Predictive and adaptive extremal control

The time-optimal predictive control strategy for second order relay or bang-bang control systems is investigated along with modifications of this strategy for third order systems. One basis of this strategy is the utilization of a model, a replica of the plant, run in a fast-time mode so as to obtain the future output of the plant under the present input. Based upon these measurements, corrections to the plant may be implemented to achieve the desired response. The concept of the fast model is a useful one in that it falls into the synthesis of the more general time-optimal trajectory and switching functions for various second, third and higher order plants. However the difficulties in providing the exact time-optimal control for these plants result in the generation of acceptable sub-optimal and near time-optimal strategies. The nature of plant sensitivity, parameter variation and identification are investigated as well as a novel self-adoptive controller which dispenses with the identification phase but identifies a certain surface in the state space and establishes a stable sub-optimal control strategy. These control techniques are applied to a small DC motor with responses close to time-optimal

Optimal Real-time Spectrum Sharing between Cooperative Relay and Ad-hoc Networks

Optimization based spectrum sharing strategies have been widely studied. However, these strategies usually require a great amount of real-time computation and significant signaling delay, and thus are hard to be fulfilled in practical scenarios. This paper investigates optimal real-time spectrum sharing between a cooperative relay network (CRN) and a nearby ad-hoc network. Specifically, we optimize the spectrum access and resource allocation strategies of the CRN so that the average traffic collision time between the two networks can be minimized while maintaining a required throughput for the CRN. The development is first for a frame-level setting, and then is extended to an ergodic setting. For the latter setting, we propose an appealing optimal real-time spectrum sharing strategy via Lagrangian dual optimization. The proposed method only involves a small amount of real-time computation and negligible control delay, and thus is suitable for practical implementations. Simulation results are presented to demonstrate the efficiency of the proposed strategies.Comment: One typo in the caption of Figure 5 is correcte

Stabilization of Linear Systems Over Gaussian Networks

The problem of remotely stabilizing a noisy linear time invariant plant over a Gaussian relay network is addressed. The network is comprised of a sensor node, a group of relay nodes and a remote controller. The sensor and the relay nodes operate subject to an average transmit power constraint and they can cooperate to communicate the observations of the plant's state to the remote controller. The communication links between all nodes are modeled as Gaussian channels. Necessary as well as sufficient conditions for mean-square stabilization over various network topologies are derived. The sufficient conditions are in general obtained using delay-free linear policies and the necessary conditions are obtained using information theoretic tools. Different settings where linear policies are optimal, asymptotically optimal (in certain parameters of the system) and suboptimal have been identified. For the case with noisy multi-dimensional sources controlled over scalar channels, it is shown that linear time varying policies lead to minimum capacity requirements, meeting the fundamental lower bound. For the case with noiseless sources and parallel channels, non-linear policies which meet the lower bound have been identified

Power allocation in wireless multi-user relay networks

In this paper, we consider an amplify-and-forward wireless relay system where multiple source nodes communicate with their corresponding destination nodes with the help of relay nodes. Conventionally, each relay equally distributes the available resources to its relayed sources. This approach is clearly sub-optimal since each user experiences dissimilar channel conditions, and thus, demands different amount of allocated resources to meet its quality-of-service (QoS) request. Therefore, this paper presents novel power allocation schemes to i) maximize the minimum signal-to-noise ratio among all users; ii) minimize the maximum transmit power over all sources; iii) maximize the network throughput. Moreover, due to limited power, it may be impossible to satisfy the QoS requirement for every user. Consequently, an admission control algorithm should first be carried out to maximize the number of users possibly served. Then, optimal power allocation is performed. Although the joint optimal admission control and power allocation problem is combinatorially hard, we develop an effective heuristic algorithm with significantly reduced complexity. Even though theoretically sub-optimal, it performs remarkably well. The proposed power allocation problems are formulated using geometric programming (GP), a well-studied class of nonlinear and nonconvex optimization. Since a GP problem is readily transformed into an equivalent convex optimization problem, optimal solution can be obtained efficiently. Numerical results demonstrate the effectiveness of our proposed approach

Decentralized Dynamic Hop Selection and Power Control in Cognitive Multi-hop Relay Systems

In this paper, we consider a cognitive multi-hop relay secondary user (SU) system sharing the spectrum with some primary users (PU). The transmit power as well as the hop selection of the cognitive relays can be dynamically adapted according to the local (and causal) knowledge of the instantaneous channel state information (CSI) in the multi-hop SU system. We shall determine a low complexity, decentralized algorithm to maximize the average end-to-end throughput of the SU system with dynamic spatial reuse. The problem is challenging due to the decentralized requirement as well as the causality constraint on the knowledge of CSI. Furthermore, the problem belongs to the class of stochastic Network Utility Maximization (NUM) problems which is quite challenging. We exploit the time-scale difference between the PU activity and the CSI fluctuations and decompose the problem into a master problem and subproblems. We derive an asymptotically optimal low complexity solution using divide-and-conquer and illustrate that significant performance gain can be obtained through dynamic hop selection and power control. The worst case complexity and memory requirement of the proposed algorithm is O(M^2) and O(M^3) respectively, where $M$ is the number of SUs

Submodularity and Optimality of Fusion Rules in Balanced Binary Relay Trees

We study the distributed detection problem in a balanced binary relay tree, where the leaves of the tree are sensors generating binary messages. The root of the tree is a fusion center that makes the overall decision. Every other node in the tree is a fusion node that fuses two binary messages from its child nodes into a new binary message and sends it to the parent node at the next level. We assume that the fusion nodes at the same level use the same fusion rule. We call a string of fusion rules used at different levels a fusion strategy. We consider the problem of finding a fusion strategy that maximizes the reduction in the total error probability between the sensors and the fusion center. We formulate this problem as a deterministic dynamic program and express the solution in terms of Bellman's equations. We introduce the notion of stringsubmodularity and show that the reduction in the total error probability is a stringsubmodular function. Consequentially, we show that the greedy strategy, which only maximizes the level-wise reduction in the total error probability, is within a factor of the optimal strategy in terms of reduction in the total error probability