Control and optimization approaches for energy-limited systems: applications to wireless sensor networks and battery-powered vehicles

This dissertation studies control and optimization approaches to obtain energy-efficient and reliable routing schemes for battery-powered systems in network settings. First, incorporating a non-ideal battery model, the lifetime maximization problem for static wireless sensor networks is investigated. Adopting an optimal control approach, it is shown that there exists a time-invariant optimal routing vector in a fixed topology network. Furthermore, under very mild conditions, this optimal policy is robust with respect to the battery model used. Then, the lifetime maximization problem is investigated for networks with a mobile source node. Redefining the network lifetime, two versions of the problem are studied: when there exist no prior knowledge about the source node’s motion dynamics vs. when source node’s trajectory is known in advance. For both cases, problems are formulated in the optimal control framework. For the former, the solution can be reduced to a sequence of nonlinear programming problems solved on line as the source node trajectory evolves. For the latter, an explicit off-line numerical solution is required. Second, the problem of routing for vehicles with limited energy through a network with inhomogeneous charging nodes is studied. The goal is to minimize the total elapsed time, including traveling and recharging time, for vehicles to reach their destinations. Adopting a game-theoretic approach, the problem is investigated from two different points of view: user-centric vs. system-centric. The former is first formulated as a mixed integer nonlinear programming problem. Then, by exploiting properties of an optimal solution, it is reduced to a lower dimensionality problem. For the latter, grouping vehicles into subflows and including the traffic congestion effects, a system-wide optimization problem is defined. Both problems are studied in a dynamic programming framework as well. Finally, the thesis quantifies the Price Of Anarchy (POA) in transportation net- works using actual traffic data. The goal is to compare the network performance under user-optimal vs. system-optimal policies. First, user equilibria flows and origin- destination demands are estimated for the Eastern Massachusetts transportation net- work using speed and capacity datasets. Then, obtaining socially-optimal flows by solving a system-centric problem, the POA is estimated

Stochastic Nonlinear Model Predictive Control with Efficient Sample Approximation of Chance Constraints

This paper presents a stochastic model predictive control approach for nonlinear systems subject to time-invariant probabilistic uncertainties in model parameters and initial conditions. The stochastic optimal control problem entails a cost function in terms of expected values and higher moments of the states, and chance constraints that ensure probabilistic constraint satisfaction. The generalized polynomial chaos framework is used to propagate the time-invariant stochastic uncertainties through the nonlinear system dynamics, and to efficiently sample from the probability densities of the states to approximate the satisfaction probability of the chance constraints. To increase computational efficiency by avoiding excessive sampling, a statistical analysis is proposed to systematically determine a-priori the least conservative constraint tightening required at a given sample size to guarantee a desired feasibility probability of the sample-approximated chance constraint optimization problem. In addition, a method is presented for sample-based approximation of the analytic gradients of the chance constraints, which increases the optimization efficiency significantly. The proposed stochastic nonlinear model predictive control approach is applicable to a broad class of nonlinear systems with the sufficient condition that each term is analytic with respect to the states, and separable with respect to the inputs, states and parameters. The closed-loop performance of the proposed approach is evaluated using the Williams-Otto reactor with seven states, and ten uncertain parameters and initial conditions. The results demonstrate the efficiency of the approach for real-time stochastic model predictive control and its capability to systematically account for probabilistic uncertainties in contrast to a nonlinear model predictive control approaches.Comment: Submitted to Journal of Process Contro