Uncertainty in Sampled Systems

The recently obtained evidence of the need for a positive real element in an adaptive system leaves us with a disturbing gap in adaptive control theory. It is a fact that in some applications adaptive controllers are performing well in practice. How can these systems behave well in practical situations which must contain modeling error? This paper introduces a preliminary result which indicates that it may be possible to maintain the needed positive real system in the presence of modeling error. The result shows that if a continuous-time system with large high frequency uncertainty is treated appropriately with antialiasing filters and sampled slowly enough, the resulting discrete-time system may contain very little uncertainty. With small enough uncertainty in the plant, a positive real system in the adaptive loop is possibl

A Direct Adaptive Controller for ATM ABR Congestion Control

One of the more challenging and yet unresolved issues which is paramount to the success of ATM networks is that of congestion control for Available Bit Rate (ABR) traffic. Unlike other ATM service categories, ABR provides a feedback mechanism, allowing interior nodes to dictate source rates. Previous work has demonstrated how linear control theory can be utilized to create a stable and efficient control system for the purposes of ATM ABR congestion control. This paper extends our previous contribution that assumed a minimum-phase plant, an assumption that is likely violated in practice. Presented here is a direct adaptive controller that uses a finite impulse response (FIR) filter to approximately invert the FIR plant. This controller is well suited for the ATM ABR non-minimum-phase plant. Other control architectures, which motivate the final proposed controller, are also discussed

Optimal Mean-Variance Portfolio Construction in Cointegrated Vector Autoregressive Systems

Abstract-We study the problem of optimal portfolio construction when the log-prices follow a discrete-time cointegrated vector autoregressive model. We follow the classical Markowitz mean-variance optimization approach, and derive expressions for the optimal portfolio weight vector over a single decision interval, both for a finite-time horizon and in the limit of an infinite horizon. It is often stated in the literature that given assets whose price dynamics exhibit cointegration, the portfolio weights should be chosen from the space of cointegrating relations, resulting in what is commonly referred to as the beta portfolio. However, we show here that the optimal action in the mean-variance sense for a finite trading interval is to buy the portfolio with a component both in the beta direction and a component in the direction of expected change. Furthermore, we prove that the beta portfolio is optimal only in the limit of an infinite trading horizon. Additionally, we derive the conditions under which the optimal portfolio is proportional to the disequilibrium readjustment forces of the cointegration model. Our results rely on a careful eigenanalysis of the underlying state space model, in which we derive a closed form solution for the optimal Markowitz portfolio, which is well-behaved despite the nonstationarity of the underlying price dynamics. We demonstrate our results with evaluations using both simulated and historical data

A linear control approach to explicit rate feedback in ATM networks

Rate-based feedback congestion control has been proposed as a form of traffic management for available bit rate traffic in ATM networks. This paper discusses applying linear control theory to these algorithms. A congestion control scheme for simple networks is designed and analyzed using the tools of classical control theory. This allows insight into the trade-offs in such schemes and suggests approaches to larger networks. I

A Practical Controller for Explicit Rate Congestion Control

This paper examines congestion control for explicit rate data networks. The Available Bit Rate (ABR) service category of Asynchronous Transfer Mode (ATM) networks serves as an example system, however the results of this paper are applicable to other explicit rate systems as well. After a plant model is established, an adaptive control strategy is presented. Several algorithm enhancements are then introduced. These enhancements reduce convergence time, improve queue depth management, and reduce parameter bias. This work differentiates itself from the other contributions in the area of rate-based congestion control in its balanced approach of retaining enough complexity as to afford attractive performance properties, but not so much complexity as to make implementation prohibitively expensive

Power and server allocation in a multi-beam satellite with time varying channels

Abstract-- We consider power and server allocation in a multibeam satellite downlink which transmits data to N different ground locations over N time-varying channels. Packets destined for each ground location are stored in separate queues, and the server rate for each queue i depends on the power p i (t) allocated to that server and the channel state c i (t) according to a concave ratepower curve µ i (p i, c i). We establish the capacity region of all arrival rate vectors (λ 1,...,λ N) which admit a stabilizable system. For the case when channel states and arrivals are iid from timeslot to timeslot, we develop a particular power allocation policy which stabilizes the system whenever the rate vector lies within the capacity region. Such stability is guaranteed even if the channel model and the specific arrival rates are unknown. As a special case, this analysis verifies stability of the “Choose-the-K-Largest-Connected-Queues ” policy when channels can be in one of two states (ON or OFF) and K servers are allocated at every timestep (K<N). These results are extended to treat a joint problem of routing and power allocation, and a throughput maximizing algorithm for this joint problem is constructed. Finally, we address the issue of inter-channel interference, and develop a modified policy when power vectors are constrained to feasible activation sets. Our analysis and problem formulation is also applicable to power control for wireless systems. I