Optimal control of the state statistics for a linear stochastic system

We consider a variant of the classical linear quadratic Gaussian regulator (LQG) in which penalties on the endpoint state are replaced by the specification of the terminal state distribution. The resulting theory considerably differs from LQG as well as from formulations that bound the probability of violating state constraints. We develop results for optimal state-feedback control in the two cases where i) steering of the state distribution is to take place over a finite window of time with minimum energy, and ii) the goal is to maintain the state at a stationary distribution over an infinite horizon with minimum power. For both problems the distribution of noise and state are Gaussian. In the first case, we show that provided the system is controllable, the state can be steered to any terminal Gaussian distribution over any specified finite time-interval. In the second case, we characterize explicitly the covariance of admissible stationary state distributions that can be maintained with constant state-feedback control. The conditions for optimality are expressed in terms of a system of dynamically coupled Riccati equations in the finite horizon case and in terms of algebraic conditions for the stationary case. In the case where the noise and control share identical input channels, the Riccati equations for finite-horizon steering become homogeneous and can be solved in closed form. The present paper is largely based on our recent work in arxiv.org/abs/1408.2222, arxiv.org/abs/1410.3447 and presents an overview of certain key results.Comment: 7 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1410.344

Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks

Estimation and Control of Robotic Radiation-Based Processes

This dissertation presents a closed-loop control and state estimation framework for a class of distributed-parameter processes employing a moving radiant actuator. These radiation-based processes have the potential to significantly reduce the energy consumption and environmental impact of traditional industrial processes. Successful implementation of these approaches in large-scale applications requires precise control systems. This dissertation provides a comprehensive framework for: 1) integration of trajectory generation and feedback control, 2) online distributed state and parameter estimation, and 3) optimal coordination of multiple manipulated variables, so as to achieve elaborate control of these radiation-based processes for improved process quality and energy efficiency. The developed framework addresses important issues for estimation and control of processes employing a moving radiant actuator from both practical and theoretical aspects. For practical systems, an integrated motion and process control approach is first developed to compensate for disturbances by adjusting either the radiant power of the actuator or the speed of the robot end effector based on available process measurements, such as temperature distribution. The control problem is then generalized by using a 1D scanning formulation that describes common characteristics of typical radiant source actuated processes. Based on this 1D scanning formulation, a distributed state and parameter estimation scheme that incorporates a dual extended Kalman filter (DEKF) approach is developed to provide real-time process estimation. In this estimation scheme, an activating policy accompanying the moving actuator is applied in order to reduce the computational cost and compensate for observability changes caused by the actuator\u27s movement. To achieve further improvements in process quality, a static optimization and a rule-based feedback control strategy are used to coordinate multiple manipulated variables in open-loop and closed-loop manners. Finally, a distributed model predictive control (MPC) framework is developed to integrate process optimization and closed-loop coordination of manipulated variables. Simulation studies conducted on a robotic ultraviolet (UV) paint curing process show that the developed estimation and control framework for radiant source actuated processes provide improved process quality and energy efficiency by adaptively compensating for disturbances and optimally coordinating multiple manipulated variables

The flow structure behind vortex generators embedded in a decelerating turbulent boundary layer

The objective of the present work is to analyse the behaviour of a turbulent decelerating boundary layer under the effect of both passive and active jets vortex generators (VGs). The stereo PIV database of Godard and Stanislas [1, 2] obtained in an adverse pressure gradient boundary layer is used for this study. After presenting the effect on the mean velocity field and the turbulent kinetic energy, the line of analysis is extended with two points spatial correlations and vortex detection in instantaneous velocity fields. It is shown that the actuators concentrate the boundary layer turbulence in the region of upward motion of the flow, and segregate the near-wall streamwise vortices of the boundary layer based on their vorticity sign

Measurements, Models, Systems and Design

531 s.