Framework for state and unknown input estimation of linear time-varying systems

The design of unknown-input decoupled observers and filters requires the assumption of an existence condition in the literature. This paper addresses an unknown input filtering problem where the existence condition is not satisfied. Instead of designing a traditional unknown input decoupled filter, a Double-Model Adaptive Estimation approach is extended to solve the unknown input filtering problem. It is proved that the state and the unknown inputs can be estimated and decoupled using the extended Double-Model Adaptive Estimation approach without satisfying the existence condition. Numerical examples are presented in which the performance of the proposed approach is compared to methods from literature.Comment: This paper has been accepted by Automatica. It considers unknown input estimation or fault and disturbances estimation. Existing approaches considers the case where the effects of fault and disturbance can be decoupled. In our paper, we consider the case where the effects of fault and disturbance are coupled. This approach can be easily extended to nonlinear system

Nonlinear disturbance attenuation control of hydraulic robotics

This paper presents a novel nonlinear disturbance rejection control for hydraulic robots. This method requires two third-order filters as well as inverse dynamics in order to estimate the disturbances. All the parameters for the third-order filters are pre-defined. The proposed method is nonlinear, which does not require the linearization of the rigid body dynamics. The estimated disturbances are used by the nonlinear controller in order to achieve disturbance attenuation. The performance of the proposed approach is compared with existing approaches. Finally, the tracking performance and robustness of the proposed approach is validated extensively on real hardware by performing different tasks under either internal or both internal and external disturbances. The experimental results demonstrate the robustness and superior tracking performance of the proposed approach

Simultaneous State and Unknown Input Set-Valued Observers for Some Classes of Nonlinear Dynamical Systems

In this paper, we propose fixed-order set-valued (in the form of l2-norm hyperballs) observers for some classes of nonlinear bounded-error dynamical systems with unknown input signals that simultaneously find bounded hyperballs of states and unknown inputs that include the true states and inputs. Necessary and sufficient conditions in the form of Linear Matrix Inequalities (LMIs) for the stability (in the sense of quadratic stability) of the proposed observers are derived for ($\mathcal{M},\gamma$)- Quadratically Constrained (($\mathcal{M},\gamma$)-QC) systems, which includes several classes of nonlinear systems: (I) Lipschitz continuous, (II) ($\mathcal{A},\gamma$)-QC* and (III) Linear Parameter-Varying (LPV) systems. This new quadratic constraint property is at least as general as the incremental quadratic constraint property for nonlinear systems and is proven in the paper to embody a broad range of nonlinearities. In addition, we design the optimal $\mathcal{H}_{\infty}$ observer among those that satisfy the quadratic stability conditions and show that the design results in Uniformly Bounded-Input Bounded-State (UBIBS) estimate radii/error dynamics and uniformly bounded sequences of the estimate radii. Furthermore, we provide closed-form upper bound sequences for the estimate radii and sufficient condition for their convergence to steady state. Finally, the effectiveness of the proposed set-valued observers is demonstrated through illustrative examples, where we compare the performance of our observers with some existing observers.Comment: Under review in Automatic

Input and State Estimation for Discrete-Time Linear Systems with Application to Target Tracking and Fault Detection

This dissertation first presents a deterministic treatment of discrete-time input reconstruction and state estimation without assuming the existence of a full-rank Markov parameter. Algorithms based on the generalized inverse of a block-Toeplitz matrix are given for 1) input reconstruction in the case where the initial state is known; 2) state estimation in the case where the initial state is unknown, the system has no invariant zeros, and the input is unknown; and 3) input reconstruction and state estimation in the case where the initial state is unknown and the system has no invariant zeros. In all cases, the unknown input is an arbitrary deterministic or stochastic signal. In addition, the reconstruction/estimation algorithm is deadbeat, which means that, in the absence of sensor noise, exact input reconstruction and state estimation are achieved in a finite number of steps. Next, asymptotic input and state estimation for systems with invariant zeros is considered. Although this problem has been widely studied, existing techniques are confined to the case where the system is minimum phase. This dissertation presents retrospective cost input estimation (RCIE), which is based on retrospective cost optimization. It is shown that RCIE automatically develops an internal model of the unknown input. This internal model provides an asymptotic estimate of the unknown input regardless of the location of the zeros of the plant, including the case of nonminimum-phase dynamics. The input and state estimation method developed in this dissertation provides a novel approach to a longstanding problem in target tracking, namely, estimation of the inertial acceleration of a body using only position measurements. It turns out that, for this problem, the discretized kinematics have invariant zeros on the unit circle, and thus the dynamics is nonminimum-phase. Using optical position data for a UAV, RCIE estimates the inertial acceleration, which is modeled as an unknown input. The acceleration estimates are compared to IMU data from onboard sensors. Finally, based on exact kinematic models for input and state estimation, this dissertation presents a method for detecting sensor faults. A numerical investigation using the NASA Generic Transport Model shows that the method can detect stuck, bias, drift, and deadzone sensor faults. Furthermore, a laboratory experiment shows that RCIE can estimate the inertial acceleration (3-axis accelerometer measurements) and angular velocity (3-axis rate-gyro measurements) of a quadrotor using vision data; comparing these estimates to the actual accelerometer and rate-gyro measurements provide the means for assessing the health of the accelerometer and rate gyro.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145813/1/ansahmad_1.pd