A maximum principle for controlled time-symmetric forward-backward doubly stochastic differential equation with initial-terminal sate constraints

In this paper, we study the optimal control problem of a controlled time-symmetric forward-backward doubly stochastic differential equation with initial-terminal sate constraints. Applying the terminal perturbation method and Ekeland's variation principle, a necessary condition of the stochastic optimal control, i.e., stochastic maximum principle is derived. Applications to backward doubly stochastic linear-quadratic control models are investigated.Comment: 22 page

Markov chains and optimality of the Hamiltonian cycle

We consider the Hamiltonian cycle problem (HCP) embedded in a controlled Markov decision process. In this setting, HCP reduces to an optimization problem on a set of Markov chains corresponding to a given graph. We prove that Hamiltonian cycles are minimizers for the trace of the fundamental matrix on a set of all stochastic transition matrices. In case of doubly stochastic matrices with symmetric linear perturbation, we show that Hamiltonian cycles minimize a diagonal element of a fundamental matrix for all admissible values of the perturbation parameter. In contrast to the previous work on this topic, our arguments are primarily based on probabilistic rather than algebraic methods

Sub-optimal boundary control of semilinear pdes using a dyadic perturbation observer

In this paper, we present a sub-optimal controller for semilinear partial differential equations, with partially known nonlinearities, in the dyadic perturbation observer (DPO) framework. The dyadic perturbation observer uses a two-stage perturbation observer to isolate the control input from the nonlinearities, and to predict the unknown parameters of the nonlinearities. This allows us to apply well established tools from linear optimal control theory to the controlled stage of the DPO. The small gain theorem is used to derive a condition for the robustness of the closed loop system

A Nonlinear Analysis of Movement Variability: Stability in a Sit to a Stand

abstract: The human body is a complex system comprised of many parts that can coordinate in a variety of ways to produce controlled action. This creates a challenge for researchers and clinicians in the treatment of variability in motor control. The current study aims at testing the utility of a nonlinear analysis measure – the Largest Lyapunov exponent (1) – in a whole body movement. Experiment 1 examined this measure, in comparison to traditional linear measure (standard deviation), by having participants perform a sit-to-stand (STS) task on platforms that were either stable or unstable. Results supported the notion that the Lyapunov measure characterized controlled/stable movement across the body more accurately than the traditional standard deviation (SD) measure. Experiment 2 tested this analysis further by presenting participants with an auditory perturbation during performance of the same STS task. Results showed that both the Lyapunov and SD measures failed to detect the perturbation. However, the auditory perturbation may not have been an appropriate perturbation. Limitations of Experiment 2 are discussed, as well as directions for future study.Dissertation/ThesisMasters Thesis Psychology 201