Sparse Sensing and Optimal Precision: Robust H∞\mathcal{H}_{\infty} Optimal Observer Design with Model Uncertainty

We present a framework which incorporates three aspects of the estimation problem, namely, sparse sensor configuration, optimal precision, and robustness in the presence of model uncertainty. The problem is formulated in the $\mathcal{H}_{\infty}$ optimal observer design framework. We consider two types of uncertainties in the system, i.e. structured affine and unstructured uncertainties. The objective is to design an observer with a given $\mathcal{H}_{\infty}$ performance index with minimal number of sensors and minimal precision values, while guaranteeing the performance for all admissible uncertainties. The problem is posed as a convex optimization problem subject to linear matrix inequalities. Numerical simulations demonstrate the application of the theoretical results presented in this work

Sparse Sensing and Optimal Precision: An Integrated Framework for H2/H∞\mathcal{H}_2/\mathcal{H}_{\infty} Optimal Observer Design

In this paper, we simultaneously determine the optimal sensor precision and the observer gain, which achieves the specified accuracy in the state estimates. Along with the unknown observer gain, the formulation parameterizes the scaling of the exogenous inputs that correspond to the sensor noise. Reciprocal of this scaling is defined as the sensor precision, and sparseness is achieved by minimizing the $l_1$ norm of the precision vector. The optimization is performed with constraints guaranteeing specified accuracy in state estimates, which are defined in terms of $\mathcal{H}_2$ or $\mathcal{H}_{\infty}$ norms of the error dynamics. The results presented in this paper are applied to the linearized longitudinal model of an F-16 aircraft

Sensor Selection and Optimal Precision in H2/H∞\mathcal{H}_2/\mathcal{H}_{\infty} Estimation Framework: Theory and Algorithms

We consider the problem of sensor selection for designing observer and filter for continuous linear time invariant systems such that the sensor precisions are minimized, and the estimation errors are bounded by the prescribed $\mathcal{H}_2/\mathcal{H}_{\infty}$ performance criteria. The proposed integrated framework formulates the precision minimization as a convex optimization problem subject to linear matrix inequalities, and it is solved using an algorithm based on the alternating direction method of multipliers (ADMM). We also present a greedy approach for sensor selection and demonstrate the performance of the proposed algorithms using numerical simulations