Reduced-complexity nonlinear H/sup /spl infin// control of discrete-time systems

In this note, we describe a reduced-complexity solution to the nonlinear H/sup /spl infin// control problem. This reduction applies to systems where some of the states are perfectly known, and is an intermediate problem between full state feedback and the standard measurement feedback problem. The reduction of computational complexity is significant and of practical importance. Online implementation is feasible with 2003 computer technology for a range of practical engineering design problems.     

A gastroesophageal electrode for atrial and ventricular pacing

Temporary transvenous cardiac pacing requires technical expertise and access to fluoroscopy. We have developed a gastroesophageal electrode capable of atrial and ventricular pacing. The flexible polythene gastroesophageal electrode is passed into the stomach under light sedation. Five ring electrodes, now positioned in the lower esophagus, are used for atrial pacing. A point source (cathode) on the distal tip of the electrode, now positioned in the gastric fundus, is used for ventricular pacing. Two configurations of atrial and ventricular pacing were compared: unipolar and bipolar. During unipolar ventricular pacing the indifferent electrode (anode) was a high impedance chest pad. For bipolar ventricular pacing the indifferent electrode was a ring electrodes placed 2 cm proximal to the tip. Unipolar atrial pacing was performed with 1 of 5 proximal ring electrodes acting as cathode ("cathodic") or as anode ("anodic") in conjunction with a chest pad. Bipolar atrial pacing was performed using combinations of 2 of 5 ring electrodes. Atrial capture was obtained in all 55 subjects attempted. When all electrode combinations were compared, atrial capture was significantly more frequent using the bipolar approach (153/210 bipolar, 65/210 unipolar; t = 7.37, P < 0.001). For unipolar atrial pacing, cathodic stimulation (from esophagus) was more successful than anodic stimulation (cathodic 62/105, anodic 20/105; t = 5.81, P < 0.001). In 43 subjects attempted unipolar ventricular pacing resulted in a higher frequency of capture than the bipolar approach (unipolar 41/43 (95.3%), bipolar 19/43 (44.2%); P < 0.001). In conclusion, atrial pacing was optimal using pairs of ring electrodes ("bipolar") while ventricular pacing was optimal using the distal electrode tip (cathode) in conjunction with a chest pad electrode ("unipolar"). This gastroesophageal electrode may be useful in the emergency management of acute bradyarrhythmias and for elective electrophysiological studies.     

Distributed dynamic programming for discrete-time stochastic control, and idempotent algorithms

Idempotent methods have been found to be extremely fast for the solution of dynamic programming equations associated with deterministic control problems. The original methods exploited the idempotent (e.g., max-plus) linearity of the associated semigroup operator. It is now known that curse-of-dimensionality-free idempotent methods do not require this linearity. Instead, it is sufficient that certain solution forms are retained through application of the associated semigroup operator. Here, we see that idempotent methods may be used to solve some classes of stochastic control problems. The key is the use of the idempotent distributive property. We demonstrate this approach for a class of nonlinear, discrete-time stochastic control problems.     

Robust/H∞ filtering for nonlinear systems

A robust (or H_∞) approach to filtering for nonlinear systems is considered. A bound on the estimate error as a function of the disturbance energy is obtained. The corresponding dynamic programming equation is a first-order PDE. This has computational ramifications. The case where the measurements are discrete time is considered also. A numerical method is discussed.     

Robust control and differential games on a finite time horizon

It is well known that theH control problem has a state space formulation in terms of differential games. For a finite time horizon control problem, the analogous differential game is considered. The disturbance is the control for the maximizing player. In order to allow forL ² disturbances, the controls for at least one player must be allowed to be unbounded. It is shown that the value of the game is the viscosity solution of the corresponding Isaacs equation under rather general conditions.     

Agency Effects in Human–Computer Interaction

The studies presented in this article explore a human-centered conceptualization of agents and agency based on the observation that people attribute agency to sufficiently complex interactive systems. Although agency attribution appears to be an unconscious human response, findings from social psychology, affective computing, and perceptual-motor studies suggest agency attribution influences human–computer interaction (HCI). Three studies are presented that examine whether recent findings on agency attribution in physical environments also apply in the virtual environments characteristic of HCI. Results of the studies indicate that agency effects operate in desktop computing environments. Agency effects, however, appear to be influenced by learning effects that preserve a previously observed relationship between perception and action but alter how this effect is expressed. Results suggest that there are both bottom-up and top-down contributions to agency effects in HCI.     

Robust/H∞ filtering for nonlinear systems

A robust (or H_∞) approach to filtering for nonlinear systems is considered. A bound on the estimate error as a function of the disturbance energy is obtained. The corresponding dynamic programming equation is a first-order PDE. This has computational ramifications. The case where the measurements are discrete time is considered also. A numerical method is discussed.     

A uniqueness result for the isaacs equation corresponding to nonlinear H∞ control

The dynamic programming equation (DPE) corresponding to nonlinear H_∞ control is considered. When the cost grows quadratically in the state, it is well known that there may be an infinite number of viscosity solutions to the DPE. In fact, there may be more than one classical solution when a classical solution exists. For the case of fixed feedback control, it is shown that there exists a unique viscosity solution in the class of solutions meeting a certain growth condition, and a representation in terms of available storage is obtained. For the active control case, where the H_∞ problem is represented by a differential game, a similar representation result is obtained under the assumption of existence of a suboptimal feedback control. This research was partially supported by AFOSR under Grant F49620-95-1-0296 and by ONR under Grant N0014-96-1-0267.     

Max-plus eigenvector representations for solution of nonlinear H/sub /spl infin// problems: basic concepts

The H/sub /spl infin// problem for a nonlinear system is considered. The corresponding dynamic programming equation is a fully nonlinear, first-order, steady-state partial differential equation (PDE), possessing a term which is quadratic in the gradient. The solutions are typically nonsmooth, and further, there is nonuniqueness among the class of viscosity solutions. In the case where one tests a feedback control to see if it yields an H/sub /spl infin// controller, the PDE is a Hamilton-Jacobi-Bellman equation. In the case where the "optimal" feedback control is being determined as well, the problem takes the form of a differential game, and the PDE is, in general, an Isaacs equation. The computation of the solution of a nonlinear, steady-state, first-order PDE is typically quite difficult. In this paper, we develop an entirely new class of methods for obtaining the "correct" solution of such PDEs. These methods are based on the linearity of the associated semigroup over the max-plus (or, in some cases, min-plus) algebra. In particular, solution of the PDE is reduced to solution of a max-plus (or min-plus) eigenvector problem for known unique eigenvalue 0 (the max-plus multiplicative identity). It is demonstrated that the eigenvector is unique, and that the power method converges to it. An example is included.     

Robust Limits of Risk Sensitive Nonlinear Filters

Deterministic filter models are considered, and a criterion for a deterministic filter to be robust is introduced. Among the candidates for robust deterministic filters are so-called minimax estimators. In the second part of the paper, a risk sensitive stochastic approach to nonlinear filtering is considered, in which the traditional expected mean squared error criterion is replaced by an expected exponential-of-mean squared error. Minimax filters are obtained as totally risk averse limits of risk sensitive filters. Date received: July 22, 1999. Date revised: June 19, 2000.