Michael Rinehart

Optimally controlling Hybrid Electric Vehicles using path forecasting

The paper examines path-dependent control of Hybrid Electric Vehicles (HEVs). In this approach we seek to improve HEV fuel economy by optimizing charging and discharging of the vehicle battery depending on the forecasted vehicle route. The route is decomposed into a series connection of route segments with (partially) known properties. The dynamic programming is used as a tool to quantify the benefits offered by route information availability.

Suboptimal Control of Switched Systems With an Application to the DISC Engine

The growing stringency of fuel economy, emissions, and drivability requirements has led to proliferation of powertrain systems that have multiple discrete operating modes. Systematic approaches to the development of optimal and robust control systems for such powertrains are needed to contain their increased development times and costs. In this paper, we propose a new approach for controlling switched systems that is applicable to powertrain systems with multiple operating modes. Our approach reduces the complexity of computing a control law to a linear programming problem defined over a finite number of states in each operating mode. The methodology is designed to be suitable for practical applications while, under appropriate conditions, providing near-optimal performance. An application to the direct injection stratified charge engine with two distinct operating modes is given to illustrate our approach.

Path dependent receding horizon control policies for Hybrid Electric Vehicles

Future Hybrid Electric Vehicles (HEVs) may use path-dependent operating policies to improve fuel economy. In our previous work, we developed a dynamic programming (DP) algorithm for prescribing the battery State of Charge (SoC) set-point, which in combination with a novel approach of route decomposition, has been shown to reduce fuel consumption over selected routes. In this paper, we propose and illustrate a receding horizon control (RHC) strategy for the on-board optimization of the fuel consumption. As compared to the DP approach, the computational requirements of the RHC strategy are lower. In addition, the RHC strategy is capable of correcting for differences between characteristics of a predicted route and a route actually traveled. Our numerical results indicate that the fuel economy potential of the RHC solution can approach that of the DP solution.

Value Iteration for (Switched) Homogeneous Systems

In this note, we prove that dynamic programming value iteration converges uniformly for discrete-time homogeneous systems and continuous-time switched homogeneous systems. For discrete-time homogeneous systems, rather than discounting the cost function (which exponentially decreases the weights of the cost of future actions), we show that such systems satisfy approximate dynamic programming conditions recently developed by Rantzer, which provides a uniform bound on the convergence rate of value iteration over a compact set. For continuous-time switched homogeneous system, we present a transformation that generates an equivalent discrete-time homogeneous system with an additional ldquosamplingrdquo input for which discrete-time value iteration is compatible, and we further show that the inclusion of homogeneous switching costs results in a continuous value function.

The Value of Side Information in Shortest Path Optimization

Consider an agent who seeks to traverse the shortest path in a graph having random edge weights. If the agent has no side information about the realizations of the edge weights, it should simply take the path of least average length. We consider a generalization of this framework whereby the agent has access to a limited amount of side information about the edge weights ahead of choosing a path. We define a measure for information quantity, provide bounds on the agents performance relative to the amount of side information it receives, and present algorithms for optimizing side information. The results are based on a new graph characterization tied to shortest path optimization.

The value of sequential information in shortest path optimization

Consider an agent who seeks to traverse the shortest path in a graph having random edge weights. If the agent has no side information about the realizations of the edge weights, it should simply take the path of least average length, a deterministic optimization. We consider a generalization of this framework whereby the agent has access to a limited amount of side information about the edge weights as it traverses the graph. Specifically, we define a notion of side information and capacity, and we provide bounds on the agents performance relative to the total amount of side information it receives. The results are based in a graph reduction for shortest path optimization and an abstraction of sequential decision-making.

A graph reduction for bounding the value of side information in shortest path optimization

Consider an agent who seeks to traverse the shortest path in a graph having random edge weights. If the agent has no side information about the realizations of the edge weights, it should simply take the path of least average length, a deterministic optimization. We consider a generalization of this framework whereby the agent has access to a limited amount of side information about the edge weights ahead of choosing a path. Specifically, we define a notion of information and information capacity, provide bounds on the agents performance relative to the amount of side information it receives, and offer algorithms for optimizing information within a capacity constraint. The results are based on a new graph reduction for shortest path optimization that strikes a balance between the amount of information about the graph and the distribution of the edge weights used to compute performance bounds.

Optimal Control of Switched Homogeneous Systems

In this paper, we present a method for designing discrete-time state-feedback controllers for a class of continuous-time switched homogeneous systems which includes switched linear systems as a special case. A discrete-time approximate value iteration over a quantization of the unit sphere is used to compute an approximation of the continuous-time value function over the entire unbounded state space. Properties of the value function and its approximations are elicited and used to provide conditions under which state- feedback controllers with provable guarantees in stability and performance can be constructed. To illustrate the results, the methodology is applied to an example switched system possessing two unstable modes, one of which is nonlinear.

Shortest path optimization under limited information

The problem of finding an optimal path in an uncertain graph arises in numerous applications, including network routing, path-planning for vehicles, and the control of finite-state systems. While techniques in robust and stochastic programming can be employed to compute, respectively, worst-case and average-optimal solutions to the shortest-path problem, we consider an alternative problem where the agent that traverses the graph can request limited information about the graph before choosing a path to traverse. In this paper, we define and quantify a notion of information that is compatible to this performance-based framework, bound the performance of the agent subject to a bound on the capacity of the information it can request, and present algorithms for optimizing information.

Optimization of spread-spectrum MSK sequences and passive, multi-resonant bandpass rectifiers for wireless power transfer with low electromagnetic interference

This paper addresses the concern for both electromagnetic interference (EMI) and human RF exposure in wireless power transfer (WPT). In many applications like medical, portable, and wearable devices, RF exposure is a greater concern, and the unrestricted ISM bands are often not optimal. Outside of the ISM bands, the restrictions on transmitter power are onerous. The computer-aided design of appropriate spread spectrum sequences to drive WPT and the associated bandpass rectifiers is presented. The sequences are optimized for a new four-quadrant inverse class D amplifier using a genetic algorithm. The wireless power is captured by a high order bandpass rectifier that is optimized using a surrogate model to alleviate the computation cost of performing time domain simulations.