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N
This thesis focuses on understanding the use of air injection as a
means of controlling rotating stall in an axial flow compressor,
involving modeling, dynamical systems analysis, and experimental
investigations.
<p>
The first step towards this understanding was the development
of a low order model for air injection control, the starting point of
which was the Moore and Greitzer model for axial flow compressors. The
Moore and Greitzer model was extended to include the effects of air
injection and bifurcation analysis was performed to determine how the closed
loop system dynamics are different from those of the open loop system.
This low order model was then used to determine the optimal placement of
the air injection actuators.
<p>
Experimental work focused on verifying that the low order model,
developed for air injection actuation, qualitatively captured the
behavior of the Caltech compressor rig. Open loop tests were performed
to determine how the placement of the air injectors on the rig
affected the performance of the compressor. The positioning of the air
injectors that provided the greatest control authority were used in
the development of air injection controllers for rotating stall. The
controllers resulted in complete elimination of the hysteresis
associated with rotating stall. The use of a throttle actuator for the
control of the surge dynamics was investigated, and then combined with
an air injection controller for rotating stall; the resulting
controller performed quite well in throttle disturbance rejection
tests.
<p>
A higher order model was developed to qualitatively match the
experimental results with a simulation. The results of this modeling
effort compared quite well with the experimental results for the open
loop behavior of the Caltech rig. The details of how the air injection
actuators affect the compressor flow were included in this model, and
the simulation predicted the same optimal controller that was
developed through experimentation.
<p>
The development of the higher order model also included the
investigation of systematic methods for determining the simulation parameters.
Based on experimental measurements of compression system transients, the
open loop simulation parameters were identified, including values for
the compressor performance characteristic in regions where direct
measurements were not possible. These methods also provided information on
parameters used in the modeling of the pressure rise delivered by the
compressor under unsteady flow conditions.
<p>
C
This tutorial describes TuLiP, the Temporal Logic Planning toolbox, a collection of tools for designing controllers
for hybrid systems from specifications in temporal logic. The
tools support a workflow that starts from a description of
desired behavior, and of the system to be controlled. The
system can have discrete state, or be a hybrid dynamical
system with a mixed discrete and continuous state space. The
desired behavior can be represented with temporal logic and
discrete transition systems. The system description can include
uncontrollable variables that take discrete or continuous values,
and represent disturbances and other environmental factors
that affect the dynamics, as well as communication signals that
affect controller decisions.
A control design problem is solved in phases that involve
abstraction, discrete synthesis, and continuous feedback control.
Abstraction yields a discrete description of system dynamics in
logic. For piecewise affine dynamical systems, this abstraction
is constructed automatically, guided by the geometry of the dynamics
and under logical constraints from the specification. The
resulting logic formulae describe admissible discrete behaviors
that capture both controlled and environment variables. The
discrete description resulting from abstraction is then conjoined
with the desired logic specification. To find a controller, the
toolbox solves a game of infinite duration. Existence of a discrete
(winning) strategy for the controlled variables in this game is a
proof certificate for the existence of a controller for the original
problem, which guarantees satisfaction of the specification. This
discrete strategy, concretized by using continuous controllers,
yields a feedback controller for the original hybrid system. The
toolbox frontend is written in Python, with backends in C,
Python, and Cython.
The tutorial starts with an overview of the theory behind
TuLiP, and of its software architecture, organized into specifi-
cation frontends and backends that implement algorithms for
abstraction, solving games, and interfaces to other tools. Then,
the main elements for writing a specification for input to TuLiP
are introduced. These include logic formulae, discrete transition
systems annotated with predicates, and hybrid dynamical systems,
with linear or piecewise affine continuous dynamics. The
working principles of the algorithms for predicate abstraction
and discrete game solving using nested fixpoints are explained,
by following the input specification through the various transformations
that compile it to a symbolic representation that
scales well to solving large games. The tutorial concludes
with several design examples that demonstrate the toolbox’s
capabilities.
N
This work develops the geometry and dynamics of mechanical systems with nonholonomic
constraints and symmetry from the perspective of Lagrangian mechanics and with a view to
control theoretical applications. The basic methodology is that of geometric mechanics
applied to the formulation of Lagrange d'Alembert, generalizing the use of connections and
momentum maps associated with a given symmetry group to this case. We begin by formulating
the mechanics of nonholonomic systems using an Ehresmann connection to model the
constraints, and show how the curvature of this connection enters into Lagrange's
equations. Unlike the situation with standard configuration space constraints, the
presence of symmetries in the nonholonomic case may or may not lead to conservation laws.
However, the momentum map determined by the symmetry group still satisfies a useful
differential equation that decouples from the group variables. This momentum equation,
which plays an important role in control problems, involves parallel transport operators
and is computed explicitly in coordinates. An alternative description using a ``body
reference frame'' relates part of the momentum equation to the components of the
Euler-Poincar\'{e} equations along those symmetry directions consistent with the
constraints. One of the purposes of this paper is to derive this evolution equation for
the momentum and to distinguish geometrically and mechanically the cases where it is
conserved and those where it is not. An example of the former is a ball or vertical disk
rolling on a flat plane and an example of the latter is the snakeboard, a modified version
of the skateboard which uses momentum coupling for locomotion generation. We construct a
synthesis of the mechanical connection and the Ehresmann connection defining the
constraints, obtaining an important new object we call the nonholonomic connection. When
the nonholonomic connection is a principal connection for the given symmetry group, we
show how to perform Lagrangian reduction in the presence of nonholonomic constraints,
generalizing previous results which only held in special cases. Several detailed examples
are given to illustrate the theory.
M
This work discusses feasibility aspects of motion planning for
groups of agents connected by a range-constrained wireless
network. Specifically, we address the difficulties encountered
when trajectories are required to preserve the connectedness of
the network. The analysis utilizes a quantity called the
connectivity robustness of the network, which can be
calculated in a distributed fashion, and thus is applicable to
distributed motion planning problems arising in control of vehicle
networks. Further, these results show that network constraints
posed as connectivity robustness constraints have minimal impact
on reachability, provided that an appropriate topology control
algorithm is implemented. This contrasts with more naive
approaches to connectivity maintenance, which can significantly
reduce the reachable set. +
D
This work examines several dynamical aspects of average consensus
in mobile networks. The results herein allow consensus on general
time-varying signals, and allow tracking analysis using standard
frequency-domain techniques. Further, the frequency-domain
analysis naturally inspires a robust small-gain version of the
algorithm, which tolerates arbitrary non-uniform time delays.
Finally, we show how to exploit a dynamical conservation property
in order to ensure consensus tracking despite splitting and
merging of the underlying mobile network. +
T
This work illuminates a theory of locomotion rooted in geometric
mechanics and nonlinear control. We regard the internal configuration
of a deformable body, together with its position and orientation in
ambient space, as a point in a trivial principal fiber bundle over the
manifold of body deformations. We obtain connections on such bundles
which describe the nonholonomic constraints, conservation laws, and
force balances to which certain propulsors are subject, and construct
and analyze control-affine normal forms for different classes of
systems. We examine the applicability of results involving geometric
phases to the practical computation of trajectories for systems
described by single connections. We propose a model for planar
carangiform swimming based on reduced Euler-Lagrange equations for the
interaction of a rigid body and an incompressible fluid, accounting
for the generation of thrust due to vortex shedding through controlled
coupling terms. We investigate the correct form of this coupling
experimentally with a robotic propulsor, comparing its observed
behavior with that predicted numerically. +
D
This work is an extension to a companion paper describing
consensus-tracking for networked agents, and shows how those
results can be applied to obtain least-squares fused estimates
based on spatially distributed measurements. This mechanism is
very robust to changes in the underlying network topology and
performance, making it an interesting candidate for sensor fusion
on autonomous mobile networks. We conclude with an example of a
preliminary application to distributed Kalman Filtering using the
proposed technique, illustrating the dependence of the performance
on the structure of the underlying network. +
C
Computing Augmented Finite Transition Systems to Synthesize Switching Protocols for Polynomial Switched Systems +
This work is motivated by the problem of synthe- sizing mode sequences for continuous-time polynomial switched systems in order to guarantee that the trajectories of the system satisfy certain high-level specifications expressed in linear temporal logic. We use augmented finite transition systems as abstract models of continuous switched systems. Augmented finite transition systems are equipped with liveness properties that can be used to enforce progress in accordance with the underlying dynamics. We then introduce abstraction and refinement relations that induce a preorder on this class of finite transition systems. By construction, the resulting pre-order respects the feasibility (i.e., realizability) of the synthesis problem. Hence, existence of a discrete switching strategy for one of these abstract finite transition systems guarantees the existence of a mode sequence for the continuous system such that all of its trajectories satisfy the specification. We also present an algorithm, which can be implemented using sum-of-squares based relaxations, to compute such high fidelity abstract models in a computationally tractable way. Finally, these ideas are illustrated on an example. +
S
This work proposes a language for describing reactive synthesis problems that integrates imperative and declarative elements. The semantics is defined in terms of two-player turn-based infinite games with full information. Currently, synthesis tools accept linear temporal logic (LTL) as input, but this description is less structured and does not facilitate the expression of sequential constraints. This motivates the use of a structured programming language to specify synthesis problems. Transition systems and guarded commands serve as imperative constructs, expressed in a syntax based on that of the modeling language Promela. The syntax allows defining which player controls data and control flow, and separating a program into assumptions and guarantees. These notions are necessary for input to game solvers. The integration of imperative and declarative paradigms allows using the paradigm that is most appropriate for expressing each requirement. The declarative part is expressed in the LTL fragment of generalized reactivity(1), which admits efficient synthesis algorithms. The implementation translates Promela to input for the Slugs synthesizer and is written in Python. +
This work proposes a symbolic algorithm for the construction of assume-guarantee specifications that allow multiple agents to coop- erate. Each agent is assigned goals expressed in a fragment of linear temporal logic known as gener- alized Streett with one pair, GR(1). These goals may be unrealizable, unless each agent makes additional assumptions, about the behavior of other agents. The algorithm constructs a con- tract among the agents, in that only the infinite behavior of the given goals is constrained, known as liveness, not the finite one, known as safety. This defers synthesis to a later stage of refinement, modularizing the design process. We prove that there exist GR(1) games that do not admit any GR(1) contract. For this reason, we formulate contracts with nested GR(1) properties and auxiliary communication variables, and prove that they always exist. The algorithmâs fixpoint structure is similar to GR(1) synthesis, enjoying time complexity polynomial in the number of states, and linear in number of recurrence goals. +
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. +
