794 research outputs found
Conservative-variable average states for equilibrium gas multi-dimensional fluxes
Modern split component evaluations of the flux vector Jacobians are thoroughly analyzed for equilibrium-gas average-state determinations. It is shown that all such derivations satisfy a fundamental eigenvalue consistency theorem. A conservative-variable average state is then developed for arbitrary equilibrium-gas equations of state and curvilinear-coordinate fluxes. Original expressions for eigenvalues, sound speed, Mach number, and eigenvectors are then determined for a general average Jacobian, and it is shown that the average eigenvalues, Mach number, and eigenvectors may not coincide with their classical pointwise counterparts. A general equilibrium-gas equation of state is then discussed for conservative-variable computational fluid dynamics (CFD) Euler formulations. The associated derivations lead to unique compatibility relations that constrain the pressure Jacobian derivatives. Thereafter, alternative forms for the pressure variation and average sound speed are developed in terms of two average pressure Jacobian derivatives. Significantly, no additional degree of freedom exists in the determination of these two average partial derivatives of pressure. Therefore, they are simultaneously computed exactly without any auxiliary relation, hence without any geometric solution projection or arbitrary scale factors. Several alternative formulations are then compared and key differences highlighted with emphasis on the determination of the pressure variation and average sound speed. The relevant underlying assumptions are identified, including some subtle approximations that are inherently employed in published average-state procedures. Finally, a representative test case is discussed for which an intrinsically exact average state is determined. This exact state is then compared with the predictions of recent methods, and their inherent approximations are appropriately quantified
Maximum Likelihood Estimation in Data-Driven Modeling and Control
Recently, various algorithms for data-driven simulation and control have been
proposed based on the Willems' fundamental lemma. However, when collected data
are noisy, these methods lead to ill-conditioned data-driven model structures.
In this work, we present a maximum likelihood framework to obtain an optimal
data-driven model, the signal matrix model, in the presence of output noise.
Data compression and noise level estimation schemes are also proposed to apply
the algorithm efficiently to large datasets and unknown noise level scenarios.
Two approaches in system identification and receding horizon control are
developed based on the derived optimal estimator. The first one identifies a
finite impulse response model. This approach improves the least-squares
estimator with less restrictive assumptions. The second one applies the signal
matrix model as the predictor in predictive control. The control performance is
shown to be better than existing data-driven predictive control algorithms,
especially under high noise levels. Both approaches demonstrate that the
derived estimator provides a promising framework to apply data-driven
algorithms to noisy data
Scalable tube model predictive control of uncertain linear systems using ellipsoidal sets
This work proposes a novel robust model predictive control (MPC) algorithm
for linear systems affected by dynamic model uncertainty and exogenous
disturbances. The uncertainty is modeled using a linear fractional perturbation
structure with a time-varying perturbation matrix, enabling the algorithm to be
applied to a large model class. The MPC controller constructs a state tube as a
sequence of parameterized ellipsoidal sets to bound the state trajectories of
the system. The proposed approach results in a semidefinite program to be
solved online, whose size scales linearly with the order of the system. The
design of the state tube is formulated as an offline optimization problem,
which offers flexibility to impose desirable features such as robust invariance
on the terminal set. This contrasts with most existing tube MPC strategies
using polytopic sets in the state tube, which are difficult to design and whose
complexity grows combinatorially with the system order. The algorithm
guarantees constraint satisfaction, recursive feasibility, and stability of the
closed loop. The advantages of the algorithm are demonstrated using two
simulation studies.Comment: Submitted to International Journal of Robust and Nonlinear Contro
Stochastic Data-Driven Predictive Control: Regularization, Estimation, and Constraint Tightening
Data-driven predictive control methods based on the Willems' fundamental
lemma have shown great success in recent years. These approaches use receding
horizon predictive control with nonparametric data-driven predictors instead of
model-based predictors. This study addresses three problems of applying such
algorithms under unbounded stochastic uncertainties: 1) tuning-free regularizer
design, 2) initial condition estimation, and 3) reliable constraint
satisfaction, by using stochastic prediction error quantification. The
regularizer is designed by leveraging the expected output cost. An initial
condition estimator is proposed by filtering the measurements with the
one-step-ahead stochastic data-driven prediction. A novel constraint-tightening
method, using second-order cone constraints, is presented to ensure
high-probability chance constraint satisfaction. Numerical results demonstrate
that the proposed methods lead to satisfactory control performance in terms of
both control cost and constraint satisfaction, with significantly improved
initial condition estimation
Computationally efficient robust MPC using optimized constraint tightening
A robust model predictive control (MPC) method is presented for linear,
time-invariant systems affected by bounded additive disturbances. The main
contribution is the offline design of a disturbance-affine feedback gain
whereby the resulting constraint tightening is minimized. This is achieved by
formulating the constraint tightening problem as a convex optimization problem
with the feedback term as a variable. The resulting MPC controller has the
computational complexity of nominal MPC, and guarantees recursive feasibility,
stability and constraint satisfaction. The advantages of the proposed approach
compared to existing robust MPC methods are demonstrated using numerical
examples.Comment: Submitted to the 61st IEEE Conference on Decision and Control 202
A Dual System-Level Parameterization for Identification from Closed-Loop Data
This work presents a dual system-level parameterization (D-SLP) method for
closed-loop system identification. The recent system-level synthesis framework
parameterizes all stabilizing controllers via linear constraints on closed-loop
response functions, known as system-level parameters. It was demonstrated that
several structural, locality, and communication constraints on the controller
can be posed as convex constraints on these system-level parameters. In the
current work, the identification problem is treated as a {\em dual} of the
system-level synthesis problem. The plant model is identified from the dual
system-level parameters associated to the plant. In comparison to existing
closed-loop identification approaches (such as the dual-Youla
parameterization), the D-SLP framework neither requires the knowledge of a
nominal plant that is stabilized by the known controller, nor depends upon the
choice of factorization of the nominal plant and the stabilizing controller.
Numerical simulations demonstrate the efficacy of the proposed D-SLP method in
terms of identification errors, compared to existing closed-loop identification
techniques
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