322 research outputs found
Stochastic MPC Design for a Two-Component Granulation Process
We address the issue of control of a stochastic two-component granulation
process in pharmaceutical applications through using Stochastic Model
Predictive Control (SMPC) and model reduction to obtain the desired particle
distribution. We first use the method of moments to reduce the governing
integro-differential equation down to a nonlinear ordinary differential
equation (ODE). This reduced-order model is employed in the SMPC formulation.
The probabilistic constraints in this formulation keep the variance of
particles' drug concentration in an admissible range. To solve the resulting
stochastic optimization problem, we first employ polynomial chaos expansion to
obtain the Probability Distribution Function (PDF) of the future state
variables using the uncertain variables' distributions. As a result, the
original stochastic optimization problem for a particulate system is converted
to a deterministic dynamic optimization. This approximation lessens the
computation burden of the controller and makes its real time application
possible.Comment: American control Conference, May, 201
A Probabilistic Approach to Robust Optimal Experiment Design with Chance Constraints
Accurate estimation of parameters is paramount in developing high-fidelity
models for complex dynamical systems. Model-based optimal experiment design
(OED) approaches enable systematic design of dynamic experiments to generate
input-output data sets with high information content for parameter estimation.
Standard OED approaches however face two challenges: (i) experiment design
under incomplete system information due to unknown true parameters, which
usually requires many iterations of OED; (ii) incapability of systematically
accounting for the inherent uncertainties of complex systems, which can lead to
diminished effectiveness of the designed optimal excitation signal as well as
violation of system constraints. This paper presents a robust OED approach for
nonlinear systems with arbitrarily-shaped time-invariant probabilistic
uncertainties. Polynomial chaos is used for efficient uncertainty propagation.
The distinct feature of the robust OED approach is the inclusion of chance
constraints to ensure constraint satisfaction in a stochastic setting. The
presented approach is demonstrated by optimal experimental design for the
JAK-STAT5 signaling pathway that regulates various cellular processes in a
biological cell.Comment: Submitted to ADCHEM 201
Stochastic Nonlinear Model Predictive Control with Efficient Sample Approximation of Chance Constraints
This paper presents a stochastic model predictive control approach for
nonlinear systems subject to time-invariant probabilistic uncertainties in
model parameters and initial conditions. The stochastic optimal control problem
entails a cost function in terms of expected values and higher moments of the
states, and chance constraints that ensure probabilistic constraint
satisfaction. The generalized polynomial chaos framework is used to propagate
the time-invariant stochastic uncertainties through the nonlinear system
dynamics, and to efficiently sample from the probability densities of the
states to approximate the satisfaction probability of the chance constraints.
To increase computational efficiency by avoiding excessive sampling, a
statistical analysis is proposed to systematically determine a-priori the least
conservative constraint tightening required at a given sample size to guarantee
a desired feasibility probability of the sample-approximated chance constraint
optimization problem. In addition, a method is presented for sample-based
approximation of the analytic gradients of the chance constraints, which
increases the optimization efficiency significantly. The proposed stochastic
nonlinear model predictive control approach is applicable to a broad class of
nonlinear systems with the sufficient condition that each term is analytic with
respect to the states, and separable with respect to the inputs, states and
parameters. The closed-loop performance of the proposed approach is evaluated
using the Williams-Otto reactor with seven states, and ten uncertain parameters
and initial conditions. The results demonstrate the efficiency of the approach
for real-time stochastic model predictive control and its capability to
systematically account for probabilistic uncertainties in contrast to a
nonlinear model predictive control approaches.Comment: Submitted to Journal of Process Contro
Hierarchical adaptive polynomial chaos expansions
Polynomial chaos expansions (PCE) are widely used in the framework of
uncertainty quantification. However, when dealing with high dimensional complex
problems, challenging issues need to be faced. For instance, high-order
polynomials may be required, which leads to a large polynomial basis whereas
usually only a few of the basis functions are in fact significant. Taking into
account the sparse structure of the model, advanced techniques such as sparse
PCE (SPCE), have been recently proposed to alleviate the computational issue.
In this paper, we propose a novel approach to SPCE, which allows one to exploit
the model's hierarchical structure. The proposed approach is based on the
adaptive enrichment of the polynomial basis using the so-called principle of
heredity. As a result, one can reduce the computational burden related to a
large pre-defined candidate set while obtaining higher accuracy with the same
computational budget
Behavioral Theory for Stochastic Systems? A Data-driven Journey from Willems to Wiener and Back Again
The fundamental lemma by Jan C. Willems and co-workers, which is deeply
rooted in behavioral systems theory, has become one of the supporting pillars
of the recent progress on data-driven control and system analysis. This
tutorial-style paper combines recent insights into stochastic and
descriptor-system formulations of the lemma to further extend and broaden the
formal basis for behavioral theory of stochastic linear systems. We show that
series expansions -- in particular Polynomial Chaos Expansions (PCE) of
-random variables, which date back to Norbert Wiener's seminal work --
enable equivalent behavioral characterizations of linear stochastic systems.
Specifically, we prove that under mild assumptions the behavior of the dynamics
of the -random variables is equivalent to the behavior of the dynamics of
the series expansion coefficients and that it entails the behavior composed of
sampled realization trajectories. We also illustrate the short-comings of the
behavior associated to the time-evolution of the statistical moments. The paper
culminates in the formulation of the stochastic fundamental lemma for linear
(descriptor) systems, which in turn enables numerically tractable formulations
of data-driven stochastic optimal control combining Hankel matrices in
realization data (i.e. in measurements) with PCE concepts.Comment: 30 pages, 8 figure
A Stochastic Nonlinear Model Predictive Control with an Uncertainty Propagation Horizon for Autonomous Vehicle Motion Control
Employing Stochastic Nonlinear Model Predictive Control (SNMPC) for real-time
applications is challenging due to the complex task of propagating
uncertainties through nonlinear systems. This difficulty becomes more
pronounced in high-dimensional systems with extended prediction horizons, such
as autonomous vehicles. To enhance closed-loop performance in and feasibility
in SNMPCs, we introduce the concept of the Uncertainty Propagation Horizon
(UPH). The UPH limits the time for uncertainty propagation through system
dynamics, preventing trajectory divergence, optimizing feedback loop
advantages, and reducing computational overhead. Our SNMPC approach utilizes
Polynomial Chaos Expansion (PCE) to propagate uncertainties and incorporates
nonlinear hard constraints on state expectations and nonlinear probabilistic
constraints. We transform the probabilistic constraints into deterministic
constraints by estimating the nonlinear constraints' expectation and variance.
We then showcase our algorithm's effectiveness in real-time control of a
high-dimensional, highly nonlinear system-the trajectory following of an
autonomous passenger vehicle, modeled with a dynamic nonlinear single-track
model. Experimental results demonstrate our approach's robust capability to
follow an optimal racetrack trajectory at speeds of up to 37.5m/s while dealing
with state estimation disturbances, achieving a minimum solving frequency of
97Hz. Additionally, our experiments illustrate that limiting the UPH renders
previously infeasible SNMPC problems feasible, even when incorrect uncertainty
assumptions or strong disturbances are present
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