Peter E. Caines

Discrete-time multivariable adaptive control

This paper establishes global convergence for a class of adaptive control algorithms applied to discrete time multi-input multi-output deterministic linear systems. It is shown that the algorithms will ensure that the system inputs and outputs remain bounded for all time and that the output tracking error converges to zero.

Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized

We consider linear quadratic Gaussian (LQG) games in large population systems where the agents evolve according to nonuniform dynamics and are coupled via their individual costs. A state aggregation technique is developed to obtain a set of decentralized control laws for the individuals which possesses an epsiv-Nash equilibrium property. A stability property of the mass behavior is established, and the effect of inaccurate population statistics on an isolated agent is also analyzed by variational techniques.

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This paper establishes global convergence of a stochastic adaptive control algorithm for discrete time linear systems. It is shown that, with probability one, the algorithm will ensure the system inputs and outputs are sample mean square bounded and the conditional mean square output tracking error achieves its global minimum possible value for linear feedback control. Thus, asymptotically, the adaptive control algorithm achieves the same performance as could be achieved if the system parameters were known.

-Nash Equilibria

We consider uplink power control for lognormal fading channels in the large population case. First, we examine the structure of the control law in a centralized stochastic optimal control setup. We analyze the effect of large populations on the individual control inputs. Next, we split the centralized cost to approach the problem in a game theoretic framework. In this context, we introduce an auxiliary LQG control system and analyze the resulting /spl epsiv/-Nash equilibrium for the control law; subsequently we generalize the methodology developed for the LQG problem to the wireless power control problem to get an approximation for the collective effect of all other users on a given user. The obtained state aggregation technique leads to highly localized control configurations in contrast to the full state based optimal control strategy.

Discrete Time Stochastic Adaptive Control

This paper describes a modelling methodology for multivariate stochastic processes. The concept of multiple causality is discussed and a procedure to detect multiple causality is suggested. The data of a major Canadian supermarket is analyzed and a multivariate autoregressive model for this supermarket is constructed and estimated. Several empirical findings are reported.

Individual and mass behaviour in large population stochastic wireless power control problems: centralized and Nash equilibrium solutions

A general class of parameter estimation methods for stochastic dynamical systems is studied. The class contains the least squares method, output-error methods, the maximum likelihood method and several other techniques. It is shown that the class of estimates so obtained are asymptotically normal and expressions for the resulting asymptotic covariance matrices are given. The regularity conditions that are imposed to obtain these results, are fairly weak. It is, for example, not assumed that the true system can be described within the chosen model set, and, as a consequence, the results in this paper form a part of the so-called approximate modeling approach to system identification. It is also noteworthy that arbitrary feedback from observed system outputs to observed system inputs is allowed and stationarity is not required

Causality Analysis and Multivariate Autoregressive Modelling with an Application to Supermarket Sales Analysis

A simple formulation is given for the notion of feedback between two stationary stochastic processes in terms of the canonical representation of the joint process. The definition presented here has an equivalent formulation in terms of filtering theory, and provides statistical criteria for the detection of feedback. A simulation example is presented and an application to the United Kingdom unemployment-gross domestic product relation is described.

Asymptotic Normality of Prediction Error Estimators for Approximate System Models

The notion of dynamical consistency is extended to hybrid systems so as to define the set of dynamically consistent hybrid partition machines associated with a continuous system S. Following the formulation of the notions of between-block and in-block controllable hybrid partition machines, the lattice HIBC(S) of hybrid in-block controllable partition machines is defined and investigated. Based on these constructions, the definition and properties of hierarchical-hybrid control systems are presented together with an example.

Feedback between stationary stochastic processes

The situation where a totally observed process yt is generated by a stochastic differential equation whose parameters evolve on a finite set {1,....N} according to a stochastic differential equation is considered. The optimal control law is sought with respect to quadratic loss functions on yt and the control ut. The auxilliary P.D.E. technique of Hijab [1983] is used together with a non-linear filter to obtain the solution whose existence depends upon that of a smooth solution to the auxillary P.D.E. and strong solutions to the system S.D.E. under the given control inputs. Work supported by the Faculty of Engineering, and, the Faculty of Graduate Studies and Research, McGill University, the NSERC International Scientific Exchange Programme and NSERC Grant A1329, while the first author was visiting McGill University for the academic year 1982-83.

Hierarchical hybrid control systems: a lattice theoretic formulation

This paper is concerned with the discrete time matrix Riccati equation. The properties established are those of minimality, convergence, uniqueness and stability. Further the convergence of the policy space approximation technique is proved. These results are analogous to those known for the continuous-time Riccati equation, but the techniques used are simpler.