10,941 research outputs found
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
Risk-Averse Model Predictive Operation Control of Islanded Microgrids
In this paper we present a risk-averse model predictive control (MPC) scheme
for the operation of islanded microgrids with very high share of renewable
energy sources. The proposed scheme mitigates the effect of errors in the
determination of the probability distribution of renewable infeed and load.
This allows to use less complex and less accurate forecasting methods and to
formulate low-dimensional scenario-based optimisation problems which are
suitable for control applications. Additionally, the designer may trade
performance for safety by interpolating between the conventional stochastic and
worst-case MPC formulations. The presented risk-averse MPC problem is
formulated as a mixed-integer quadratically-constrained quadratic problem and
its favourable characteristics are demonstrated in a case study. This includes
a sensitivity analysis that illustrates the robustness to load and renewable
power prediction errors
Sets and Constraints in the Analysis Of Uncertain Systems
This thesis is concerned with the analysis of dynamical systems in the presence of model uncertainty. The approach of robust control theory has been to describe uncertainty in terms of a structured set of models, and has proven successful for questions, like stability, which call for a worst-case evaluation over this set. In this respect, a first contribution of this thesis is to provide robust stability tests for the situation of combined time varying, time invariant and parametric uncertainties.
The worst-case setting has not been so attractive for questions of disturbance rejection, since the resulting performance criteria (e.g., ℋ∞,) treat the disturbance as an adversary and ignore important spectral structure, usually better characterized by the theory of stochastic processes. The main contribution of this thesis is to show that the set-based methodology can indeed be extended to the modeling of white noise, by employing standard statistical tests in order to identify a typical set, and performing subsequent analysis in a worst-case setting. Particularly attractive sets are those described by quadratic signal constraints, which have proven to be very powerful for the characterization of unmodeled dynamics. The combination of white noise and unmodeled dynamics constitutes the Robust ℋ2 performance problem, which is rooted in the origins of robust control theory. By extending the scope of the
quadratic constraint methodology we obtain a solution to this problem in terms of a convex condition for robustness analysis, which for the first time places it on an equal footing with the ℋ∞ performance measure.
A separate contribution of this thesis is the development of a framework for analysis of uncertain systems in implicit form, in terms of equations rather than input-output maps. This formulation is motivated from first principles modeling, and provides an extension of the standard input-output robustness theory. In particular, we obtain in this way a standard form for robustness analysis problems with constraints, which also provides a common setting
for robustness analysis and questions of model validation and system identification
Learning stable and predictive structures in kinetic systems: Benefits of a causal approach
Learning kinetic systems from data is one of the core challenges in many
fields. Identifying stable models is essential for the generalization
capabilities of data-driven inference. We introduce a computationally efficient
framework, called CausalKinetiX, that identifies structure from discrete time,
noisy observations, generated from heterogeneous experiments. The algorithm
assumes the existence of an underlying, invariant kinetic model, a key
criterion for reproducible research. Results on both simulated and real-world
examples suggest that learning the structure of kinetic systems benefits from a
causal perspective. The identified variables and models allow for a concise
description of the dynamics across multiple experimental settings and can be
used for prediction in unseen experiments. We observe significant improvements
compared to well established approaches focusing solely on predictive
performance, especially for out-of-sample generalization
Hedging Complexity in Generalization via a Parametric Distributionally Robust Optimization Framework
Empirical risk minimization (ERM) and distributionally robust optimization
(DRO) are popular approaches for solving stochastic optimization problems that
appear in operations management and machine learning. Existing generalization
error bounds for these methods depend on either the complexity of the cost
function or dimension of the random perturbations. Consequently, the
performance of these methods can be poor for high-dimensional problems with
complex objective functions. We propose a simple approach in which the
distribution of random perturbations is approximated using a parametric family
of distributions. This mitigates both sources of complexity; however, it
introduces a model misspecification error. We show that this new source of
error can be controlled by suitable DRO formulations. Our proposed parametric
DRO approach has significantly improved generalization bounds over existing ERM
and DRO methods and parametric ERM for a wide variety of settings. Our method
is particularly effective under distribution shifts and works broadly in
contextual optimization. We also illustrate the superior performance of our
approach on both synthetic and real-data portfolio optimization and regression
tasks.Comment: Preliminary version appeared in AISTATS 202
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