1,154 research outputs found
Online Optimization of Switched LTI Systems Using Continuous-Time and Hybrid Accelerated Gradient Flows
This paper studies the design of feedback controllers that steer the output
of a switched linear time-invariant system to the solution of a possibly
time-varying optimization problem. The design of the feedback controllers is
based on an online gradient descent method, and an online hybrid controller
that can be seen as a regularized Nesterov's accelerated gradient method. Both
of the proposed approaches accommodate output measurements of the plant, and
are implemented in closed-loop with the switched dynamical system. By design,
the controllers continuously steer the system output to an optimal trajectory
implicitly defined by the time-varying optimization problem without requiring
knowledge of exogenous inputs and disturbances. For cost functions that are
smooth and satisfy the Polyak-Lojasiewicz inequality, we demonstrate that the
online gradient descent controller ensures uniform global exponential stability
when the time-scales of the plant and the controller are sufficiently separated
and the switching signal of the plant is slow on the average. Under a strong
convexity assumption, we also show that the online hybrid Nesterov's method
guarantees tracking of optimal trajectories, and outperforms online controllers
based on gradient descent. Interestingly, the proposed hybrid accelerated
controller resolves the potential lack of robustness suffered by standard
continuous-time accelerated gradient methods when coupled with a dynamical
system. When the function is not strongly convex, we establish global practical
asymptotic stability results for the accelerated method, and we unveil the
existence of a trade-off between acceleration and exact convergence in online
optimization problems with controllers using dynamic momentum. Our theoretical
results are illustrated via different numerical examples
Robust nonlinear control of vectored thrust aircraft
An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations
Data-Driven Control of Linear Time-Varying Systems
An identification-free control design strategy for discrete-time linear time-varying systems with unknown dynamics is introduced. The closed-loop system (under state feedback) is parametrised with data-dependent matrices obtained from an ensemble of input-state trajectories collected offline. This data-driven system representation is used to classify control laws yielding trajectories which satisfy a certain bound and to solve the linear quadratic regulator problem - both using data-dependent linear matrix inequalities only. The results are illustrated by means of a numerical example
Parameter-Dependent Lyapunov Functions for Linear Systems With Constant Uncertainties
Robust stability of linear time-invariant systems with respect to structured uncertainties is considered. The small gain condition is sufficient to prove robust stability and scalings are typically used to reduce the conservatism of this condition. It is known that if the small gain condition is satisfied with constant scalings then there is a single quadratic Lyapunov function which proves robust stability with respect to all allowable time-varying perturbations. In this technical note we show that if the small gain condition is satisfied with frequency-varying scalings then an explicit parameter dependent Lyapunov function can be constructed to prove robust stability with respect to constant uncertainties. This Lyapunov function has a rational quadratic dependence on the uncertainties
Minimum-Information LQG Control - Part I: Memoryless Controllers
With the increased demand for power efficiency in feedback-control systems,
communication is becoming a limiting factor, raising the need to trade off the
external cost that they incur with the capacity of the controller's
communication channels. With a proper design of the channels, this translates
into a sequential rate-distortion problem, where we minimize the rate of
information required for the controller's operation under a constraint on its
external cost. Memoryless controllers are of particular interest both for the
simplicity and frugality of their implementation and as a basis for studying
more complex controllers. In this paper we present the optimality principle for
memoryless linear controllers that utilize minimal information rates to achieve
a guaranteed external-cost level. We also study the interesting and useful
phenomenology of the optimal controller, such as the principled reduction of
its order
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