10 research outputs found
Dynamic Actuator Selection and Robust State-Feedback Control of Networked Soft Actuators
The design of robots that are light, soft, powerful is a grand challenge.
Since they can easily adapt to dynamic environments, soft robotic systems have
the potential of changing the status-quo of bulky robotics. A crucial component
of soft robotics is a soft actuator that is activated by external stimuli to
generate desired motions. Unfortunately, there is a lack of powerful soft
actuators that operate through lightweight power sources. To that end, we
recently designed a highly scalable, flexible, biocompatible Electromagnetic
Soft Actuator (ESA). With ESAs, artificial muscles can be designed by
integrating a network of ESAs. The main research gap addressed in this work is
in the absence of system-theoretic understanding of the impact of the realtime
control and actuator selection algorithms on the performance of networked
soft-body actuators and ESAs. The objective of this paper is to establish a
framework that guides the analysis and robust control of networked ESAs. A
novel ESA is described, and a configuration of soft actuator matrix to resemble
artificial muscle fiber is presented. A mathematical model which depicts the
physical network is derived, considering the disturbances due to external
forces and linearization errors as an integral part of this model. Then, a
robust control and minimal actuator selection problem with logistic constraints
and control input bounds is formulated, and tractable computational routines
are proposed with numerical case studies.Comment: To appear at the 2018 International Conference on Robotics and
Automation (ICRA), Brisbane, Australia, May 21, 2018--May 25, 201
Output Controllability of a Linear Dynamical System with Sparse Controls
In this paper, we study the conditions to be satisfied by a discrete-time
linear system to ensure output controllability using sparse control inputs. A
set of necessary and sufficient conditions can be directly obtained by
extending the Kalman rank test for output controllability. However, the
verification of these conditions is computationally heavy due to their
combinatorial nature. Therefore, we derive non-combinatorial conditions for
output sparse controllability which can be verified with polynomial time
complexity. Our results also provide bounds on the minimum sparsity level
required to ensure output controllability of the system. This additional
insight is useful for designing sparse control input that drives the system to
any desired output.Comment: 10 pages, no figure
Controllability of a Linear System with Nonnegative Sparse Controls
This paper studies controllability of a discrete-time linear dynamical system
using nonnegative and sparse inputs. These constraints on the control input
arise naturally in many real-life systems where the external influence on the
system is unidirectional, and activating each input node adds to the cost of
control. We derive the necessary and sufficient conditions for controllability
of the system, without imposing any constraints on the system matrices. Unlike
the well-known Kalman rank based controllability criteria, the conditions
presented in this paper can be verified in polynomial time, and the
verification complexity is independent of the sparsity level. The proof of the
result is based on the analytical tools concerning the properties of a convex
cone. Our results also provide a closed-form expression for the minimum number
of control nodes to be activated at every time instant to ensure
controllability of the system using positive controls.Comment: 6 pages, no figure
Controllability of Linear Dynamical Systems Under Input Sparsity Constraints
In this work, we consider the controllability of a discrete-time linear
dynamical system with sparse control inputs. Sparsity constraints on the input
arises naturally in networked systems, where activating each input variable
adds to the cost of control. We derive algebraic necessary and sufficient
conditions for ensuring controllability of a system with an arbitrary transfer
matrix. The derived conditions can be verified in polynomial time complexity,
unlike the more traditional Kalman-type rank tests. Further, we characterize
the minimum number of input vectors required to satisfy the derived conditions
for controllability. Finally, we present a generalized Kalman
decomposition-like procedure that separates the state-space into subspaces
corresponding to sparse-controllable and sparse-uncontrollable parts. These
results form a theoretical basis for designing networked linear control systems
with sparse inputs.Comment: 11 page
Data-Driven Selection of Actuators for Optimal Control of Airfoil Separation
We present a systematic approach for determining the optimal actuator
location for separation control from input-output response data, gathered from
numerical simulations or physical experiments. The Eigensystem Realization
Algorithm is used to extract state-space descriptions from the response data
associated with a candidate set of actuator locations. These system
realizations are then used to determine the actuator location among the set
that can drive the system output to an arbitrary value with minimal control
effort. The solution of the corresponding minimum energy optimal control
problem is evaluated by computing the generalized output controllability
Gramian. We use the method to analyze high-fidelity numerical simulation data
of the lift and separation-angle responses to a pulse of localized body-force
actuation from six distinct locations on the upper surface of a NACA 65(1)-412
airfoil. We find that the optimal location for controlling lift is different
from the optimal location for controlling separation angle. In order to explain
the physical mechanisms underlying these differences, we conduct
controllability analyses of the flowfield by leveraging the dynamic mode
decomposition with control algorithm. These modal analyses of flowfield
response data reveal that excitation of coherent structures in the wake benefit
lift control; whereas, excitation of coherent structures in the shear layer
benefit separation-angle control
Simultaneous Sensor and Actuator Selection/Placement through Output Feedback Control
In most dynamic networks, it is impractical to measure all of the system
states; instead, only a subset of the states are measured through sensors.
Consequently, and unlike full state feedback controllers, output feedback
control utilizes only the measured states to obtain a stable closed-loop
performance. This paper explores the interplay between the selection of minimal
number of sensors and actuators (SaA) that yield a stable closed-loop system
performance. Through the formulation of the static output feedback control
problem, we show that the simultaneous selection of minimal set of SaA is a
combinatorial optimization problem with mixed-integer nonlinear matrix
inequality constraints. To address the computational complexity, we develop two
approaches: The first approach relies on integer/disjunctive programming
principles, while the second approach is a simple algorithm that is akin to
binary search routines. The optimality of the two approaches is also discussed.
Numerical experiments are included showing the performance of the developed
approaches.Comment: 6 page
Sensor Placement Strategies for Some Classes of Nonlinear Dynamic Systems via Lyapunov Theory
In this paper, the problem of placing sensors for some classes of nonlinear
dynamic systems (NDS) is investigated. In conjunction with mixed-integer
programming, classical Lyapunov-based arguments are used to find the minimal
sensor configuration such that the NDS internal states can be observed while
still optimizing some estimation metrics. The paper's approach is based on two
phases. The first phase assumes that the encompassed nonlinearities belong to
one of the following function set classifications: bounded Jacobian, Lipschitz
continuous, one-sided Lipschitz, or quadratically inner-bounded. To
parameterize these classifications, two approaches based on stochastic
point-based and interval-based optimization methods are explored. Given the
parameterization, the second phase formulates the sensor placement problem for
various NDS classes through mixed-integer convex programming. The theoretical
optimality of the sensor placement alongside a state estimator design are then
given. Numerical tests on traffic network models showcase that the proposed
approach yields sensor placements that are consistent with conventional wisdom
in traffic theory.Comment: Presented in the 58th Conference on Decision and Control - Nice,
France - December 11th-13th 201
Time-Varying Sensor and Actuator Selection for Uncertain Cyber-Physical Systems
We propose methods to solve time-varying, sensor and actuator (SaA) selection
problems for uncertain cyber-physical systems. We show that many SaA selection
problems for optimizing a variety of control and estimation metrics can be
posed as semidefinite optimization problems with mixed-integer bilinear matrix
inequalities (MIBMIs). Although this class of optimization problems are
computationally challenging, we present tractable approaches that directly
tackle MIBMIs, providing both upper and lower bounds, and that lead to
effective heuristics for SaA selection. The upper and lower bounds are obtained
via successive convex approximations and semidefinite programming relaxations,
respectively, and selections are obtained with a novel slicing algorithm from
the solutions of the bounding problems. Custom branch-and-bound and
combinatorial greedy approaches are also developed for a broad class of systems
for comparison. Finally, comprehensive numerical experiments are performed to
compare the different methods and illustrate their effectiveness
On A Relaxation of Time-Varying Actuator Placement
We consider the time-varying actuator placement in continuous time, where the
goal is to maximize the trace of the controllability Grammian. A natural
relaxation of the problem is to allow the binary variable indicating
whether an actuator is used at a given time to take on values in the closed
interval . We show that all optimal solutions of both the original and
the relaxed problems can be given via an explicit formula, and that, as long as
the input matrix has no zero columns, the solutions sets of the original and
relaxed problem coincide
Deterministic and Randomized Actuator Scheduling With Guaranteed Performance Bounds
In this paper, we investigate the problem of actuator selection for linear
dynamical systems. We develop a framework to design a sparse actuator schedule
for a given large-scale linear system with guaranteed performance bounds using
deterministic polynomial-time and randomized approximately linear-time
algorithms. First, we introduce systemic controllability metrics for linear
dynamical systems that are monotone and homogeneous with respect to the
controllability Gramian. We show that several popular and widely used
optimization criteria in the literature belong to this class of controllability
metrics. Our main result is to provide a polynomial-time actuator schedule that
on average selects only a constant number of actuators at each time step,
independent of the dimension, to furnish a guaranteed approximation of the
controllability metrics in comparison to when all actuators are in use. Our
results naturally apply to the dual problem of sensor selection, in which we
provide a guaranteed approximation to the observability Gramian. We illustrate
the effectiveness of our theoretical findings via several numerical simulations
using benchmark examples