This paper deals with the identification of a linear parameter-varying (LPV) system whose parameter dependence can be written as a linear-fractional transformation (LFT). We formulate an output-error identification problem and present a parameter estimation scheme in which a prediction error-based cost function is minimized using nonlinear programming; its gradients and (approximate) Hessians can be computed using LPV filters and inner products, and identifiable model sets (i.e., local canonical forms) are obtained efficiently using a natural geometrical approach. Some computational issues and experiences are discussed, and a simple numerical example is provided for illustration.

This paper considers the identifiability of state space models for a system that is expressed as a linear fractional transformation (LFT): a constant matrix (containing identified parameters) in feedback with a finite-dimensional, block-diagonal (“structured”) linear operator. This model structure can represent linear time-invariant, linear parameter-varying, uncertain, and multidimensional systems. Families of input-output equivalent realizations are characterized as manifolds in the parameter space whose tangent spaces — and orthogonal complements — can be obtained via singular value decomposition. As illustrated by a numerical example, restricting iterative parameter estimation algorithms (e.g., maximum-likelihood with nonlinear programming) to the orthogonal directions offers significant computational advantages.

Plane-wave scintillation is shown to impose multiconjugate adaptive optics (MCAO) correctability limitations that are independent of wavefront sensing and reconstruction. Residual phase and log-amplitude variances induced by scintillation in weak turbulence are derived using linear (diffraction-based) diffractive MCAO spatial filters or (diffraction-ignorant) geometric MCAO proportional gains as open-loop control parameters. In the case of Kolmogorov turbulence, expressions involving the Rytov variance and/or weighted C(2)(n) integrals apply. Differences in performance between diffractive MCAO and geometric MCAO resemble chromatic errors. Optimal corrections based on least squares imply irreducible performance limits that are validated by wave-optic simulations.

Recent results in parameter-dependent control of linear parameter-varying systems are applied to the problem of designing gain-scheduled pitch rate controllers for the F-16 Variable-Stability In-Flight Simulator Test Aircraft. These methods, based on parameter-dependent quadratic Liapunov functions, take advantage of known a priori bounds on the parameters' rates of variation (the bounds may themselves be parameter-varying). The controller achieves an induced-two-norm performance objective; Level 1 flying qualities are predicted. Suboptimal solutions are obtained by solving a convex optimization problem described by linear matrix inequalities. Incorporation of D-K iteration with 'constant D-scales' provides robustness to time-varying uncertainty. Parameter-varying performance weights are used to shape the desired performance at different points in the design envelope. (Author) AbstractRecent results in parameter-dependent control of linear parameter-varying (LPV) systems are applied to the problem of designing gain-scheduled pitch rate controllers for the F-16 VISTA (Variable-Stability In-Flight Simulator Test Aircraft). These methods, based on parameter-dependent quadratic Lyapunov functions, take advantage of known a priori bounds on the parameters' rates of variation (the bounds may themselves be parameter-varying). The controller achieves an induced-£2-norm performance objective; Level 1 flying qualities are predicted. Suboptimal solutions are obtained by solving a convex optimization problem described by linear matrix inequalities (LMIs). Incorporation of D-K iteration with "constant £)-scales" provides robustness to time-varying uncertainty. Parameter-varying performance weights are used to shape the desired performance at different points in the design envelope.

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