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  1. 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.
  2. We present a simple model-free control algorithm that is able to robustly learn and stabilize an unknown discrete time linear system with full control and state feedback subject to arbitrary bounded disturbance and noise sequences. The controller does not require any prior knowledge of the system dynamics, disturbances or noise, yet can guarantee robust stability, uniform asymptotic bounds and uniform worst-case bounds on the state-deviation. Rather than the algorithm itself, we would like to highlight the new approach taken towards robust stability analysis which served as a key enabler in providing the presented stability and performance guarantees. We will conclude with simulation results that show that despite the generality and simplicity, the controller demonstrates good closed-loop performance.
  3. 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). Themore »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« less
  4. We will present a new general framework for robust and adaptive control that allows for distributed and scalable learning and control of large systems of interconnected linear subsystems. The control method is demonstrated for a linear time-invariant system with bounded parameter uncertainties, disturbances and noise. The presented scheme continuously collects measurements to reduce the uncertainty about the system parameters and adapts dynamic robust controllers online in a stable and performance-improving way. A key enabler for our approach is choosing a time-varying dynamic controller implementation, inspired by recent work on System Level Synthesis [1]. We leverage a new robustness result for this implementation to propose a general robust adaptive control algorithm. In particular, the algorithm allows us to impose communication and delay constraints on the controller implementation and is formulated as a sequence of robust optimization problems that can be solved in a distributed manner. The proposed control methodology performs particularly well when the interconnection between systems is sparse and the dynamics of local regions of subsystems depend only on a small number of parameters. As we will show on a five-dimensional exemplary chain-system, the algorithm can utilize system structure to efficiently learn and control the entire system while respecting communicationmore »and implementation constraints. Moreover, although current theoretical results require the assumption of small initial uncertainties to guarantee robustness, we will present simulations that show good closed-loop performance even in the case of large uncertainties, which suggests that this assumption is not critical for the presented technique and future work will focus on providing less conservative guarantees.« less
  5. 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.