Bounded Measurement Noise Research Articles

Rigid body pose estimation based on the Lagrange–d’Alembert principle

Stable estimation of rigid body pose and velocities from noisy measurements, without any knowledge of the dynamics model, is treated using the Lagrange–d’Alembert principle from variational mechanics. With body-fixed vision and inertial sensor measurements, a Lagrangian is obtained as the difference between a kinetic energy-like term that is quadratic in velocity estimation error and the sum of two artificial potential functions; one obtained from a generalization of Wahba’s function for attitude estimation and another which is quadratic in the position estimate error. An additional dissipation term that is linear in the velocity estimation error is introduced, and the Lagrange–d’Alembert principle is applied to the Lagrangian with this dissipation. A Lyapunov analysis shows that the state estimation scheme so obtained provides stable asymptotic convergence of state estimates to actual states in the absence of measurement noise, with an almost global domain of attraction. This estimation scheme is discretized for computer implementation using discrete variational mechanics, as a first order Lie group variational integrator. The discrete estimation scheme can also estimate velocities from such onboard sensor measurements. Moreover, all states can be estimated during time periods when measurements of only two inertial vectors, the angular velocity vector, and one feature point position vector are available in body frame. In the presence of bounded measurement noise in the vector measurements, numerical simulations show that the estimated states converge to a bounded neighborhood of the true states.

Control of a family of nonlinear dynamic systems under measurements with bounded disturbances

We consider a control synthesis problem for nonlinear dynamic systems under parametric uncertainty and bounded measurement noises. Because of bounded disturbances in measurements of the state vector and the nonlinearity in the control object, the initially formulated control synthesis problem for a family of nonlinear systems as a generalized Zubov problem is transformed into a symbiosis of generalized Zubov–Bulgakov problems. The main result of the paper is the analytic solution of a minimax synthesis problem, which yields a constructive method for finding an invariant set.

Fault Diagnosis for Actuators in a Class of Nonlinear Systems Based on an Adaptive Fault Detection Observer

The problem of actuators’ fault diagnosis is pursued for a class of nonlinear control systems that are affected by bounded measurement noise and external disturbances. A novel fault diagnosis algorithm has been proposed by combining the idea of adaptive control theory and the approach of fault detection observer. The asymptotical stability of the fault detection observer is guaranteed by setting the adaptive adjusting law of the unknown fault vector. A theoretically rigorous proof of asymptotical stability has been given. Under the condition that random measurement noise generated by the sensors of control systems and external disturbances exist simultaneously, the designed fault diagnosis algorithm is able to successfully give specific estimated values of state variables and failures rather than just giving a simple fault warning. Moreover, the proposed algorithm is very simple and concise and is easy to be applied to practical engineering. Numerical experiments are carried out to evaluate the performance of the fault diagnosis algorithm. Experimental results show that the proposed diagnostic strategy has a satisfactory estimation effect.

Robust adaptive parameter estimation of sinusoidal signals

A novel two step adaptive identification framework is proposed for sinusoidal signals to estimate the unknown offset, amplitude, frequency and phase, where only the output measurements are used. After representing the sinusoidal signal as a linearly parameterized form, several adaptive laws are developed. The proposed adaptive laws are driven by parameter estimation error information that is derived by applying filter operations on the output measurements, so that globally exponential convergence of the parameter estimation is proved. By using the sliding mode technique, we further improve the design of adaptations to achieve finite-time (FT) parameter estimation. The proposed approaches are independent of any observer/predictor design and robust to bounded measurement noises. The developed estimation methods are finally extended to the full parameter estimation of multi-sinusoids with only output measurements. Comparative simulation results are provided to illustrate the efficacy of the proposed methods.

Rigid body attitude estimation based on the Lagrange–d’Alembert principle

Estimation of rigid body attitude and angular velocity without any knowledge of the attitude dynamics model is treated using the Lagrange–d’Alembert principle from variational mechanics. It is shown that Wahba’s cost function for attitude determination from two or more non-collinear vector measurements can be generalized and represented as a Morse function of the attitude estimation error on the Lie group of rigid body rotations. With body-fixed sensor measurements of direction vectors and angular velocity, a Lagrangian is obtained as the difference between a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential obtained from Wahba’s function. An additional dissipation term that depends on the angular velocity estimation error is introduced, and the Lagrange–d’Alembert principle is applied to the Lagrangian with this dissipation. A Lyapunov analysis shows that the state estimation scheme so obtained provides stable asymptotic convergence of state estimates to actual states in the absence of measurement noise, with an almost global domain of attraction. These estimation schemes are discretized for computer implementation using discrete variational mechanics. A first order Lie group variational integrator is obtained as a discrete-time implementation. In the presence of bounded measurement noise, numerical simulations show that the estimated states converge to a bounded neighborhood of the actual states.

A New Approach for Guaranteed Ellipsoidal State Estimation

This paper proposes a new ellipsoid-based guaranteed state estimation approach for linear discrete-time systems with bounded perturbations and bounded measurement noise. This approach is based on the minimization of the radius of the ellipsoidal state estimation set. Firstly, the ellipsoidal state estimation is computed by off-line solving a Linear Matrix Inequality optimization problem. Secondly, a new online method is developed in order to improve the accuracy of the estimation but it leads to an increase of the online computation load. A new scaling technique is proposed to reduce the computation time, while keeping a good accuracy of the state estimation. An illustrative example is analyzed in order to show the advantages of the proposed approach.

Global attitude and gyro bias estimation based on set-valued observers

The problem of attitude and rate gyro bias estimation is addressed by resorting to measurements acquired from rate gyros and vector observations. A Set-Valued Observer (SVO) is proposed that has no singularities and that, for any initial conditions, provides a bounding set with guarantees of containing the actual (unknown) rotation matrix. The sensor readings are assumed to be corrupted by bounded measurement noise and constant gyro bias. Conditions for the boundedness of the estimated sets are established and implementation details are discussed. The feasibility of the technique is demonstrated in simulation.

Bounded-error identification of linear systems with input and output backlash

In this paper we present a single-stage procedure for computing bounds on the parameters of linear systems with input and output backlash from output data corrupted by bounded measurement noise. By properly selecting a sequence of input/output measurements, the problem of evaluating parameter bounds is formulated as a collection of sparse nonconvex optimization problems. Convex-relation techniques are exploited to efficiently compute guaranteed bounds on system parameters by means of semidefinite programming.

Attitude State Estimation with Multirate Measurements for Almost Global Attitude Feedback Tracking

A state estimation scheme that does not depend on the statistical distribution of bounded measurement noise is presented. This scheme is used to provide state estimates for feedback in an attitude tracking control scheme that exhibits almost global asymptotically stable tracking of a desired attitude trajectory with perfect state measurements. The control and estimation schemes use the global, unique representation of rigid body attitude provided by rotation matrices. Attitude and angular velocity state estimate updates are obtained from discrete multi-rate measurements using a deterministic filtering scheme. Propagation of discrete state estimates is carried out with a Lie group variational integrator, which preserves the orthogonality of rotation matrices during numerical propagation without reprojection. This integrator is also used to numerically simulate the feedback system. The performance of this attitude tracking control scheme is then compared with that of a recently reported quaternion observer-based continuous feedback attitude tracking scheme. This quaternion-based attitude tracking scheme is shown to exhibit unstable, unwinding behavior. Numerical

Multirate Lyapunov-based distributed model predictive control of nonlinear uncertain systems

Abstract In this work, we consider the design of a network-based distributed model predictive control system using multirate sampling for large-scale nonlinear uncertain systems composed of several coupled subsystems. Specifically, we assume that the states of each local subsystem can be divided into fast sampled states (which are available every sampling time) and slowly sampled states (which are available every several sampling times). The distributed model predictive controllers are connected through a shared communication network and cooperate in an iterative fashion at time instants in which full system state measurements (both fast and slow) are available, to guarantee closed-loop stability. When local subsystem fast sampled state information is only available, the distributed controllers operate in a decentralized fashion to improve closed-loop performance. In the proposed control architecture, the controllers are designed via Lyapunov-based model predictive control techniques taking into account bounded measurement noise, process disturbances and communication noise. Sufficient conditions under which the state of the closed-loop system is ultimately bounded in an invariant region containing the origin are derived. The theoretical results are demonstrated through a nonlinear chemical process example.

Attracting manifolds for attitude estimation in flatland and otherlands

Non-convex and non-affine parameterizations of uncertainty are intrinsic within every attitude estimation problem given the fact that minimal and/or nonsingular representations of the attitude matrix are invariably nonlinear functions of the unknown attitude variables. Of course, this fact remains true for rotation matrices both in the 2-D plane (flatland) and in higher dimensional spaces (otherlands). Therefore, estimation problems involving minimal nonsingular representations of unknown attitude matrices bring significant challenges to the adaptive estimation community. This paper develops a novel algorithm for attitude estimation. The proposed algorithm relies upon the design of an adaptive update law for the attitude estimate while preserving its inherent orthogonal structure. The underlying approach borrows from the classical Poisson differential equation in rigid-body rotational kinematics and endows certain manifold attractivity features within the adaptive estimation algorithm. Consequently, we are not only able to efficiently handle the non-affine and non-convex nature of the parameter uncertainty, but are also ensured of estimation algorithm stability and robustness under bounded measurement noise. In addition to a rigorous discussion on the overall methodology, the paper provides example simulations that help demonstrate the effectiveness of the attracting manifolds design.

Accuracy of Construction of Approximating Models under Bounded Measurement Noises

If the "output" of a system is measured under an additive noise with predefined set-valued estimate, then there is an optimal size for the vector of parameters of the approximating model under which the guaranteed approximation error is minimal. This result is extended to the case in which the a priori noise estimate depends on the measured parameter.

A new equal-partition measurement encoding scheme for networked control systems

In this paper, a new encoding strategy is proposed for data exchange through limited bandwidth communication networks. The proposed strategy belongs to the family of finitely recursive equal-partition schemes. Convergence results are proposed under bounded measurement noises. When the noise probability density function is known, heuristic procedure is proposed to optimize the encoding scheme’s parameters. This is done using the discrete-time Markov chains tool. Simulations may be viewed at http://www.lag.ensieg.inpg.fr/alamir/Network.electrics/alamir_commault.pdf

Fault detection using an adaptive fuzzy system

A fault detection approach is presented for Lipschitz non-linear dynamic systems with bounded measurement noises. This approach does not require any nominal models of actual systems in the presence or absence of faults. It uses an adaptive fuzzy system (AFS) to remember the past behaviour, and it continually updates the mathematical representation of the actual system. The basic framework of the updating process is the same as Wang and Mendel's, but the description of fuzzy rules, the creation of the combined fuzzy rule base, the defuzzification strategy and some other details are greatly different from Wang and Mendel's. This updating process also consists of five steps. The first four steps are devoted to the AFS updating, the last step with the determination of the AFS output mapping. Based on the error analysis on the AFS, this paper proposes a fault-detection strategy that depends on the deviation of the actual system output from the AFS output. Simulations show that this approach can be used effectively in the detection of abrupt or incipient sensor faults. Although this approach is designed for systems with bounded measurement noises, it can also be used for systems with unbounded measurement noises -- if a limited bound that covers most of the measurement noises exists.

A fast autonomous star-acquisition algorithm for spacecraft

An algorithm capable of real-time autonomous star recognition from large star catalogues, with minimal storage requirements, is described. The algorithm is based on a locally optimised binary tree-search technique that systematically divides the search space until a small set of stars is left in the identification set. Simulation results are presented to verify that the search algorithm can always identify the correct star, even in the presence of bounded measurement noise, not necessarily uniquely, but at least to within a small set of possibilities. Implementing the algorithm in Matlab on a 486DX25 PC, a search time of less than 100ms for a 20074-entry star catalogue is demonstrated.

Output feedback control of uncertain coupled systems

The stabilization of uncertain dynamical systems on ℝ n that admit a decomposition into two coupled subsystems of dimension nc and nr respectively, is studied. We refer to the nc -dimensional sybsystem as the reduced-order system and to the nr -dimensional subsystem as the residual system: the overall n-dimensional system is termed the full system—the prototype for which is a mechanical model arising in the study of the active control of structures. Each subsystem is modelled by a differential equation with a linear nominal part and a nonlinear perturbation of a specified class. The output available for feedback purposes is an ℝ nc -valued linear combination of the state components of the full system and is subject to bounded measurement noise (with known bound). An output feedback strategy is described and sufficient conditions are obtained for the existence of a (calculable) global uniform compact attractor (containing the state origin) for controlled systems of this class.

Two new estimation algorithms for linear models with unknown but bounded measurement noise

Attention is given to linear systems described by y=A/sub theta /+e where the measurement error vector e is unknown but bounded. Two algorithms for sequential parameter identification are introduced. Their convergence properties are illustrated and compared with those of existing algorithms. A simulation study is carried out using simulated data to investigate the possible practical use of the algorithms. Their performances are compared with those of other offline algorithms as well as with those of the widely used least-squares estimates.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>