# MiniSymposium-11: Stochastic Modeling and Control

This mini symposium focuses on stochastic modeling and control with applications. The solutions to stochastic optimal control and stochastic differential games are presented with a noise being modelled by Rosenblatt process which is non- Gaussian. The mean-variance portfolio selection problem for partially-observed point processes is studied and the optimal strategy based on the filtering estimators is derived. Mathematical modeling of lithium-ion batteries is a central challenge in advanced battery management. Two new frameworks to integrate physics-based model with machine learning to achieve high-precision modeling for the batteries are presented. New developments and new challenges in noise models for stochastic control and adaptive control problems are further discussed. All talks present interdisciplinary research with stochastic systems and control playing the central role in it.

## Organizer:

**Bozenna Pasik-Duncan**, University of Kansas

## Saturday, October 2, 2021 at 2:40 – 4:00 pm (CST)

**Tyrone Duncan**

University of Kansas

2:40 pm

*Some Control and Differential Games with Rosenblatt Processes*

Some solutions of stochastic control and stochastic differential games for linear equations driven by Rosenblatt processes are presented. These Rosenblatt processes are not Gaussian and seem to be appropriate for models where the noise is non-Gaussian. This work includes joint work with B. Pasik-Duncan, P. Coupek and B. Maslowski.

**Yong Zeng**

University of Missouri-Kansas City

3:00 pm

*Mean Variance Portfolio Selection for Partially-Observed Point Processes*

We study the mean-variance portfolio selection problem for a class of models well fit time-stamped transactions data. The price process of each stock is described by a collection of partially observed point processes. They are the noisy observation of an intrinsic value process, mildly assumed to be Markovian. However, the control problem with partial information is non-Markovian and depends on an infinite-dimensional measure-valued input. To solve the challenging problem, we first establish a separation principle, which divides the filtering and the control problems and reduces the infinite-dimensional input to finite-dimensional ones. Building upon the result of nonlinear filtering with counting process observations, we solve the control problem by employing the stochastic maximum principle for control with forward-backward SDEs developed in [SIAM J. Control Optim. 48 (2009), pp. 2945-2976]. We explicitly obtain the efficient frontier and derive the optimal strategy based on the filtering estimators. This work is joint with Jie Xiong and Shuaiqi Zhang.

**Hao Tu**

University of Kansas

3:20 pm

*Integrating Physics-Based Modeling with Machine Learning for Lithium-ion Batteries*

Mathematical modeling of lithium-ion batteries (LiBs) is a central challenge in advanced battery management. This work presents two new frameworks to integrate physics-based model with machine learning to achieve high-precision modeling for LiBs. These two new frameworks uniquely propose to inform the machine learning model of the state information of the physical model, enabling a deep integration between physics and machine learning. We construct a series of hybrid models based on the two frameworks, which blend electrochemical model or equivalent circuit model with a feedforward neural network to achieve physics-informed learning of a LiB's dynamical behavior.

The constructed hybrid models are parsimonious in structure and can provide considerable predictive accuracy under a broad range of C-rates, as shown by extensive simulations and experiments. This is joint work with Huazhen Fang.

**Bozenna Pasik-Duncan**

University of Kansas

3:40 pm

*Interdisciplinary Research: The Central Role of Stochastic Systems and Adaptive Control*

Many continuous time stochastic systems that are modeled by SDE and SPDE have been limited to noise processes being Brownian motions. Brownian motion models have developed stochastic calculus and limiting behaviors that reflect the martingale, Markov and Gaussian properties of Brownian motion. However, for many physical systems the empirical data do not justify the use of Brownian motion as the model for random disturbances. In fact, Brownian motions provide models that are often far from the physical data. Thus, it is necessary to find more general noise models and tractable methods to solve the associated problems of control or adaptive control. These other noise models include more general Gaussian processes and non-Gaussian processes. The talk focuses on new developments and new challenges in noise models for stochastic control and adaptive control problems. It also shows the power, beauty and excitement of interdisciplinary research with stochastic systems and control playing the central role in it.