Reduction of delayed optimal control problems to nondelayed problems

A method is exhibited which transforms a large class of optimal control problems with fixed delays to nondelayed problems, thus permitting classical results to be used in their analysis.     

Asymptotically decoupled systems

In this paper, two linear-quadratic systems are shown to be asymptotically decoupled. We obtain the steady-state term and the first-order transient term of optimal controls. We also obtain an estimate of the rate at which the first-order transient term diminishes and approaches zero.     

Optimal control of systems with multiple criteria when disturbances are present

Optimal control problems with a vector performance index and uncertainty in the state equations are investigated. Nature chooses the uncertainty, subject to magnitude bounds. For these problems, a definition of optimality is presented. This definition reduces to that of a minimax control in the case of a scalar cost and to Pareto optimality when there is no uncertainty or disturbance present. Sufficient conditions for a control to satisfy this definition of optimality are derived. These conditions are in terms of a related two-player zero-sum differential game and suggest a technique for determining the optimal control. The results are illustrated with an example.This research was supported by AFOSR under Grant No. 76-2923.     

On the discrete-time regulator problem in infinite-dimensional spaces

The linear, discrete-time regulator problem is considered in infinite-dimensional spaces without posing in advance any positivity conditions on quadratic criterion. The convergence of the finite-time optimum solution is studied, when time increases to infinity with a stable, stabilizable, and detectable system.The author thanks Professors P. Karttunen and H. Koivo for helpful discussions regarding this note.     

Deterministic optimal control,given only a partial observation of the initial state

The deterministic linear-system, quadratic-cost optimal control problem is considered when the only state information available is a partial linear observation of the initial statex ₀. Thus, it is only known that the initial condition belongs to a particular linear variety. A control function is found which is optimal, in the sense (roughly) that (i) it can be computed using available information aboutx ₀ and (ii) no other control function which can be found using that information gives lower cost than it does for every initial condition that could have given rise to the information. The optimal control can be found easily from the conventional Riccati equation of optimal control. Applications are considered in the presence of unknown exponential disturbances and to the case with a sequence of partial state observations.     

Solution of nonlinear optimal control problems in Hilbert spaces by means of linear programming techniques

Optimal control problems in Hilbert spaces are considered in a measure-theoretical framework. Instead of minimizing a functional defined on a class of admissible trajectory-control pairs, we minimize one defined on a set of measures; this set is defined by the boundary conditions and the differential equation of the problem. The new problem is an infinite-dimensionallinear programming problem; it is shown that it is possible to approximate its solution by that of a finite-dimensional linear program of sufficiently high dimensions, while this solution itself can be approximated by a trajectory-control pair. This pair may not be strictly admissible; if the dimensionality of the finite-dimensional linear program and the accuracy of the computations are high enough, the conditions of admissibility can be said to be satisfied up to any given accuracy. The value given by this pair to the functional measuring the performance criterion can be about equal to theglobal infimum associated with the classical problem, or it may be less than this number. It appears that this method may become a useful technique for the computation of optimal controls, provided the approximations involved are acceptable.     

On the optimum design of piston rings

We study a family of control problems that arise in the design of dynamically loaded bearings which have a minimum power loss; in particular, we study the design of piston rings with minimum parasitic power loss.This research was partially supported by NSF Grant No. MCS-77-05624.     

On Brunovský's example

The example due to Brunovský [Eq. (1)] is analyzed, and further paradoxical properties are exhibited.     

Opportunistic Multi-Access: Multiuser Diversity, Relay-Aided Opportunistic Scheduling, and Traffic-Aided Smooth Admission Control

We study multi-access control in opportunistic communication systems, and propose two new schemes to address channel asymmetry and throughput-guaranteed admission control, respectively. We first devise a relay-aided opportunistic scheduling (RAOS) scheme, in which a user can choose to communicate with the base station either directly or using multiple hops (relay transmissions). We develop relay/direct link construction algorithms using either a channel-capacity-based criterion or a throughput-based criterion, and devise opportunistic scheduling schemes accordingly. Our results show that in the presence of channel asymmetry across users, the RAOS scheme performs significantly better than Qualcomm's HDR scheme. Next, we propose a traffic-aided smooth admission control (SAC) scheme that aims to guarantee throughput provisioning. Simply put, in the SAC scheme, the admission decision is spread over a trial period, by increasing gradually the amount of the time resource allocated to incoming users. Specifically, using the modified weighted proportional fair (WPF) scheduling, we devise a QoS driven weight adaptation algorithm, and the weights assigned to new users are increased in a guarded manner. Then an admission decision is made based on the measured throughput within a time-out window. A key feature is that we exploit explicitly the traffic information and throughput requirements in devising the back-off time. Our results show that the proposed SAC scheme works well in opportunistic communication systems.     

The Number of Neighbors Needed for Connectivity of Wireless Networks

Wireless Networks - Unlike wired networks, wireless networks do not come with links. Rather, links have to be fashioned out of the ether by nodes choosing neighbors to connect to. Moreover the...