## Program

Mechanical Engineering

## College

Engineering

## Student Level

Doctoral

## Location

PAÍS Building

## Start Date

10-11-2022 11:00 AM

## End Date

10-11-2022 1:00 PM

## Abstract

A complex heating, ventilation, and air conditioning (HVAC) system is hard to model and identify. Due to the diversity of building applications and the coupling of dynamics of the equipment and the building, plant models have significant uncertainty. Black-box modeling of such system e.g. nonlinear autoregressive models, and neural network models can become ill-conditioned, and problematic for control input design. In this research we aim to perform prediction and control based on data for a general nonlinear system subject to constraints. We consider the discrete-time nonlinear state evolution x+ = f (x, u) of the system, where the output y = h(x, u) ∈ Rny is a static map of the state x ∈ Rnx and input u ∈ Rnu . Input limitations u ∈ U, state constraints x ∈ X , and output constraints y ∈ Y demand safety-critical controllers. The ultimate safe set for a system is defined as the maximum controlled invariant (MCI) set of the system, which is the largest set C, where for any x ∈ C there exists an input u such that x+ = f (x, u) ∈ C. Let us first consider the uncontrolled system where state dynamics x+ = f (x) ∈ C and output y = h(x) evolve autonomously. In this case the ultimate safe set is defined as the maximum positively invariant (MPI) set, which is the largest set C, where for any x ∈ C we have x+ = f (x, u) ∈ C. In order to extract these properties of the system from the data, we find the basis functions for Koopman operator of the system, which spans the space, where observables φ(x) ∈ Rnφ evolve linearly in time, existence of which is guaranteed for forward-complete system. We use the linearity of the Koopman operator to approximate the MPI set, where the accuracy is enhanced by removing redundant basis functions using active learning. For the controlled version, we are looking for a promising way to include the control or reference input in the formulation of the Koopman operator to get the MCI set

Model-Free Data-Driven Control for Nonlinear Systems

PAÍS Building

A complex heating, ventilation, and air conditioning (HVAC) system is hard to model and identify. Due to the diversity of building applications and the coupling of dynamics of the equipment and the building, plant models have significant uncertainty. Black-box modeling of such system e.g. nonlinear autoregressive models, and neural network models can become ill-conditioned, and problematic for control input design. In this research we aim to perform prediction and control based on data for a general nonlinear system subject to constraints. We consider the discrete-time nonlinear state evolution x+ = f (x, u) of the system, where the output y = h(x, u) ∈ Rny is a static map of the state x ∈ Rnx and input u ∈ Rnu . Input limitations u ∈ U, state constraints x ∈ X , and output constraints y ∈ Y demand safety-critical controllers. The ultimate safe set for a system is defined as the maximum controlled invariant (MCI) set of the system, which is the largest set C, where for any x ∈ C there exists an input u such that x+ = f (x, u) ∈ C. Let us first consider the uncontrolled system where state dynamics x+ = f (x) ∈ C and output y = h(x) evolve autonomously. In this case the ultimate safe set is defined as the maximum positively invariant (MPI) set, which is the largest set C, where for any x ∈ C we have x+ = f (x, u) ∈ C. In order to extract these properties of the system from the data, we find the basis functions for Koopman operator of the system, which spans the space, where observables φ(x) ∈ Rnφ evolve linearly in time, existence of which is guaranteed for forward-complete system. We use the linearity of the Koopman operator to approximate the MPI set, where the accuracy is enhanced by removing redundant basis functions using active learning. For the controlled version, we are looking for a promising way to include the control or reference input in the formulation of the Koopman operator to get the MCI set