Probabilistic Framework for Sensor Management

A probabilistic sensor management framework is introduced, which maximizes the utility of sensor systems with many different sensing modalities by dynamically configuring the sensor system in the most beneficial way. For this purpose, techniques from stochastic control and Bayesian estimation are combined such that long-term effects of possible sensor configurations and stochastic uncertainties resulting from noisy measurements can be incorporated into the sensor management decisions

Stochastic Nonlinear Model Predictive Control with Guaranteed Error Bounds Using Compactly Supported Wavelets

In model predictive control, a high quality of control can only be achieved, if the model of the system reflects the real-world process as precisely as possible. Therefore, the controller should be capable of both handling a nonlinear system description and systematically incorporating uncertainties affecting the system. Since stochastic nonlinear model predictive control (SNMPC) problems in general cannot be solved in closed form, either the system model or the occurring densities have to be approximated. In this paper, we present an SNMPC framework, which approximates the densities and the reward function by their wavelet expansions. Due to the few requirements on the shape and family of the densities or reward function, the presented technique can be applied to a large class of SNMPC problems. For accelerating the optimization, we additionally present a novel thresholding technique, the so-called dynamic thresholding, which neglects coefficients that are insignificant, while at the same time guaranteeing that the optimal control input is still chosen. The capabilities of the proposed approach are demonstrated by simulations with a path planning scenario

Stochastic Event-Based Control and Estimation

Digital controllers are traditionally implemented using periodic sampling, computation, and actuation events. As more control systems are implemented to share limited network and CPU bandwidth with other tasks, it is becoming increasingly attractive to use some form of event-based control instead, where precious events are used only when needed. Forms of event-based control have been used in practice for a very long time, but mostly in an ad-hoc way. Though optimal solutions to most event-based control problems are unknown, it should still be viable to compare performance between suggested approaches in a reasonable manner. This thesis investigates an event-based variation on the stochastic linear-quadratic (LQ) control problem, with a fixed cost per control event. The sporadic constraint of an enforced minimum inter-event time is introduced, yielding a mixed continuous-/discrete-time formulation. The quantitative trade-off between event rate and control performance is compared between periodic and sporadic control. Example problems for first-order plants are investigated, for a single control loop and for multiple loops closed over a shared medium. Path constraints are introduced to model and analyze higher-order event-based control systems. This component-based approach to stochastic hybrid systems allows to express continuous- and discrete-time dynamics, state and switching constraints, control laws, and stochastic disturbances in the same model. Sum-of-squares techniques are then used to find bounds on control objectives using convex semidefinite programming. The thesis also considers state estimation for discrete time linear stochastic systems from measurements with convex set uncertainty. The Bayesian observer is considered given log-concave process disturbances and measurement likelihoods. Strong log-concavity is introduced, and it is shown that the observer preserves log-concavity, and propagates strong log-concavity like inverse covariance in a Kalman filter. A recursive state estimator is developed for systems with both stochastic and set-bounded process and measurement noise terms. A time-varying linear filter gain is optimized using convex semidefinite programming and ellipsoidal over-approximation, given a relative weight on the two kinds of error

Directional Estimation for Robotic Beating Heart Surgery

In robotic beating heart surgery, a remote-controlled robot can be used to carry out the operation while automatically canceling out the heart motion. The surgeon controlling the robot is shown a stabilized view of the heart. First, we consider the use of directional statistics for estimation of the phase of the heartbeat. Second, we deal with reconstruction of a moving and deformable surface. Third, we address the question of obtaining a stabilized image of the heart

Directional Estimation for Robotic Beating Heart Surgery

In robotic beating heart surgery, a remote-controlled robot can be used to carry out the operation while automatically canceling out the heart motion. The surgeon controlling the robot is shown a stabilized view of the heart. First, we consider the use of directional statistics for estimation of the phase of the heartbeat. Second, we deal with reconstruction of a moving and deformable surface. Third, we address the question of obtaining a stabilized image of the heart

Uncertainty Quantification via Polynomial Chaos Expansion – Methods and Applications for Optimization of Power Systems

Fossil fuels paved the way to prosperity for modern societies, yet alarmingly, we can exploit our planet’s soil only so much. Renewable energy sources inherit the burden to quench our thirst for energy, and to reduce the impact on our environment simultaneously. However, renewables are inherently volatile; they introduce uncertainties. What is the effect of uncertainties on the operation and planning of power systems? What is a rigorous mathematical formulation of the problems at hand? What is a coherent methodology to approaching power system problems under uncertainty? These are among the questions that motivate the present thesis that provides a collection of methods for uncertainty quantification for (optimization of) power systems. We cover power flow (PF) and optimal power flow (OPF) under uncertainty (as well as specific derivative problems). Under uncertainty---we view "uncertainty" as continuous random variables of finite variance---the state of the power system is no longer certain, but a random variable. We formulate PF and OPF problems in terms of random variables, thusly exposing the infinite-dimensional nature in terms of L2-functions. For each problem formulation we discuss a solution methodology that renders the problem tractable: we view the problem as a mapping under uncertainty; uncertainties are propagated through a known mapping. The method we employ to propagate uncertainties is called polynomial chaos expansion (PCE), a Hilbert space technique that allows to represent random variables of finite variance in terms of real-valued coefficients. The main contribution of this thesis is to provide a rigorous formulation of several PF and OPF problems under uncertainty in terms of infinite-dimensional problems of random variables, and to provide a coherent methodology to tackle these problems via PCE. As numerical methods are moot without numerical software another contribution of this thesis is to provide PolyChaos.jl: an open source software package for orthogonal polynomials, quadrature rules, and PCE written in the Julia programming language