104,236 research outputs found
A Data-driven Approach to Robust Control of Multivariable Systems by Convex Optimization
The frequency-domain data of a multivariable system in different operating
points is used to design a robust controller with respect to the measurement
noise and multimodel uncertainty. The controller is fully parametrized in terms
of matrix polynomial functions and can be formulated as a centralized,
decentralized or distributed controller. All standard performance
specifications like , and loop shaping are considered in a
unified framework for continuous- and discrete-time systems. The control
problem is formulated as a convex-concave optimization problem and then
convexified by linearization of the concave part around an initial controller.
The performance criterion converges monotonically to a local optimal solution
in an iterative algorithm. The effectiveness of the method is compared with
fixed-structure controllers using non-smooth optimization and with full-order
optimal controllers via simulation examples. Finally, the experimental data of
a gyroscope is used to design a data-driven controller that is successfully
applied on the real system
LMI approach to mixed performance objective controllers: application to Robust â„‹2 Synthesis
The problem of synthesizing a controller for plants subject to arbitrary, finite energy disturbances and white noise disturbances via Linear Matrix Inequalities (LMIs) is presented. This is achieved by considering white noise disturbances as belonging to a constrained set in â„“2. In the case of where only white noise disturbances are present, the procedure reduces to standard â„‹2 synthesis. When arbitrary, finite energy disturbances are also present, the procedure may be used to synthesize general mixed performance objective controllers, and for certain cases, Robust â„‹2 controllers
Robust â„‹2 Performance: Guaranteeing Margins for LQG Regulators
This paper shows that ℋ2 (LQG) performance specifications can be combined with structured uncertainty in the system, yielding robustness analysis conditions of the same nature and computational complexity as the corresponding conditions for ℋ∞ performance. These conditions are convex feasibility tests in terms of Linear Matrix Inequalities, and can be proven to be necessary and sufficient under the same conditions as in the ℋ∞ case.
With these results, the tools of robust control can be viewed as coming full circle to treat the problem where it all began: guaranteeing margins for LQG regulators
Robust Stability Under Mixed Time Varying, Time Invariant and Parametric Uncertainty
Robustness analysis is considered for systems with structured uncertainty involving a combination of linear time-invariant and linear time-varying perturbations, and parametric uncertainty. A necessary and sufficient condition for robust stability in terms of the structured singular value μ is obtained, based on a finite augmentation of the original problem. The augmentation corresponds to considering the system at a fixed number of frequencies. Sufficient conditions based on scaled small-gain are also considered and characterized
<i>H</i><sub>2</sub> and mixed <i>H</i><sub>2</sub>/<i>H</i><sub>∞</sub> Stabilization and Disturbance Attenuation for Differential Linear Repetitive Processes
Repetitive processes are a distinct class of two-dimensional systems (i.e., information propagation in two independent directions) of both systems theoretic and applications interest. A systems theory for them cannot be obtained by direct extension of existing techniques from standard (termed 1-D here) or, in many cases, two-dimensional (2-D) systems theory. Here, we give new results towards the development of such a theory in H2 and mixed H2/H∞ settings. These results are for the sub-class of so-called differential linear repetitive processes and focus on the fundamental problems of stabilization and disturbance attenuation
Tight, robust, and feasible quantum speed limits for open dynamics
Starting from a geometric perspective, we derive a quantum speed limit for
arbitrary open quantum evolution, which could be Markovian or non-Markovian,
providing a fundamental bound on the time taken for the most general quantum
dynamics. Our methods rely on measuring angles and distances between (mixed)
states represented as generalized Bloch vectors. We study the properties of our
bound and present its form for closed and open evolution, with the latter in
both Lindblad form and in terms of a memory kernel. Our speed limit is provably
robust under composition and mixing, features that largely improve the
effectiveness of quantum speed limits for open evolution of mixed states. We
also demonstrate that our bound is easier to compute and measure than other
quantum speed limits for open evolution, and that it is tighter than the
previous bounds for almost all open processes. Finally, we discuss the
usefulness of quantum speed limits and their impact in current research.Comment: Main: 11 pages, 3 figures. Appendix: 2 pages, 1 figur
Theory and Applications of Robust Optimization
In this paper we survey the primary research, both theoretical and applied,
in the area of Robust Optimization (RO). Our focus is on the computational
attractiveness of RO approaches, as well as the modeling power and broad
applicability of the methodology. In addition to surveying prominent
theoretical results of RO, we also present some recent results linking RO to
adaptable models for multi-stage decision-making problems. Finally, we
highlight applications of RO across a wide spectrum of domains, including
finance, statistics, learning, and various areas of engineering.Comment: 50 page
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