718 research outputs found
Controller design for robust invariance from noisy data
For an unknown linear system, starting from noisy open-loop input-state data
collected during a finite-length experiment, we directly design a linear
feedback controller that guarantees robust invariance of a given polyhedral set
of the state in the presence of disturbances. The main result is a necessary
and sufficient condition for the existence of such a controller, and amounts to
the solution of a linear program. The benefits of large and rich data sets for
the solution of the problem are discussed. A numerical example about a
simplified platoon of two vehicles illustrates the method
Superstabilizing Control of Discrete-Time ARX Models under Error in Variables
This paper applies a polynomial optimization based framework towards the
superstabilizing control of an Autoregressive with Exogenous Input (ARX) model
given noisy data observations. The recorded input and output values are
corrupted with L-infinity bounded noise where the bounds are known. This is an
instance of Error in Variables (EIV) in which true internal state of the ARX
system remains unknown. The consistency set of ARX models compatible with noisy
data has a bilinearity between unknown plant parameters and unknown noise
terms. The requirement for a dynamic compensator to superstabilize all
consistent plants is expressed using polynomial nonnegativity constraints, and
solved using sum-of-squares (SOS) methods in a converging hierarchy of
semidefinite programs in increasing size. The computational complexity of this
method may be reduced by applying a Theorem of Alternatives to eliminate the
noise terms. Effectiveness of this method is demonstrated on control of example
ARX models.Comment: 12 pages, 0 figures, 5 table
Formulas for Data-driven Control: Stabilization, Optimality and Robustness
In a paper by Willems and coauthors it was shown that persistently exciting
data can be used to represent the input-output behavior of a linear system.
Based on this fundamental result, we derive a parametrization of linear
feedback systems that paves the way to solve important control problems using
data-dependent Linear Matrix Inequalities only. The result is remarkable in
that no explicit system's matrices identification is required. The examples of
control problems we solve include the state and output feedback stabilization,
and the linear quadratic regulation problem. We also discuss robustness to
noise-corrupted measurements and show how the approach can be used to stabilize
unstable equilibria of nonlinear systems.Comment: Revised version of the paper "On Persistency of Excitation and
Formulas for Data-driven Control". Abridged version to appear in the 58th
IEEE Conference on Decision and Control, Nice, France, 2019. First submitted
on 15 March 201
Investigations of Model-Free Sliding Mode Control Algorithms including Application to Autonomous Quadrotor Flight
Sliding mode control is a robust nonlinear control algorithm that has been used to implement tracking controllers for unmanned aircraft systems that are robust to modeling uncertainty and exogenous disturbances, thereby providing excellent performance for autonomous operation. A significant advance in the application of sliding mode control for unmanned aircraft systems would be adaptation of a model-free sliding mode control algorithm, since the most complex and time-consuming aspect of implementation of sliding mode control is the derivation of the control law with incorporation of the system model, a process required to be performed for each individual application of sliding mode control. The performance of four different model-free sliding mode control algorithms was compared in simulation using a variety of aerial system models and real-world disturbances (e.g. the effects of discretization and state estimation). The two best performing algorithms were shown to exhibit very similar behavior. These two algorithms were implemented on a quadrotor (both in simulation and using real-world hardware) and the performance was compared to a traditional PID-based controller using the same state estimation algorithm and control setup. Simulation results show the model-free sliding mode control algorithms exhibit similar performance to PID controllers without the tedious tuning process. Comparison between the two model-free sliding mode control algorithms showed very similar performance as measured by the quadratic means of tracking errors. Flight testing showed that while a model-free sliding mode control algorithm is capable of controlling realworld hardware, further characterization and significant improvements are required before it is a viable alternative to conventional control algorithms. Large tracking errors were observed for both the model-free sliding mode control and PID based flight controllers and the performance was characterized as unacceptable for most applications. The poor performance of both controllers suggests tracking errors could be attributed to errors in state estimation, which effectively introduce unknown dynamics into the feedback loop. Further testing with improved state estimation would allow for more conclusions to be drawn about the performance characteristics of the model-free sliding mode control algorithms
New Approaches in Automation and Robotics
The book New Approaches in Automation and Robotics offers in 22 chapters a collection of recent developments in automation, robotics as well as control theory. It is dedicated to researchers in science and industry, students, and practicing engineers, who wish to update and enhance their knowledge on modern methods and innovative applications. The authors and editor of this book wish to motivate people, especially under-graduate students, to get involved with the interesting field of robotics and mechatronics. We hope that the ideas and concepts presented in this book are useful for your own work and could contribute to problem solving in similar applications as well. It is clear, however, that the wide area of automation and robotics can only be highlighted at several spots but not completely covered by a single book
Trade-offs in learning controllers from noisy data
In data-driven control, a central question is how to handle noisy data. In
this work, we consider the problem of designing a stabilizing controller for an
unknown linear system using only a finite set of noisy data collected from the
system. For this problem, many recent works have considered a disturbance model
based on energy-type bounds. Here, we consider an alternative more natural
model where the disturbance obeys instantaneous bounds. In this case, the
existing approaches, which would convert instantaneous bounds into energy-type
bounds, can be overly conservative. In contrast, without any conversion step,
simple arguments based on the S-procedure lead to a very effective controller
design through a convex program. Specifically, the feasible set of the latter
design problem is always larger, and the set of system matrices consistent with
data is always smaller and decreases significantly with the number of data
points. These findings and some computational aspects are examined in a number
of numerical examples
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