Robust observer design under measurement noise

We prove new results on robust observer design for systems with noisy measurement and bounded trajectories. A state observer is designed by dominating the incrementally homogeneous nonlinearities of the observation error system with its linear approximation, while gain adaptation and incremental observability guarantee an asymptotic upper bound for the estimation error depending on the limsup of the norm of the measuremen noise. The gain adaptation is implemented as the output of a stable filter using the squared norm of the measured output estimation error and the mismatch between each estimate and its saturated value

Sequential processing and performance optimization in nonlinear state estimation

We propose a framework for designing observers for noisy nonlinear systems with global convergence properties and performing robustness and noise sensitivity. Our state observer is the result of the combination of a state norm estimator with a bank of Kalman-type lters, parametrized by the state norm estimator. The state estimate is sequentially processed through the bank of lters. In general, existing nonlinear state observers are responsible for estimation errors which are sensitive to model uncertainties and measurement noise, depending on the initial state conditions. Each Kalman-type lter of the bank contributes to improve the estimation error performances to a certain degree in terms of sensitivity with respect to noise and initial state conditions. A sequential processing algorithm for performance optimization is given and simulations show the eectiveness of these sequential lters

Leader-Following consensus for nonlinear agents with measurement feedback

The leader-following consensus problem is investigated for large classes of nonlinear identical agents. Sufficient conditions are provided for achieving consensus via state and measurement feedback laws based on a local (ie, among neighbors) information exchange. The leader's trajectories are assumed bounded without knowledge of the containing compact set and the agents' trajectories possibly unbounded under the action of a bounded input. Generalizations to heterogeneous agents and robustness are also discussed

A stability with optimality analysis of consensus-based distributed filters for discrete-time linear systems

In this paper we investigate how stability and optimality of consensus-based distributed filters depend on the number of consensus steps in a discrete-time setting for both directed and undirected graphs. By introducing two new algorithms, a simpler one based on dynamic averaging of the estimates and a more complex version where local error covariance matrices are exchanged as well, we are able to derive a complete theoretical analysis. In particular we show that dynamic averaging alone suffices to approximate the optimal centralized estimate if the number of consensus steps is large enough and that the number of consensus steps needed for stability can be computed in a distributed way. These results shed light on the advantages as well as the fundamental limitations shared by all the existing proposals for this class of algorithms in the basic case of linear time-invariant systems, that are relevant for the analysis of more complex situations

Basic Logic and Quantum Entanglement

As it is well known, quantum entanglement is one of the most important features of quantum computing, as it leads to massive quantum parallelism, hence to exponential computational speed-up. In a sense, quantum entanglement is considered as an implicit property of quantum computation itself. But...can it be made explicit? In other words, is it possible to find the connective "entanglement" in a logical sequent calculus for the machine language? And also, is it possible to "teach" the quantum computer to "mimic" the EPR "paradox"? The answer is in the affirmative, if the logical sequent calculus is that of the weakest possible logic, namely Basic logic. A weak logic has few structural rules. But in logic, a weak structure leaves more room for connectives (for example the connective "entanglement"). Furthermore, the absence in Basic logic of the two structural rules of contraction and weakening corresponds to the validity of the no-cloning and no-erase theorems, respectively, in quantum computing.Comment: 10 pages, 1 figure,LaTeX. Shorter version for proceedings requirements. Contributed paper at DICE2006, Piombino, Ital

LQ non-Gaussian Control with I/O packet losses

The paper concerns the Linear Quadratic non-Gaussian (LQnG) sub-optimal control problem when the input and output signals travel through an unreliable network, namely Gilbert-Elliot channels. In particular, the input/output packet losses are modeled by Bernoulli sequences, and we assume that the moments of the non-Gaussian noises up to the fourth order are known. By mean of a suitable rewriting of the system through an intermittent output injection term, and by considering an augmented system with the second-order Kronecker power of the measurements, a simple solution is provided by substituting the Kalman predictor with intermittent observations of the LQG control law with a quadratic optimal predictor. Numerical simulations show the effectiveness of the proposed method

A topos for algebraic quantum theory

The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to construct new foundations for quantum logic and quantum spaces. Motivated by Bohr's idea that the empirical content of quantum physics is accessible only through classical physics, we show how a C*-algebra of observables A induces a topos T(A) in which the amalgamation of all of its commutative subalgebras comprises a single commutative C*-algebra. According to the constructive Gelfand duality theorem of Banaschewski and Mulvey, the latter has an internal spectrum S(A) in T(A), which in our approach plays the role of a quantum phase space of the system. Thus we associate a locale (which is the topos-theoretical notion of a space and which intrinsically carries the intuitionistic logical structure of a Heyting algebra) to a C*-algebra (which is the noncommutative notion of a space). In this setting, states on A become probability measures (more precisely, valuations) on S(A), and self-adjoint elements of A define continuous functions (more precisely, locale maps) from S(A) to Scott's interval domain. Noting that open subsets of S(A) correspond to propositions about the system, the pairing map that assigns a (generalized) truth value to a state and a proposition assumes an extremely simple categorical form. Formulated in this way, the quantum theory defined by A is essentially turned into a classical theory, internal to the topos T(A).Comment: 52 pages, final version, to appear in Communications in Mathematical Physic

Semiglobal stabilization via measurement feedback for systems in triangular form

In this paper we consider the problem of semiglobally stabilizing a wide class of uncertain nonlinear system, which is made up of a linear nominal system affected by model uncertainties or nonlinearities. Our approach is based on H∞ control tools and recovers existing results on the semiglobal stabilization via output feedback. We will prove that, if the uncertainties satisfy both a triangularity property (TS) and a linearity property (LS) with respect to some state variables, we can achieve semiglobal stabilization via measurement feedback. The resulting measurement feedback is itself 'optimal' with respect to a 'meaningful' cost functional. Our result also allows to take into account output nonlinear effects such as saturations and backlash

Stabilization of Nonlinear Systems with Norm Bounded Uncertainties

In this paper, we give a necessary and sufficient condition in terms of Hamilton-Jacobi inequalities for globally stabilizing a nonlinear system, robustly with respect to unstructured uncertainties, depending both on unknown time-varying parameters Δ(t) and state x and norm-bounded for each x. This condition essentially states that global robust stabilization via smooth (except possibly at the origin) controllers is equivalent to the existence of a robust control Lyapunov function, which requires the solution of a suitable Hamilton Jacobi inequality, and generalizes a well-known condition for linear systems. This clarifies also the connection between robust stabilization and H∞ control for nonlinear systems