David L. Kleinman

Stabilizing a discrete, constant, linear system with application to iterative methods for solving the Riccati equation

A constructive proof is given for easily finding constant feedback gains that stabilize a linear, time-invariant, discrete system. The results are directly applicable to initializing certain iterative methods that find steady-state gains for the discrete optimal regulator.

Optimization of detection networks. I. Tandem structures

A distributed binary detection problem with binary communications, wherein the nodes (sensors, decision-makers) of the system are organized in a series configuration, is considered. It is shown that this problem is isomorphic to a deterministic, multistage nonlinear optimal control problem. Necessary and sufficient conditions of optimality are derived using Bayes risk as the optimization criterion, and a physical interpretation of how the costates relate to the decision threshold at each node is provided. A computationally efficient algorithm based on the min-H method is proposed to solve for the optimal decision strategy, and is extended to solve the problem with a Neyman-Pearson criterion to obtain the optimal team (network) receiver operating characteristic curve. The optimal strategies are illustrated by several numerical examples related to organizational design. The results can be extended to directed acyclic networks with at most a single directed path between any pair of nodes (which include directed tree networks as a special case).<<ETX>>

An algorithm for determining the decision thresholds in a distributed detection problem

A decentralized binary hypothesis-testing problem is considered in which a number of subordinate decision-makers (DMs) transmit their opinions based on their data to a primary decisionmaker who, in turn, combines the opinions with his own data to make the final team decision. The necessary conditions for the optimal decision rules of the DMs are derived. A nonlinear Gauss-Seidel iterative algorithm is developed for solving the decision thresholds of a person-by-person optimal strategy, and its monotonic convergence is established. The algorithm is illustrated with several examples, and implications for distributed organizational design are pointed out.<<ETX>>

A dynamic decision model of human task selection performance

Human information processing and task selection procedures in a dynamic multitask supervisory control environment are discussed. The results of a joint experimental and analytic program were assimilated into a normative dynamic-decision model for predicting human task-selection performance. To this end a general multitask experimental paradigm has been developed, wherein tasks of different value, time requirement, and deadline compete for a humans attention. Via this framework, the effects of various task related variables on human-decision processes have been studied empirically. Conceptually the normative dynamic-decision model (DDM) is an outgrowth of the well-known optimal control modeling technology as applied to multitask situations. Thus the analytic framework of the DDM is rooted in modern control, estimation, and semiMarkov decision-process theories. In order to validate the model via comparison with experimental results, several time history and scalar measures of performance similarity are proposed. Excellent model-data agreement is obtained for all the experimental conditions studied.

Optimal Team and Individual Decision Rules in Uncertain Dichotomous Situations

In this paper, we consider the problem of determining the optimalteam decision rules in uncertain, binary (dichotomous) choice situations. We show that the Relative (Receiver) Operating Characteristic (ROC) curve plays a pivotal role in characterizing these rules. Specifically, the problem of finding the optimal aggregation rule involves finding a set ofcoupled operating points on the individual ROCs. Introducing the concept of a “team ROC curve”, we extend the method of characterizing decision capabilities of an individual decisionmaker (DM) to a team of DMs. Given the operating points of the individual DMs on their ROC curves, we show that the best aggregation rule is a likelihood ratio test. When the individual opinions are conditionally independent, the aggregation rule is a weighted majority rule, but with different asymmetric weights for the ‘yes’ and ‘no’ decisions. We show that the widely studied weighted majority rule with symmetric weights is a special case of the asymmetric weighted majority rule, wherein the competence level of each DM corresponds to the intersection of the main diagonal and the DMs ROC curve. Finally, we demonstrate that the performance of the team can be improved by jointly optimizing the aggregation rule and the individual decision rules, the latter possibly requiring a shift from the isolated (non-team) optimal operating point of each DM.

Optimization of detection networks with multiple event structures

Considers a multilevel hierarchical decision network faced with a distributed binary detection problem with partial information at the individual decisionmaker (DM). The partial information is modeled by different local events at the DMs, and these local events are probabilistically related to one another. Solution to this generalized hypothesis testing problem is obtained using the optimal control approach, where the optimization criterion is the expected decision cost of the network. The impacts of variations in the correlation of events at two communicating nodes on the aggregated expertise of the network and on the overall decision cost are illustrated via a numerical example. >

Some new control theoretic models for human operator display monitoring

Control theoretic techniques are applied to develop two new models for predicting human operator performance when monitoring an automatically controlled system. In one case it is assumed that the human monitors the instruments in order to rapidly detect failures. The second approach assumes that the instruments are sampled to best reconstruct the system status information. The relation of these models to existing prediction schemes, e.g., equal attention and the Senders model is explored. It is concluded that a combination of failure detection and status estimation models offers the best potential for human operator application.

Distributed detection in teams with partial information: a normative-descriptive model

A hierarchical team faced with a binary detection problem, wherein decision makers (DMs) have access to different subsets of noise-corrupted information about the true state of the environment, is considered. A normative model is developed that aggregates the individual expertise of DMs at different levels of the hierarchy. The resulting team expertise is characterized in the form of a team receiver operating characteristic (ROC) curve, thereby replacing the team by an equivalent single decision-making node. The normative model is tested against human teams in a laboratory experiment. The team objective is to minimize the cost of errors in the final decision at the primary DM, where the cost structure and the information structure are treated as independent variables. Discrepancies between normative predictions and experimental results are attributed to inherent limitations and cognitive biases of humans. >

Extensions to the Bartels-Stewart algorithm for linear matrix equations

It is shown that the Bartels-stewart algorithm can be extended to treat the adjoint and nonsymmetric matrix equations, while taking advantage of substantial savings in computer time afforded by the sequential solution property of the algorithm.

Optimal measurement scheduling for state estimation

We consider the problem of optimal allocation of measurement resources, when: (1) the total measurement budget and time duration of measurements are fixed, and (2) the cost of an individual measurement varies inversely with the (controllable) measurement accuracy. The objective is to determine the time-distribution of measurement variances that minimizes a measure of error in estimating a discrete-time, vector stochastic process with known auto-correlation matrix using a linear estimator. The metric of estimation error is the trace of weighted sum of estimation error covariance matrices at various time indices. We show that this problem reduces to a nonlinear optimization problem with linear equality and inequality constraints. The solution to this problem is obtained via a variation of the projected Newton method. For the special case when the vector stochastic process is the state of a linear, finite-dimensional stochastic system, the problem reduces to the solution of a nonlinear optimal control problem. In this case, the gradient and Hessian with respect to the measurement costs are obtained via the solution of a two-point boundary value problem and the resulting optimization problem is solved via a variation of the projected Newton method. The proposed method is illustrated using four examples. >