348 research outputs found
Economic MPC of Nonlinear Systems with Non-Monotonic Lyapunov Functions and Its Application to HVAC Control
This paper proposes a Lyapunov-based economic MPC scheme for nonlinear sytems
with non-monotonic Lyapunov functions. Relaxed Lyapunov-based constraints are
used in the MPC formulation to improve the economic performance. These
constraints will enforce a Lyapunov decrease after every few steps. Recursive
feasibility and asymptotical convergence to the steady state can be achieved
using Lyapunov-like stability analysis. The proposed economic MPC can be
applied to minimize energy consumption in HVAC control of commercial buildings.
The Lyapunov-based constraints in the online MPC problem enable the tracking of
the desired set-point temperature. The performance is demonstrated by a virtual
building composed of two adjacent zones
Data-driven computation of invariant sets of discrete time-invariant black-box systems
We consider the problem of computing the maximal invariant set of
discrete-time black-box nonlinear systems without analytic dynamical models.
Under the assumption that the system is asymptotically stable, the maximal
invariant set coincides with the domain of attraction. A data-driven framework
relying on the observation of trajectories is proposed to compute
almost-invariant sets, which are invariant almost everywhere except a small
subset. Based on these observations, scenario optimization problems are
formulated and solved. We show that probabilistic invariance guarantees on the
almost-invariant sets can be established. To get explicit expressions of such
sets, a set identification procedure is designed with a verification step that
provides inner and outer approximations in a probabilistic sense. The proposed
data-driven framework is illustrated by several numerical examples.Comment: A shorter version with the title "Scenario-based set invariance
verification for black-box nonlinear systems" is published in the IEEE
Control Systems Letters (L-CSS
A data-driven method for computing polyhedral invariant sets of black-box switched linear systems
In this paper, we consider the problem of invariant set computation for
black-box switched linear systems using merely a finite set of observations of
system trajectories. In particular, this paper focuses on polyhedral invariant
sets. We propose a data-driven method based on the one step forward reachable
set. For formal verification of the proposed method, we introduce the concepts
of -contractive sets and almost-invariant sets for switched linear
systems. The convexity-preserving property of switched linear systems allows us
to conduct contraction analysis on the computed set and derive a probabilistic
contraction property. In the spirit of non-convex scenario optimization, we
also establish a chance-constrained guarantee on set invariance. The
performance of our method is then illustrated by numerical examples.Comment: To appear in IEEE Control Systems Letter
Probabilistic guarantees on the objective value for the scenario approach via sensitivity analysis
This paper is concerned with objective value performance of the scenario
approach for robust convex optimization. A novel method is proposed to derive
probabilistic bounds for the objective value from scenario programs with a
finite number of samples. This method relies on a max-min reformulation and the
concept of complexity of robust optimization problems. With additional
continuity and regularity conditions, via sensitivity analysis, we also provide
explicit bounds which outperform an existing result in the literature. To
illustrate the improvements of our results, we also provide a numerical
example
Immersion-based model predictive control of constrained nonlinear systems: Polyflow approximation
In the framework of Model Predictive Control (MPC), the control input is
typically computed by solving optimization problems repeatedly online. For
general nonlinear systems, the online optimization problems are non-convex and
computationally expensive or even intractable. In this paper, we propose to
circumvent this issue by computing a high-dimensional linear embedding of
discrete-time nonlinear systems. The computation relies on an algebraic
condition related to the immersibility property of nonlinear systems and can be
implemented offline. With the high-dimensional linear model, we then define and
solve a convex online MPC problem. We also provide an interpretation of our
approach under the Koopman operator framework.Comment: Accepted to the European Control Conferenc
DISTRIBUTED MODEL PREDICTIVE CONTROL OF CONSTRAINED LINEAR SYSTEMS
Ph.DDOCTOR OF PHILOSOPH
Computation of the maximal invariant set of discrete-time linear systems subject to a class of non-convex constraints
We consider the problem of computing the maximal invariant set of
discrete-time linear systems subject to a class of non-convex constraints that
admit quadratic relaxations. These non-convex constraints include semialgebraic
sets and other smooth constraints with Lipschitz gradient. With these quadratic
relaxations, a sufficient condition for set invariance is derived and it can be
formulated as a set of linear matrix inequalities. Based on the sufficient
condition, a new algorithm is presented with finite-time convergence to the
actual maximal invariant set under mild assumptions. This algorithm can be also
extended to switched linear systems and some special nonlinear systems. The
performance of this algorithm is demonstrated on several numerical examples.Comment: Accepted in Automatic
Data-driven control of switched linear systems with probabilistic stability guarantees
This paper tackles state feedback control of switched linear systems under
arbitrary switching. We propose a data-driven control framework that allows to
compute a stabilizing state feedback using only a finite set of observations of
trajectories with quadratic and sum of squares (SOS) Lyapunov functions. We do
not require any knowledge on the dynamics or the switching signal, and as a
consequence, we aim at solving \emph{uniform} stabilization problems in which
the feedback is stabilizing for all possible switching sequences. In order to
generalize the solution obtained from trajectories to the actual system,
probabilistic guarantees on the obtained quadratic or SOS Lyapunov function are
derived in the spirit of scenario optimization. For the quadratic Lyapunov
technique, the generalization relies on a geometric analysis argument, while,
for the SOS Lyapunov technique, we follow a sensitivity analysis argument. In
order to deal with high-dimensional systems, we also develop parallelized
schemes for both techniques. We show that, with some modifications, the
data-driven quadratic Lyapunov technique can be extended to LQR control design.
Finally, the proposed data-driven control framework is demonstrated on several
numerical examples.Comment: This is an extended version to the previous pape
A pipeline for improved QSAR analysis of peptides: physiochemical property parameter selection via BMSF, near-neighbor sample selection via semivariogram, and weighted SVR regression and prediction
In this paper, we present a pipeline to perform improved QSAR analysis of peptides. The modeling involves a double selection procedure that first performs feature selection and then conducts sample selection before the final regression analysis. Five hundred and thirty-one physicochemical property parameters of amino acids were used as descriptors to characterize the structure of peptides. These high-dimensional descriptors then go through a feature selection process given by the Binary Matrix Shuffling Filter (BMSF) to obtain a set of important low dimensional features. Each descriptor that passed the BMSF filtering also receives a weight defined through its contribution to reduce the estimation error. These selected features were served as the predictors for subsequent sample selection and modeling. Based on the weighted Euclidean distances between samples, a common range was determined with high-dimensional semivariogram and then used as a threshold to select the near-neighbor samples from the training set. For each sample to be predicted, the QSAR model was established using SVR with the weighted, selected features based on the exclusive set of near-neighbor training samples. Prediction was conducted for each test sample accordingly. The performances of this pipeline are tested with the QSAR analysis of angiotensin-converting enzyme (ACE) inhibitors and HLA-A*0201 data sets. Improved prediction accuracy was obtained in both applications. This pipeline can optimize the QSAR modeling from both the feature selection and sample selection perspectives. This leads to improved accuracy over single selection methods. We expect this pipeline to have extensive application prospect in the field of regression prediction
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