of much of the authors' optimization is dynamical systems.
Abstract: Much of engineering is concerned with the topic of optimization, and at the heart of much of our optimization is dynamical systems. Dynamical systems can be thought of as either non-linear continuous-time differential equations or difference equations. Chaos occurs in dynamical systems, and frequently in engineering we seek to avoid chaos. At times chaos becomes the central fascination.