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The internal model-based [H.sub.[infinity]] full information steady-state bumpless transfer synthesis procedure is developed and demonstrated to provide near optimal robust stability and robust performance for a much larger class of controller uncertainty than the earlier developed LQ state/output transfer. It is also pointed out that the steady-state bumpless transfer under controller uncertainty represents, in general, a hybrid mode of system behavior--a controlled discrete transition. Index Terms--Bumpless transfer, computational speedup, controller uncertainty, robust control.

We consider the design of quantizers for parameter identification under communication constraints. The objective is to find coarse quantization methods that achieve reasonable performance based on an [H.sup.[infinity]] criterion. We make use of feedback in communication and show that the problem induces a class of quantizers similar to logarithmic Ones. We then exhibit through examples that the proposed identifier is advantageous over a conventional prefiltering scheme, especially when quantization error is large. Index Terms--[H.sub.[infinity]] synthesis, quantization, robust identification.

In this note, we study the problem of distributed control over communication channels, where a number of distributed stations collaborate to stabilize a linear system. We quantify the rate requirements and obtain optimal signaling, coding and control schemes for decentralized stabilizability in such multicontroller systems. We show that in the absence of a centralized decoder at the plant, there is in general a rate loss in decentralized systems as compared to a centralized system. This result is in contrast with the absence of rate loss in the stabilization of multisensor systems. Furthermore, there is rate loss even if explicit channels are available between the stations. We obtain the minimum data rates needed in terms of the open-loop system matrix and the connectivity graph of the decentralized system, and obtain the optimal signaling policies. We also present constructions leading to stability. In addition, we show that if there are dedicated channels connecting the controllers, rate requirements become more lenient, and as a result strong connectivity is not required for decentralized stabilizability. We determine the minimum number of such external channels leading to a stable system, in case strong connectivity is absent. Index Terms--Cooperative control, decentralized stabilization, distributed control, information theory.

In this note, we study communication requirements for decentralized control schemes when sensors and controllers are connected via noiseless digital channels and system noises are bounded. Under various information structures, and within the class of time-invariant encoding and control policies, we quantify achievable rates, and obtain fixed-rate and delayless encoders and decoders that achieve boundedness in the state estimation errors at the controllers. We use distributed coding theoretic approaches to show that when the sensors do not collaborate, it is sufficient for the controllers to share information amongst themselves but not with the sensors. Sensor collaboration, however, leads to improvement in rate performance. Index Terms--Control under communication constraints, decentralized control, distributed coding, multi-agent systems, quantization.

This paper studies rate requirements for state estimation in linear time-invariant (LTI) systems where the controller and the plant are connected via a noiseless channel with limited capacity. Using information theoretic arguments, we obtain first for scalar systems, and subsequently for multidimensional systems, lower bounds on the data rates required for state estimation under three different stability criteria, namely monotonic boundedness of entropy, asymptotic stability of distortion, and support size stability. Further, the minimum data rate achievable by any sourceencoder is computed under each of these criteria, and the best rate achievable with quantization is shown to be in agreement with the information-theoretic bounds in some specific cases (such as if the system coefficient is an integer or if the criterion is an asymptotic one). Existence of optimal variable-length and fixed-length quantizers are studied and optimal quantizers are constructed under each of these criteria. One observation is that, the uniform quantizer is, in addition to being simple, efficient in linear control systems. Index Terms--Networked control, quantization, stability.

In this paper, we consider the design of globally asymptotically stabilizing state-dependent switching rules for multimodal systems, first restricting attention to linear time-invariant (LTI) systems with only two states for the switch, and then generalizing the results to multimodal LTI systems and to nonlinear systems. In all cases, the systems considered do not allow the construction of a single quadratic Lyapunov function and, hence, fall in the class of problems that require multiple Lyapunov functions and thus are nonconvex. To address the challenge of nonconvexity, we introduce probabilistic algorithms, and prove their probability-one convergence under a new notion of convergence. Then, to reduce complexity, we develop modified versions of the algorithm. We also present a class of more general nonconvex problems to which this approach can be applied. The results are illustrated using two- and three-dimensional systems with multiple switch states. Index Terms--Multiple Lyapunov function, nonconvexity, randomized algorithms, switched systems, switching rule design.

This work considers small-time local controllability (STLC) of single- and multiple-input systems, x = [f.sub.0](x) [[summation over.sup.m.sub.i=1] [f.sub.i][u.sub.i] where [f.sub.0](x) contains homogeneous polynomials and [f.sub.1], ... ,[f.sub.m] are constant vector fields. For single-input systems, it is shown that even-degree homogeneity precludes STLC if the state dimension is larger than one. This, along with the obvious result that for odd-degree homogeneous systems STLC is equivalent to accessibility, provides a complete characterization of STLC for this class of systems. In the multiple-input case, transformations on the input space are applied to homogeneous systems of degree two, an example of this type of system being motion of a rigid-body in a plane. Such input transformations are related via consideration of a tensor on the tangent space to congruence transformation of a matrix to one with zeros on the diagonal. Conditions are given for successful neutralization of bad type (1,2) brackets via congruence transformations. Index Terms--Controllability, Lie algebras, nonlinear systems.

This note investigates the control of stochastic nonlinear systems with parametric uncertainty. The class of systems considered are single-input-single-output and in strict-feedback form, with the performance measured with respect to a risk-sensitive cost criterion. The uncertainty in the system description is assumed to be linearly parameterized, where the unmeasured parameters are generated by stochastic differential equations. By employing the backstepping design technique on the estimates of the unmeasured states, provided by a simple state estimator, an output-feedback adaptive controller is constructed which maintains an arbitrarily small average value for the risk-sensitive cost. The controller designed achieves boundedness in probability for all closed-loop signals and, under certain conditions, the tracking error converges to zero almost surely. Index Terms--Adaptive backstepping, risk-sensitive control, stochastic systems, strict-feedback systems.

We consider a noncooperative game framework for combined muting and flow control in a network of parallel links, where the number of users (players) is arbitrarily large. The utility function of each user is related to the power criterion, and is taken as the ratio of some positive power of the total throughput of that user to the average delay seen by the user. The utility function is nonconcave in the flow rates of the user, for which we introduce a scaling to make it well defined as the number of users, N, becomes arbitrarily large. In spite of the lack of concavity, we obtain explicit expressions for the flow rates of the users and their associated muting decisions, which are in O(1/N) Nash equilibrium. This O(1/N) equilibrium solution, which is symmetric across different users and could be multiple in some cases, exhibits a delay-equalizing feature among the links which carry positive flow. The paper also provides the complete optimal solution to the single-user case, and includes several numerical examples to illustrate different features of the solutions in the single- as well as N-user cases, as N becomes arbitrarily large. Index Terms--Asymptotic Nash equilibria, flow control, networks, noncooperative equilibria, nonzero-sum games, muting.

We study a class of noncooperative general topology networks shared by N users. Each user has a given flow which it has to ship from a source to a destination. We consider a class of polynomial link cost functions adopted originally in the context of road traffic modeling, and show that these costs have appealing properties that lead to predictable and efficient network flows. In particular, we show that the Nash equilibrium is unique, and is moreover efficient. These properties make the polynomial cost structure attractive for traffic regulation and link pricing in telecommunication networks. We finally discuss the computation of the equilibrium in the special case of the affine cost structure for a topology of parallel links. Index Terms--Networks, noncooperative equilibria, nonzero-sum games, routing.

The authors develop a systematic procedure for obtaining robust adaptive controllers that achieve asymptotic tracking and disturbance attenuation for a class of nonlinear systems that are described in the parametric strict-feedback form and are subject to additional exogenous disturbance inputs. Their approach to adaptive control is performance-based, where the objective for the controller design is not only to find an adaptive controller, but also to construct an appropriate cost functional, compatible with desired asymptotic tracking and disturbance attenuation specifications, with respect to which the adaptive controller is "worst case optimal." In this respect, they also depart from the standard worst case (robust) controller design paradigm where the performance index is fixed priori. Three main ingredients of the paper are the backstepping methodology, worst case identification schemes, and singular perturbations analysis. Under full state measurements, closed-form expressions have been obtained for an adaptive controller and the corresponding value function, where the latter satisfies a Hamilton-Jacobi-Isaacs equation (or inequality) associated with the underlying cost function, thereby leading to satisfaction of a dissipation inequality for the former. An important by-product of the analysis is the finding that the adaptive controllers that meet the dual specifications of asymptotic tracking and disturbance attenuation are generally not certainty-equivalent, but are asymptotically so as the measure quantifying the designer's confidence in the parameter estimate goes to infinity. To illustrate the main results, the authors include a numerical example involving a third-order system. Index Terms - Adaptive control, backstepping, disturbance attenuation, nonlinear systems, tracking.

This paper addresses the worst-case parameter identification problem for uncertain single-input/single-output (SISO) and multi-input/multi-output (MIMO) linear systems under partial state measurements and derives worst-case identifiers using the cost-to-come function method. In the SISO case, the worst-case identifier obtained subsumes the Kreisselmeier observer as part of its structure with parameters set at some optimal values. Its structure is different from the common least-squares (LS) identifier, however, in the sense that there is additional dynamics for the state estimate, coupled with the dynamics of the parameter estimate in a nontrivial way. In the MIMO case as well, the worst-case identifier has additional dynamics for the state estimate which do not appear in the conventional LS-based schemes. Also for both SISO and MIMO problems, approximate identifiers are obtained which are numerically much better conditioned when the disturbances in the measurement equations are "small." The theoretical results are then illustrated on an extensive numerical example to demonstrate the effectiveness of the identification schemes developed.

In this paper we study the H(super infinity)-optimal control of singularly perturbed linear systems under general imperfect measurements, for both finite- and infinite-horizon formulations. Using a differential game theoretic approach, we first show that as the singular perturbation parameter (say, Epsilon > 0) approaches zero, the optimal disturbance attenuation level for the full-order system under a quadratic performance index converges to a value that is bounded above by (and in some cases equal to) the maximum of the optimal disturbance attenuation levels for the slow and fast subsystems under appropriate 'slow' and 'fast' quadratic cost functions, with the bound being computable independently of Epsilon and knowing only the slow and fast dynamics of the system. We then construct a controller based on the slow subsystem only and obtain conditions under which it delivers a desired performance level even though the fast dynamics are completely neglected. The ultimate performance level achieved by this 'slow' controller can be uniformly improved upon, however, by a composite controller that uses some feedback from the output of the fast subsystem. We construct one such controller, via a two-step sequential procedure, which uses static feedback from the fast output and dynamic feedback from an appropriate slow output, each one obtained by solving appropriate Epsilon-independent lower dimensional H(super infinity)-optimal control problems under some informational constraints. We provide a detailed analysis of the performance achieved by this lower-dimensional Epsilon-independent composite controller when applied to the full-order system and illustrate the theory with some numerical results on some prototype systems.