Transformed Path Integral Based Approaches for Stochastic Dynamical Systems: Prediction, Filtering, and Optimal Control

The study of stochastic systems, their characterization, prediction, and control are of great importance to many fields in science and engineering. This often involves obtaining accurate estimates of quantities of interest such as the system state distribution and/or the expected cost in nonlinear dynamical systems subjected to random forces. The computational prediction and control of such systems are often challenging (and involve large computational costs) due to the presence of nonlinearities, model and measurement uncertainties. Novel path integral–based frameworks for efficient solutions to problems in prediction, nonlinear filtering, and optimal control of stochastic dynamical systems are presented to address several key challenges. The presented frameworks are as follows: (1) the transformed path integral (TPI) approach for solution of the Fokker-Planck equation in stochastic dynamical systems with a full rank diffusion coefficient matrix, (2) the generalized transformed path integral (GTPI) approach—a non-trivial extension of the TPI to stochastic dynamical systems with rank deficient diffusion coefficient matrices, (3) the generalized transformed path integral filter (GTPIF) for solution of nonlinear filtering problems, and (4) the generalized transformed path integral control (GTPIC) for solution of a large class of stochastic optimal control problems are presented. The proposed frameworks are based on the underlying short-time propagators and dynamic transformations of the state variables that ensure the appropriate distributions in the transformed space (state distributions in TPI and GTPI; and corresponding conditional distributions in GTPIF and GTPIC) always have zero mean and identity covariance. In systems where the dynamics are linear with respect to the state variables and initial distribution is Gaussian, the appropriate distributions in the transformed space remain invariant with a standard normal distribution as expected. The frameworks thus allow for the underlying distributions necessary for evaluating the quantities of interest to be accurately represented and evolved in a transformed computational domain. Compared to conventional fixed grid approaches and Monte-Carlo simulations, the challenges in dynamical systems with large drift, diffusion, and concentration of PDF can be addressed more efficiently using the proposed frameworks. In addition, straightforward error bounds for the underlying distributions in the transformed space can be established via Chebyshev's inequality

Communication skills: what do employers' expect? (workplace communication skills for engineering graduates)

A brilliant engineer who cannot communicate is a matter to be taken seriously. What will happen to Malaysia if we keep churning out thousands of brilliant engineers but when it comes to employability skills, they are retarded? Malaysian engineering graduates especially are handicapped when it comes to communicating in English. English language is the international language used for education, business and technology. Therefore, it is crucial that an engineer masters the art of communicating in English as well as engineering knowledge. Thus, this research is conducted to find out what communication skills that the employers in the industry deem that their employees should have? However, this research only focuses on engineering graduates and the manufacturing industry. The researcher intends to learn the importance that is given to communication skills by the industry and whether it helps an engineering graduate to be promoted and be successful in their jobs. After obtaining the results from the employers, the researcher will suggest recommendation to improve the course content of KUiTTHO's Communication Skills course to be parallel with the demands of the industry

Quantum inspired algorithms for learning and control of stochastic systems

Motivated by the limitations of the current reinforcement learning and optimal control techniques, this dissertation proposes quantum theory inspired algorithms for learning and control of both single-agent and multi-agent stochastic systems. A common problem encountered in traditional reinforcement learning techniques is the exploration-exploitation trade-off. To address the above issue an action selection procedure inspired by a quantum search algorithm called Grover\u27s iteration is developed. This procedure does not require an explicit design parameter to specify the relative frequency of explorative/exploitative actions. The second part of this dissertation extends the powerful adaptive critic design methodology to solve finite horizon stochastic optimal control problems. To numerically solve the stochastic Hamilton Jacobi Bellman equation, which characterizes the optimal expected cost function, large number of trajectory samples are required. The proposed methodology overcomes the above difficulty by using the path integral control formulation to adaptively sample trajectories of importance. The third part of this dissertation presents two quantum inspired coordination models to dynamically assign targets to agents operating in a stochastic environment. The first approach uses a quantum decision theory model that explains irrational action choices in human decision making. The second approach uses a quantum game theory model that exploits the quantum mechanical phenomena \u27entanglement\u27 to increase individual pay-off in multi-player games. The efficiency and scalability of the proposed coordination models are demonstrated through simulations of a large scale multi-agent system --Abstract, page iii