Property:Abstract
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A
We analyze the performance of an approximate distributed Kalman filter proposed
in recent work on distributed coordination. This approach to
distributed estimation is novel in that it admits a systematic
analysis of its performance as various network quantities such as
connection density, topology, and bandwidth are varied. Our main
contribution is a frequency-domain characterization of the
distributed estimator's steady-state performance; this is quantified in terms
of a special matrix associated with the connection topology called
the graph Laplacian, and also the rate of message exchange
between immediate neighbors in the communication network. +
C
We consider a discrete time linear feedback control system with additive noise where the control signals are
to be sent across a data link from the controller to the actuators. Due to network constraints it is desired to reduce the transmission frequency of the control signals. We show that by
including a finite sequence of predicted control signals in each
communication packet the frequency of transmission can be reduced by transmitting only when the previously sent sequence has run out. The price to pay is that the closed loop error
will increase. We introduce a novel communication protocol, which we call Input Difference Transmission Scheme (IDTS), which transmits control packets when the difference between the newly computed control sequence and the predicted control
sequence previously transmitted is larger than a certain thresh-
old. This threshold is a design parameter and we show how
the closed loop behavior varies with this threshold. Simulation
results are provided to augment the theory and show how the
protocol works. +
P
We consider a network of identical agents with arbitrary linear time-invariant (LTI) dynamics such that the network reaches consensus asymptotically. Uniform time delay is taken into account in the communication channels. The goal of this paper is to maximize the delay (so-called delay margin) that the system can tolerate before becoming unstable by implementing a low-order controller to a single agent. A parametric design method is investigated to guarantee the stability and consensusability. The set of all feasible low-order controllers based on the frequency response data is characterized by combining the argument principle and the generalized Nyquist criterion. Based on this, the algorithm of computing the delay margin is proposed for a given controlled agent. By combining all the possible margins for each controlled agent, we then can obtain the maximal delay margin for the whole network and the corresponding local controller. +
L
We consider identifiability of linear systems driven by white noise using a combination of distributional and time series measurements. Specifically, we assume that the system has no control inputs available and can only be observed at stationarity. The user is able to measure the full stationary state distribution as well as observe time correlations for small subsets of the state. We formulate theoretical conditions on identifiability of parameters from distributional information alone. We then give a sufficient condition and an effective necessary condition for identifiability using a combination of distributional and time series measurements. We illustrate the ideas with some simple examples as well as a biologically inspired example of a transcription and degradation process. +
R
We consider mobile robot navigation in dense human crowds. In particular, we explore two questions. Can we design a navigation algorithm that encourages humans to coop- erate with a robot? Would such cooperation improve navigation performance? We address the first question by developing a probabilistic predictive model of cooperative collision avoidance and goal-oriented behavior. Specifically, this model extends the recently introduced interacting Gaussian processes approach to the case of multiple goals and stochastic movement duration. We answer the second question by empirically validating our model in a natural environment (a university cafeteria), and in the process, carry out the first extensive quantitative study of robot navigation in dense human crowds (completing 488 runs). The âmultiple goalâ interacting Gaussian processes algorithm performs comparably with human teleoperators in crowd densities near 1 person/m2, while a state of the art noncooperative planner exhibits unsafe behavior more than 3 times as often as our planner. Furthermore, a reactive planner based on the âdynamic windowâ approachâwidely used for robotic tour guide experimentsâfails for crowd densities above 0.55 people/m2. We conclude that a cooperation model is critical for safe and efficient robot navigation in dense human crowds. +
O
We consider optimal control for a system subject to temporal logic constraints. We minimize a weighted average cost function that generalizes the commonly used average cost function from discrete-time optimal control. Dynamic programming algorithms are used to construct an optimal trajectory for the system that minimizes the cost function while satisfying a temporal logic specification. Constructing an optimal trajectory takes only polynomially more time than constructing a feasible trajectory. We demonstrate our methods on simulations of autonomous driving and robotic surveillance tasks. +
B
We consider the bootstrapping problem, which consists in learning a model of the agent's sensors and actuators starting from zero prior informa- tion, and we take the problem of servoing as a cross-modal task to validate the learned models. We study the class of sensors with bilinear dynamics, for which the derivative of the observations is a bilinear form of the control commands and the observations themselves. This class of models is simple, yet general enough to represent the main phenomena of three representative sensors (field sampler, camera, and range-finder), apparently very different from one another. It also allows a bootstrapping algorithm based on Hebbian learning, and a simple bioplausible control strategy. The convergence proper- ties of learning and control are demonstrated with extensive simulations and by analytical arguments. +
R
We consider the control of dynamically decoupled
subsystems whose state vectors are coupled in the cost
function of a finite horizon optimal control problem. For a
given cost structure, we generate distributed optimal control
problems for each subsystem and establish that a distributed
receding horizon implementation is asymptotically stabilizing.
The communication requirements at each receding
horizon update include the exchange of the previous optimal
control trajectory between subsystems with coupling in
the cost function. The key requirements for stability are that
each distributed optimal control not deviate too far from the
previous one, and that the receding horizon updates happen
sufficiently fast. A simulation example of multi-vehicle
formation stabilization is provided. +
D
We consider the control of interacting subsystems whose dynamics and constraints
are uncoupled, but whose state vectors are coupled non-separably in a single centralized
cost function of a finite horizon optimal control problem. For a given centralized
cost structure, we generate distributed optimal control problems for each subsystem
and establish that the distributed receding horizon implementation is asymptotically
stabilizing. The communication requirements between subsystems with coupling in the
cost function are that each subsystem obtain the previous optimal control trajectory of
those subsystems at each receding horizon update. The key requirements for stability
are that each distributed optimal control not deviate too far from the previous optimal
control, and that the receding horizon updates happen sufficiently fast. The theory is
applied in simulation for stabilization of a formation of vehicles. +
M
We consider the estimation of a vector state based on m measurements that can be potentially manipulated by an adversary. The attacker is assumed to have limited resources and can only manipulate up to l of the m measurements. However, it can the compromise measurements arbitrarily. The problem is formulated as a minimax optimization, where one seeks to construct an optimal estimator that minimizes the âworst-caseâ error against all possible manipulations by the attacker and all possible sensor noises. We show that if the system is not observable after removing 2l sensors, then the worst-case error is infinite, regardless of the estimation strategy. If the system remains observable after removing arbitrary set of 2l sensor, we prove that the optimal state estimation can be computed by solving a semidefinite programming problem. A numerical example is provided to illustrate the effectiveness of the proposed state estimator. +
R
We consider the maneuver planning problem for automated vehicles when they share the road with human- driven cars and interact with each other using a finite set of maneuvers. Each maneuver is calculated considering input constraints, actuator disturbances and sensor noise, so that we can use a maneuver automaton to perform high-level planning that is robust against low-level effects. In order to model the behavior of human-driven cars in response to the intent of the automated vehicle, we use control improvisation to build a probabilistic model. To accommodate for potential mismatches between the learned human model and human driving behaviors, we use a conditional value-at-risk objective function to obtain the optimal policy for the automated vehicle. We demonstrate through simulations that our motion planning framework allows an automated vehicle to exploit human behaviors with different levels of robustness. +
A
We consider the problem of attitude stabilization using exclusively visual sensory input, and we look for a solution which can satisfy the constraints of a ``bio-plausible'' computation. We obtain a PD controller which is a bilinear form of the goal image, and the current and delayed visual input. Moreover, this controller can be learned using classic neural networks algorithms. The structure of the resulting computation, derived from general principles by imposing a bilinear computation, has striking resemblances with existing models for visual information processing in insects (Reichardt Correlators and lobula plate tangential cells). We validate the algorithms using faithful simulations of the fruit fly visual input. +
C
We consider the problem of average consensus seeking in networked multi-agent systems. Based
on local information and a simple distributed algorithm, states of all agents automatically converge to
the average value of the initial conditions, where the convergence speed is determined by the algebraic
connectivity of the underlying communication network. In order to achieve an average consensus quickly,
we propose a new type of consensus protocol, multi-hop relay protocol, in which each agent expands
its knowledge by employing multi-hop communication links. We explicitly show that multi-hop relay
protocol increases the convergence speed without physically changing the network topology. Moreover,
accumulated delays along communication links are discussed. We show that, for multi-hop relay protocol,
the faster the protocol converges, the more sensitive it is to the delay. This tradeoff is identified when
we investigate the stable delay margin using frequency sweep method. +
D
We consider the problem of controlling a linear time invariant process when the controller is located at a location remote from where the sensor measurements are being generated. The communication from the sensor to the controller is supported by a communication network with arbitrary topology composed of analog erasure channels. Using a separation principle, we prove that the optimal LQG controller consists of an LQ optimal regulator along with an estimator that estimates the state of the process across the communication network mentioned above. We then determine the optimal information processing strategy that should be followed by each node in the network so that the estimator is able to compute the best possible estimate in the minimum mean squared error sense. The algorithm is optimal for any packet-dropping process and at every time step, even though it is recursive and hence requires a constant amount of memory, processing and transmission at every node in the network per time step. For the case when the packet drop processes are memoryless and independent across links, we analyze the stability properties and the performance of the closed loop system. The algorithm is an attempt to escape the more commonly used viewpoint of treating a network of communication links as a single end-to-end link with the probability of successful transmission determined by some measure of the reliability of the network. +
We consider the problem of designing distributed control protocols -for aircraft vehicle management systems- that cooperatively allocate electric power while meeting certain higher level goals and requirements, and dynamically reacting to the changes in the internal system state and external environment. A decentralized control problem is posed where each power distribution unit is equipped with a controller that implements a local protocol to allocate power to a certain subset of loads. We use linear temporal logic as the specification language for describing correct behaviors of the system (e.g., safe operating conditions) as well as the admissible dynamic behavior of the environment due to, for example, wind gusts and changes in system health. We start with a global specification and decompose it into local ones. These decompositions allow the protocols for each local controller to be separately synthe- sized and locally implemented while guaranteeing the global specifications to hold. Through a design example, we show that by refining the interface rules between power distribution units, it is possible to reduce the total power requirement. +
R
We consider the problem of designing policies for partially observable Markov decision processes (POMDPs) with dynamic coherent risk objectives. Synthesizing risk-averse optimal policies for POMDPs requires infinite memory and thus undecidable. To overcome this difficulty, we propose a method based on bounded policy iteration for designing stochastic but finite state (memory) controllers, which takes advantage of standard convex optimization methods. Given a memory budget and optimality criterion, the proposed method modifies the stochastic finite state controller leading to sub-optimal solutions with lower coherent risk. +
We consider the problem of designing policies for Markov decision processes (MDPs) with dynamic coherent risk objectives and constraints. We begin by formulating the problem in a Lagrangian framework. Under the assumption that the risk objectives and constraints can be represented by a Markov risk transition mapping, we propose an optimization-based method to synthesize Markovian policies that lower-bound the constrained risk-averse problem. We demonstrate that the formulated optimization problems are in the form of difference convex programs (DCPs) and can be solved by the disciplined convex-concave programming (DCCP) framework. We show that these results generalize linear programs for constrained MDPs with total discounted expected costs and constraints. Finally, we illustrate the effectiveness of the proposed method with numerical experiments on a rover navigatio +
C
We consider the problem of designing policies for Markov decision processes (MDPs) with dynamic coherent risk objectives and constraints. We begin by formulating the problem in a Lagrangian framework. Under the assumption that the risk objectives and constraints can be represented by a Markov risk transition mapping, we propose an optimization-based method to synthesize Markovian policies that lower-bound the constrained risk-averse problem. We demonstrate that the formulated optimization problems are in the form of difference convex programs (DCPs) and can be solved by the disciplined convex-concave programming (DCCP) framework. We show that these results generalize linear programs for constrained MDPs with total discounted expected costs and constraints. Finally, we illustrate the effectiveness of the proposed method with numerical experiments on a rover navigation problem involving conditional-value-at-risk (CVaR) and entropic-value-at-risk (EVaR) coherent risk measures. +
D
Dynamic State Estimation in Distributed Aircraft Electric Control Systems via Adaptive Submodularity +
We consider the problem of estimating the discrete state of an aircraft electric system under a distributed control architecture through active sensing. The main idea is to use a set of controllable switches to reconfigure the system in order to gather more information about the unknown state. By adaptively making a sequence of reconfiguration decisions with uncertain outcome and by correlating the measurements and prior information to make the next decision, we aim to reduce the uncertainty. A greedy strategy is developed that maximizes the one-step expected uncertainty reduction. By exploiting recent results on adaptive submodularity, we give theoretical guarantees on the worst-case performance of the greedy strategy. We apply the proposed method in a fault de- tection scenario where the discrete state captures possible faults in various circuit components. In addition, simple abstraction rules are proposed to alleviate state space explosion and to scale up the strategy. Finally, the efficiency of the proposed method is demonstrated empirically on different circuits. +
E
We consider the problem of estimating the subset of test conditions under which a simplified model—or set of simplified models—accurately approximates the behavior of a true system. We approach the problem by proposing a compact set of possible test conditions, and an unknown but samplable continous validity function over that set that quantifies the accuracy of the model under each possible condition. We propose a novel Bayes estimator that optimally directs function sampling to greedily minimize the expected posterior misclassification rate of the valid set, which we call minimum posterior misclassification sampling (GP-MPM), and we show that the the method can be extended to approximate the valid sets of a partially ordered set of models, with sample complexity growing sublinearly with the number of models. In testing against a safety-focused model, we show that the algorithm’s estimated valid set approaches the true valid set much more quickly than undirected sampling, even with small sample sizes. +
