Stable state and signal estimation in a network context

Power grid, communications, computer and product reticulation networks are frequently layered or subdivided by design. The layering divides responsibilities and can be driven by operational, commercial, regulatory and privacy concerns. From a control context, a layer, or part of a layer, in a network isolates the authority to manage, i.e. control, a dynamic system with connections into unknown parts of the network. The topology of these connections is fully prescribed but the interconnecting signals, currents in the case of power grids and bandwidths in communications, are largely unavailable, through lack of sensing and even prohibition. Accordingly, one is driven to simultaneous input and state estimation methods. We study a class of algorithms for this joint task, which has the unfortunate issue of inverting a subsystem, which if it has unstable transmission zeros leads to an unstable and unimplementable estimator. Two modifications to the algorithm to ameliorate this problem were recently proposed involving replacing the troublesome subsystem with its outer factor from its inner-outer factorization or using a high-variance white signal model for the unknown inputs. Here, we establish the connections between the original estimation problem for state and input signal and the estimates from the algorithm applied solely to the outer factor. It is demonstrated that the state of the outer factor and that of the original system asymptotically coincide and that the estimate of the input signal to the outer factor has asymptotically stationary second-order statistics which are in one-to-one correspondence with those of the input signal to the original system, when this signal is itself stationary. Thus, the simultaneous input and state estimation algorithm applied just to the outer factor yields an unbiased state estimate for control and the statistics of the interface signals.Comment: 12 pages, 1 figur

Adaptive Optimal Control The Thinking Man's GPC

Exploring connections between adaptive control theory and practice, this book treats the techniques of linear quadratic optimal control and estimation (Kalman filtering), recursive identification, linear systems theory and robust arguments

The Nehari Shuffle: FIR(q) Filter Design With Guaranteed Error Bounds

This paper presents a new approach to the problem of designing a finite impulse response filter of specified length, q, which approximates in uniform frequency (L-infinity) norm a given desired (possibly infinite impulse responmse) causal, stable filter transfer function. We derive an algorithm-independent lower bound on the achievable approximation error and then present and approximation method which involves the solution of a fixed number of all-pass (Nehari) extension problems and so is called the Nehari shuffle. Upper and lower bounds on the approximation error are derived for the algorithm. These bounds are calculable a priori so the length of the filter can be found before designing the filter. Examples indicate that the method closely approaches the derived global lower bound. We compare the new method with the Preuss (complex Remez exchange) algorithm in some examples

FIR(q) Filter Design Without the Linear Phase Contraint

This paper presents a new approach to the problem of designing a finite impulse response filter of specified length, q, which approximates in uniform frequency norm a given desired (possibly infinite impulse response) filter transfer function