Method for Solving State-Path Constrained Optimal Control Problems Using Adaptive Radau Collocation

A new method is developed for accurately approximating the solution to state-variable inequality path constrained optimal control problems using a multiple-domain adaptive Legendre-Gauss-Radau collocation method. The method consists of the following parts. First, a structure detection method is developed to estimate switch times in the activation and deactivation of state-variable inequality path constraints. Second, using the detected structure, the domain is partitioned into multiple-domains where each domain corresponds to either a constrained or an unconstrained segment. Furthermore, additional decision variables are introduced in the multiple-domain formulation, where these additional decision variables represent the switch times of the detected active state-variable inequality path constraints. Within a constrained domain, the path constraint is differentiated with respect to the independent variable until the control appears explicitly, and this derivative is set to zero along the constrained arc while all preceding derivatives are set to zero at the start of the constrained arc. The time derivatives of the active state-variable inequality path constraints are computed using automatic differentiation and the properties of the chain rule. The method is demonstrated on two problems, the first being a benchmark optimal control problem which has a known analytical solution and the second being a challenging problem from the field of aerospace engineering in which there is no known analytical solution. When compared against previously developed adaptive Legendre-Gauss-Radau methods, the results show that the method developed in this paper is capable of computing accurate solutions to problems whose solution contain active state-variable inequality path constraints.Comment: 31 pages, 7 figures, 5 table

Throughput Optimization in High Speed Downlink Packet Access (HSDPA)

In this paper, we investigate throughput optimization in High Speed Downlink Packet Access (HSDPA). Specifically, we propose offline and online algorithms for adjusting the Channel Quality Indicator (CQI) used by the network to schedule data transmission. In the offline algorithm, a given target BLER is achieved by adjusting CQI based on ACK/NAK history. By sweeping through different target BLERs, we can find the throughput optimal BLER offline. This algorithm could be used not only to optimize throughput but also to enable fair resource allocation among mobile users in HSDPA. In the online algorithm, the CQI offset is adapted using an estimated short term throughput gradient without specifying a target BLER. An adaptive stepsize mechanism is proposed to track temporal variation of the environment. We investigate convergence behavior of both algorithms. Simulation results show that the proposed offline algorithm can achieve the given target BLER with good accuracy. Both algorithms yield up to 30% HSDPA throughput improvement over that with 10% target BLER