Property:Abstract
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A
A modal interface contract theory for guarded input/output automata with an application in traffic system design +
To contribute to efforts of bringing formal design-by-contract methods to hybrid systems, we introduce a variant of modal interface contract theory based on input/output automata with guarded transitions. We present an algebra of operators for interface composition, contract composition, contract conjunction, contract refinement and some theorems demonstrating that our contract object has reasonably universal semantics. As an application, we apply our framework to the design of a networked control systems of traffic. +
M
Traditional feedback control systems give little attention to issues associated with the flow of information through the feedback loop. Typically implemented with dedicated communication links that deliver nearly precise, reliable, and non-delayed information, researchers have not needed to concern themselves with issues related to quantized, delayed, and even lost information. With the advent of newer technologies and application areas that pass information through non-reliable networks, these issues cannot be ignored. In recent years the field of Networked Control Systems (NCS) has emerged to describe situations where these issues are present. The research in this field focuses on quantifying performance degradations in the presence of network effects and proposing algorithms for managing the information flow to counter those negative effects. In this thesis I propose and analyze algorithms for managing information flow for several Networked Control Systems scenarios: state estimation with lossy measurement signals, using input buffers to reduce the frequency of communication with a remote plant, and performing state estimation when control signals are transmitted to a remote plant via a lossy communication link with no acknowledgement signal at the estimator. Multi-agent coordinated control systems serve as a prime example of an emerging area of feedback control systems that utilize feedback loops with information passed through possibly imperfect communication networks. In these systems, agents use a communication network to exchange information in order to achieve a desired global ob jective. Hence, managing the information flow has a direct impact on the performance of the system. I also explore this area by focusing on the problem of multi-agent average consensus. I propose an algorithm based on a hierarchical decomposition of the communication topology to speed up the time to convergence. For all these topics I focus on designing intuitive algorithms that intelligently manage the information flow and provide analysis and simulations to illustrate their effectiveness.
O
Observability and Local Observer Construction for Unknown Parameters in Linearly and Nonlinearly Parameterized Systems +
Using geometric concepts from observability theory for nonlinear
systems, we propose an approach for parameter estimation for linearly and
nonlinearly parameterized systems that does not rely on persistence of
excitation conditions. The proposed approach relies on extending a
parameter estimation problem to a state estimation problem by introducing
the parameters as auxiliary state variables. Applying tools from geometric
nonlinear control theory we give an observability check for parameters,
and, in case the parameters are observable, we provide a constructive way
to design a local parameter observer with established speed of
convergence. +
S
Using tools from dynamical systems and
systems identification we develop a framework for the study of
decomposition of
human motion. The objective is understanding human motion by decomposing
it into a sequence of elementary building blocks, which we refer to as
movemes, that belong to a known alphabet of dynamical
systems.
We develop classification and segmentation algorithms with error analysis
and we test them on human drawing data. +
D
Using tools from dynamical systems and systems identification we develop a framework for the study
of primitives for human motion, which we refer to as movemes. The objective is understanding human
motion by decomposing it into a sequence of elementary building blocks that belong to a known alphabet
of dynamical systems. In this work we address the problem of defining conditions under which
collections of signals are well-posed according to a dynamical model class M and then can generate
movemes. Based on the assumption of well-posedness, we develop segmentation and classification algorithms
in order to reduce a complex activity into the sequence of movemes that have generated it.
Using examples we show that the definition of well-posedness can be applied in practice and show
analytically that the proposed algorithms are robust with respect to noise and model uncertainty. We
test our ideas on data sampled from five human subjects who were drawing figures using a computer
mouse. Our experiments show that we are able to distinguish between movemes and recognize them
even when they take place in activities containing more than one moveme at a time. +
P
Using tools from dynamical systems theory and systems identification theory
we develop the study of primitives for human motion which we refer to as <i>movemes</i>. We
introduce basic definitions of dynamical independence of LTI systems and segmentability of
signals and, for two dimensional motions, we develop classification and segmentation algorithms.
We test our ideas on data sampled from four human subjects who were engaged in a
simple real-life activity including two movemes. Our experiments show that we are able to
distinguish between the two movemes and recognise them even when they take place in an
activity containing more than one moveme. +
I
Vehicles in formation often lack global information regarding the state of
all the vehicles, a deficiency which can lead to instability and poor performance. In
this paper, we demonstrate how exchange of minimal amounts of information between
vehicles can be designed to realize a dynamical system which supplies each vehicle with
a shared reference trajectory. When the information flow law is placed in the control
loop, a separation principle is proven which guarantees stability of the formation and
convergence of the information flow law regardless of the information flow topology. +
D
We address the problem of estimating discrete variables in a class of deterministic
transition systems where the continuous variables are available for measurement. This
simplified scenario has practical interest, for example, in the case of decentralized multi-robot
systems. In these systems, the continuous variables represent physical quantities such as the
position and velocity of a robot, while discrete variables may represent the state of the logical
system that is used for control and coordination. We propose a novel approach to the
estimation of discrete variables using basic lattice theory that overcomes some of the severe
complexity issues encountered in previous work. We show how to construct the proposed
estimator for a multi-robot system performing a cooperative assignment task. +
O
We analyze a jump linear Markov system being stabilized using a zero-order hold controller. We consider the case when the Markov state is associated with the probability distribution of a measured variable. We assume that the Markov state is not known, but rather is being estimated based on the observations of the variable. We present conditions for the stability of such a system and also solve the optimal LQR control problem for the case when the state estimate update uses only the last observation value. In particular we consider a suboptimal causal version of the Viterbi estimation algorithm and show that a separtion property does not hold between the optimal control and the Markov state estimate. Some simple examples are also presented. +
S
We analyze a network of dynamic agents where the
topology of the network specifies the information
flow between the agents. We present an analysis
method for such a system for both consensus and
formation stabilization problems. We consider the
case of agent dynamics being a single integrator in
more detail to show the general features introduced
by the information flow. Then we show that the
method of analysis can be extended to more general cases of complicated agent dynamics, non-ideal
links for information flow, etc. We also consider the
case when the topology of the network is changing
over time. The focus of the paper is on obtaining
conditions for the stability of the formation that
can be checked in a decentralized way. Some simple examples are also presented. +
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. +
