Observability and Detectability Analysis of Singular Linear Systems with Unknown Inputs

International audienceWe study the observability problem of a general class of singular linear systems with unknown inputs. It is shown that, under some assumptions, the problem is equivalent to study the observability of a standard linear system with unknown inputs satisfying algebraic constraints. We obtain necessary and sufficient conditions for observability in terms of the zeros of the system matrix

A Unified Filter for Simultaneous Input and State Estimation of Linear Discrete-time Stochastic Systems

In this paper, we present a unified optimal and exponentially stable filter for linear discrete-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense, without making any assumptions on the direct feedthrough matrix. We also derive input and state observability/detectability conditions, and analyze their connection to the convergence and stability of the estimator. We discuss two variations of the filter and their optimality and stability properties, and show that filters in the literature, including the Kalman filter, are special cases of the filter derived in this paper. Finally, illustrative examples are given to demonstrate the performance of the unified unbiased minimum-variance filter.Comment: Preprint for Automatic

On Redundant Observability: From Security Index to Attack Detection and Resilient State Estimation

The security of control systems under sensor attacks is investigated. Redundant observability is introduced, explaining existing security notions including the security index, attack detectability, and observability under attacks. Equivalent conditions between redundant observability and existing notions are presented. Based on a bank of partial observers utilizing Kalman decomposition and a decoder exploiting redundancy, an estimator design algorithm is proposed enhancing the resilience of control systems. This scheme substantially improves computational efficiency utilizing far less memory

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

A family of asymptotically stable control laws for flexible robots based on a passivity approach

A general family of asymptotically stabilizing control laws is introduced for a class of nonlinear Hamiltonian systems. The inherent passivity property of this class of systems and the Passivity Theorem are used to show the closed-loop input/output stability which is then related to the internal state space stability through the stabilizability and detectability condition. Applications of these results include fully actuated robots, flexible joint robots, and robots with link flexibility

Kalman filtering for temperature estimation of electric motors

Due to their high power density and good efficiency, permanent magnet synchronous machines (PMSM) have been increasingly employed in high-power applications such as vehicular propulsion (electrical/hybrid vehicles), industrial drives and power generation. Since high temperatures can significantly shorten the lifetime of the motor components and cause non-reversible demagnetization of the permanent magnets, there is a growing trend towards real-time monitoring the internal temperatures of such machines during operation. Therefore, to guarantee optimal utilization of the machine, maximizing its efficiency while assuring safer operation modes, the temperature at some key points within the motor needs to be measured. While the temperature at the stator can be easily accessed by embedding thermal sensors, rotor temperatures are difficult to measure in practice. As an alternative to conventional direct/indirect measurement approaches, model-based methods have been investigated in the past decades. In this work, the feasibility of using the Kalman algorithm, as a thermal observer for temperature estimation, is investigated. This model-based approach starts from a simplified linear time invariant finite element model through which the performance of such strategy is evaluated to be able to apply it to more complex PMSM models