Wassim M. Haddad

LQG control with an H/sup infinity / performance bound: a Riccati equation approach

An LQG (linear quadratic Gaussian) control-design problem involving a constraint on H/sup infinity / disturbance attenuation is considered. The H/sup infinity / performance constraint is embedded within the optimization process by replacing the covariance Lyapunov equation by a Riccati equation whose solution leads to an upper bound on L/sub 2/ performance. In contrast to the pair of separated Riccati equations of standard LQG theory, the H/sup infinity /-constrained gains are given by a coupled system of three modified Riccati equations. The coupling illustrates the breakdown of the separation principle for the H/sup infinity /-constrained problem. Both full- and reduced-order design problems are considered with an H/sup infinity / attenuation constraint involving both state and control variables. An algorithm is developed for the full-order design problem and illustrative numerical results are given. >

Controller design with regional pole constraints

A design procedure is developed that combines linear-quadratic optimal control with regional pole placement. Specifically, a static and dynamic output-feedback control problem is addressed in which the poles of the closed-loop system are constrained to lie in specified regions of the complex plane. These regional pole constraints are embedded within the optimization process by replacing the covariance Lyapunov equation by a modified Lyapunov equation whose solution, in certain cases, leads to an upper bound on the quadratic cost functional. The results include necessary and sufficient conditions for characterizing static output-feedback controllers with bounded performance and regional pole constraints. Sufficient conditions are also presented for the fixed-order (i.e. full- and reduced-order) dynamic output-feedback problem with regional pole constraints. Circular, elliptical, vertical strip, parabolic, and section regions are considered. >

Finite-Time Semistability and Consensus for Nonlinear Dynamical Networks

This paper focuses on semistability and finite-time stability analysis and synthesis of systems having a continuum of equilibria. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. In this paper, we merge the theories of semistability and finite-time stability to develop a rigorous framework for finite-time semistability. In particular, finite-time semistability for a continuum of equilibria of continuous autonomous systems is established. Continuity of the settling-time function as well as Lyapunov and converse Lyapunov theorems for semistability are also developed. In addition, necessary and sufficient conditions for finite-time semistability of homogeneous systems are addressed by exploiting the fact that a homogeneous system is finite-time semistable if and only if it is semistable and has a negative degree of homogeneity. Unlike previous work on homogeneous systems, our results involve homogeneity with respect to semistable dynamics, and require us to adopt a geometric description of homogeneity. Finally, we use these results to develop a general framework for designing semistable protocols in dynamical networks for achieving coordination tasks in finite time.

Brief paper: Distributed nonlinear control algorithms for network consensus

In this paper, we develop a thermodynamic framework for addressing consensus problems for nonlinear multiagent dynamical systems with fixed and switching topologies. Specifically, we present distributed nonlinear static and dynamic controller architectures for multiagent coordination. The proposed controller architectures are predicated on system thermodynamic notions resulting in controller architectures involving the exchange of information between agents that guarantee that the closed-loop dynamical network is consistent with basic thermodynamic principles.

Steady-state Kalman filtering with an H ∞ error bound

Abstract An estimator design problem is considered which involves both L 2 (least squares) and H ∞ (worst-case frequency-domain) aspects. Specifically, the goal of the problem is to minimize an L 2 state-estimation error criterion subject to a prespecified H ∞ constraint on the state-estimation error. The H ∞ estimation-error constraint is embedded within the optimization process by replacing the covariance Lyapunov equation by a Riccati equation whose solution leads to an upper bound on the L 2 state-estimation error. The principal result is a sufficient condition for characterizing fixed-order (i.e., full- and reduced-order) estimators with bounded L 2 and H ∞ estimation error. The sufficient condition involves a system of modified Riccati equations coupled by an oblique projection, i.e., idempotent matrix. When the H ∞ constraint is absent, the sufficient condition specializes to the L 2 state-estimation result given in [2].

Drug dosing control in clinical pharmacology

In this paper, the potential applications of control technology to clinical pharmacology are discussed, specifically the control of drug dosing. The use of closed-loop control for clinical pharmacology can significantly advance the understanding of the effects of pharmacological agents and anesthetics, as well as advance the state-of-the-art in drug delivery systems. In addition to delivering sedation to critically ill patients in an acute care environment, potential applications of closed-loop control include glucose, heart rate, and blood pressure regulation.

Robust stabilization with positive real uncertainty: beyond the small gain theory

In many applications of feedback control, phase information is available concerning the plant uncertainty. For example, lightly damped flexible structures with colocated rate sensors and force actuators give rise to positive real transfer functions. Closed-loop stability is thus guaranteed by means of negative feedback with strictly positive real compensators. In this paper, the properties of positive real transfer functions are used to guarantee robust stability in the presence of positive real (but otherwise unknown) plant uncertainty. These results are then used for controller synthesis to address the problem of robust stabilization in the presence of positive real uncertainty. One of the principal motivations for these results is to utilize phase information in guaranteeing robust stability. In this these sense results go beyond the usual limitations the small gain theorem and quadratic Lyapunov functions which may be conservative when phase information is available. The results of this paper are based upon a Riccati equation formulation of the positive real lemma and thus are in the spirit of recent Riccati-based approaches to bounded real (H∞) control.

Robust stability and performance via fixed-order dynamic compensation with guaranteed cost bounds

A feedback control-design problem involving structured plant parameter uncertainties is considered. Two robust control-design issues are addressed. The Robust Stability Problem involves deterministic bounded structured parameter variations, while the Robust Performance Problem includes, in addition, a quadratic performance criterion averaged over stochastic disturbances and maximized over the admissible parameter variations. The optimal projection approach to fixed-order, dynamic compensation is merged with the guaranteed cost control approach to robust stability and performance to obtain a theory of full- and reduced-order robust control design. The principle result is a sufficient condition for characterizing dynamic controllers of fixed dimension which are guaranteed to provide both robust stability and performance. The sufficient conditions involve a system of modified Riccati and Lyapunov equations coupled by an oblique projection and the uncertainty bounds. The full-order result involves a system of two modified Riccati equations and two modified Lyapunov equations coupled by the uncertainty bounds. The coupling illustrates the breakdown of the separation principle for LQG control with structured plant parameter variations.

Robust resilient dynamic controllers for systems with parametric uncertainty and controller gain variations

A feedback control design problem involving structured plant parameter uncertainties and controller gain variations is considered. Specifically, the robust fixed-structure guaranteed cost controller synthesis framework is extended to address the design of robust resilient fixed-order (i.e., full- and reduced-order) dynamic controllers for systems with structured parametric uncertainty and controller gain uncertainty. Several examples are provided which clearly demonstrate the need for robust resilient control.

Mixed-norm H 2 /H ∞ regulation and estimation: the discrete-time case

Abstract A discrete-time H2 static output feedback design problem involving a constraint on H∞ disturbance attenuation is addressed and state space formulae are derived. The dual problem of discrete-time dynamic estimation with an H∞ error bound is also addressed. These results are analogous to results obtained previously for the continuous-time problem.