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Deterministic and stochastic approaches to handle uncertainties may incur very different complexities in computation and memory, in addition to different uncertainty models. For linear systems with delay and rate constrained communications between the observer and controller, previous work shows that the deterministic approach l_infty control has low complexity but only handles bounded disturbance. In this paper, we take a stochastic approach and propose an LQ controller that can handle arbitrarily large disturbance but has large complexity in time/space. The differences in robustness and complexity of the l_infty and LQ controllers motivate the design of a hybrid controller that interpolates between the two: The l_infty controller is applied when the disturbance is not too large (normal mode) and the LQ controller is resorted to otherwise (acute mode). We characterize the switching behavior between the normal and acute modes. Using theoretical bounds and supplementary numerical experiments, we show that the hybrid controller can achieve a sweet spot in robustness-complexity tradeoff, ie, reject occasional large disturbance while operating with low complexity most of the time. 

Nervous systems sense, communicate, compute, and actuate movement, using distributed hardware with tradeoffs in speed and accuracy. The resulting sensorimotor control is nevertheless remarkably fast and accurate due to highly effective layered architectures. However, such architectures have received little attention in neuroscience due to the lack of theory that connects the system and hardware level speed-accuracy tradeoffs. In this paper, we present a theoretical framework that connects the speed-accuracy tradeoffs of sensorimotor control and neurophysiology. We characterize how the component SATs in spiking neuron communication and their sensory and muscle endpoints constrain the system SATs in both stochastic and deterministic models. The results show that appropriate speed -accuracy diversity at the neurons/muscles levels allow nervous systems to improve the speed and accuracy in control performance despite using slow or inaccurate hardware. Then, we characterize the fundamental limits of layered control systems and show that appropriate diversity in planning and reaction layers leads to both fast and accurate system despite being composed of slow or inaccurate layers. We term these phenomena “Diversity Sweet Spots.” The theory presented here is illustrated in a companion paper, which introduces simple demos and a new inexpensive and easy-to-use experimental platform. 

This paper describes several surprisingly rich but simple demos and a new experimental platform for human sensorimotor control research and also controls education. The platform safely simulates a canonical sensorimotor task of riding a mountain bike down a steep, twisting, bumpy trail using a standard display and inexpensive off-the-shelf gaming steering wheel with a force feedback motor. We use the platform to verify our theory, presented in a companion paper. The theory tells how component hardware speed-accuracy tradeoffs (SATs) in control loops impose corresponding SATs at the system level and how effective architectures mitigate the deleterious impact of hardware SATs through layering and “diversity sweet spots” (DSSs). Specifically, we measure the impacts on system performance of delays, quantization, and uncertainties in sensorimotor control loops, both within the subject's nervous system and added externally via software in the platform. This provides a remarkably rich test of the theory, which is consistent with all preliminary data. Moreover, as the theory predicted, subjects effectively multiplex specific higher layer planning/tracking of the trail using vision with lower layer rejection of unseen bump disturbances using reflexes. In contrast, humans multitask badly on tasks that do not naturally distribute across layers (e.g. texting and driving). The platform is cheap to build and easy to program for both research and education purposes, yet verifies our theory, which is aimed at closing a crucial gap between neurophysiology and sensorimotor control. The platform can be downloaded at https://github.com/Doyle-Lab/WheelCon. 

Nervous systems use highly effective layered architectures in the sensorimotor control system to minimize the harmful effects of delay and inaccuracy in biological components. To study what makes effective architectures, we develop a theoretical framework that connects the component speed–accuracy trade-offs (SATs) with system SATs and characterizes the system performance of a layered control system. We show that diversity in layers (e.g., planning and reflex) allows fast and accurate sensorimotor control, even when each layer uses slow or inaccurate components. We term such phenomena “diversity-enabled sweet spots (DESSs).” DESSs explain and link the extreme heterogeneities in axon sizes and numbers and the resulting robust performance in sensorimotor control.