Risk-sensitivity and the mean-variance trade-off: decision making in sensorimotor control.

Numerous psychophysical studies suggest that the sensorimotor system chooses actions that optimize the average cost associated with a movement. Recently, however, violations of this hypothesis have been reported in line with economic theories of decision-making that not only consider the mean payoff, but are also sensitive to risk, that is the variability of the payoff. Here, we examine the hypothesis that risk-sensitivity in sensorimotor control arises as a mean-variance trade-off in movement costs. We designed a motor task in which participants could choose between a sure motor action that resulted in a fixed amount of effort and a risky motor action that resulted in a variable amount of effort that could be either lower or higher than the fixed effort. By changing the mean effort of the risky action while experimentally fixing its variance, we determined indifference points at which participants chose equiprobably between the sure, fixed amount of effort option and the risky, variable effort option. Depending on whether participants accepted a variable effort with a mean that was higher, lower or equal to the fixed effort, they could be classified as risk-seeking, risk-averse or risk-neutral. Most subjects were risk-sensitive in our task consistent with a mean-variance trade-off in effort, thereby, underlining the importance of risk-sensitivity in computational models of sensorimotor control.

Risk sensitivity in a motor task with speed-accuracy trade-off.

When a racing driver steers a car around a sharp bend, there is a trade-off between speed and accuracy, in that high speed can lead to a skid whereas a low speed increases lap time, both of which can adversely affect the driver's payoff function. While speed-accuracy trade-offs have been studied extensively, their susceptibility to risk sensitivity is much less understood, since most theories of motor control are risk neutral with respect to payoff, i.e., they only consider mean payoffs and ignore payoff variability. Here we investigate how individual risk attitudes impact a motor task that involves such a speed-accuracy trade-off. We designed an experiment where a target had to be hit and the reward (given in points) increased as a function of both subjects' endpoint accuracy and endpoint velocity. As faster movements lead to poorer endpoint accuracy, the variance of the reward increased for higher velocities. We tested subjects on two reward conditions that had the same mean reward but differed in the variance of the reward. A risk-neutral account predicts that subjects should only maximize the mean reward and hence perform identically in the two conditions. In contrast, we found that some (risk-averse) subjects chose to move with lower velocities and other (risk-seeking) subjects with higher velocities in the condition with higher reward variance (risk). This behavior is suboptimal with regard to maximizing the mean number of points but is in accordance with a risk-sensitive account of movement selection. Our study suggests that individual risk sensitivity is an important factor in motor tasks with speed-accuracy trade-offs.

Dynamic programming solutions for decentralized state-feedback LQG problems with communication delays

This paper presents explicit solutions for a class of decentralized LQG problems in which players communicate their states with delays. A method for decomposing the Bellman equation into a hierarchy of independent subproblems is introduced. Using this decomposition, all of the gains for the optimal controller are computed from the solution of a single algebraic Riccati equation. © 2012 AACC American Automatic Control Council).

Product life trade-offs: what if products fail early?

Increasing product life allows the embodied emissions in products to be spread across a longer period but can mean that opportunities to improve use-phase efficiency are foregone. In this paper, a model that evaluates this trade-off is presented and used to estimate the optimal product life for a range of metal-intensive products. Two strategies that have potential to save emissions are explored: (1) adding extra embodied emissions to make products more sturdy, increasing product life, and (2) increasing frequency of use, causing early product failure to take advantage of improvements in use-phase efficiency. These strategies are evaluated for two specific case studies (long-life washing machines and more frequent use of vehicles through car clubs) and for a range of embodied and use-phase intensive products under different use-phase improvement rate assumptions. Particular emphasis is placed on the fact that products often fail neither at their design life nor at their optimal life. Policy recommendations are then made regarding the targeting of these strategies according to product characteristics and the timing of typical product failure relative to optimal product life.

Output feedback H2 model matching for decentralized systems with delays

This paper gives a new solution to the output feedback H2 model matching problem for a large class of delayed information sharing patterns. Existing methods for similar problems typically reduce the decentralized problem to a centralized problem of higher state dimension. In contrast, this paper demonstrates that the decentralized model matching solution can be constructed from the original centralized solution via quadratic programming. © 2013 AACC American Automatic Control Council.

Design trade-offs for energy regeneration and control in vehicle suspensions

This paper investigates the fundamental trade-offs involved in designing energy-regenerative suspensions, in particular, focusing on efficiency of power extraction and its effect on vehicle dynamics and control. It is shown that typical regenerative devices making use of linear-to-rotational elements can be modelled as a parallel arrangement of an inerter and a dissipative admittance. Taking account of typical adjustable parameters of the generator, it is shown, for a given suspension damping coefficient, that the power efficiency ratio scales with inertance. For a typical passenger vehicle, it is shown that there is a feasible compromise, namely that good efficiency is achievable with an inertance value that is not detrimental to vehicle performance. A prototype is designed and tested with a resistive termination and experimental results show good agreement between ideal and experimental admittances. The possibility to use dynamic (rather than purely resistive) loads to improve vehicle control without limiting the energy recovery is discussed. © 2013 Copyright Taylor and Francis Group, LLC.