Event

Abstract:

In network estimation and control systems like sensor networks or industrial robotic systems, there are often restrictions or uncertainties that must be taken into account. For example, bandwidth and communication constraints on the estimators or controllers are a common issue. Additionally, sometimes the dynamics model is unknown. And finally stochastic noise or deterministic exogenous disturbances can adversely affect your system.

In the first problem of the thesis, we study state estimation applications in sensor networks that are affected by limitations on battery life and bandwidth capacity. The available sensing resources must be frugally used to minimize estimation errors. The estimation error criteria can either be the minimum mean square error as in the Kalman filter or the min-max error in the robust setting. The limitation on sensor resources can be addressed by capping the number of times a sensor is activated. This is the problem of sensor sampling. Additionally, we can cap the number of sensors that are activated at any given time. This is the problem of sensor scheduling. The sensor sampling and scheduling problem can be formulated as a mixed-integer convex problem. One major question is, does the structure of the problem lend itself to manageable algorithms to solve the optimization problem. Additionally, can we find suitable upper bounds on the solution and can we bound how suboptimal the solution is?

In the first problem all sensor nodes communicate with a central hub. Because of communication restrictions, this type of centralized communication may not be possible. In the second problem, we investigate distributed risk-sensitive or robust control. Distributed, in this case, means agents in a multi-agent system do not communicate with a central hub but rather with their immediate neighbors. Each agent has a local cost function. The goal is that the agents should collaboratively minimize the global cost function despite only having access to their local neighborhoods. We propose a distributed algorithm where an agent's controller gain is the average of the controller gains of the neighbors. We show bounds on the suboptimality of this distributed controller.

However, it is not always the case in a control problem that the dynamics are known. In the third part of the thesis, we investigate discrete time risk-sensitive or robust control problems in the linear quadratic setting when the dynamics are unknown. One proposed solution is to directly solve this risk-sensitive control problem using gradients of the cost function. When the dynamics are unknown, the gradients can be approximated via simulation. Additionally, we can solve this problem with a model-based solution where we first estimate the unknown dynamics by least squares and then incorporate uncertainty in the estimator when calculating the risk-sensitive controller.