Worst-Case Optimal Data-Driven Estimators for Switched Discrete-Time Linear Systems
This paper proposes a data-driven framework to address the worst-case estimation problem for switched discrete-time linear systems based solely on the measured data (input & output) and an ℓ ∞ bound over the noise. We start with the problem of designing a worst-case optimal estimator for a single system and show that this problem can be recast as a rank minimization problem and efficiently solved using standard relaxations of rank. Then we extend these results to the switched case. Our main result shows that, when the mode variable is known, the problem can be solved proceeding in a similar manner. To address the case where the mode variable is unmeasurable, we impose the hybrid decoupling constraint(HDC) in order to reformulate the original problem as a polynomial optimization which can be reduced to a tractable convex optimization using moments-based techniques.
Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10176074
Journal Name:
2019 IEEE 58th Conference on Decision and Control (CDC)
Page Range or eLocation-ID:
3417 to 3422
1. Human development is a threat to biodiversity and conservation organizations (COs) are purchasing land to protect areas for biodiversity preservation. COs have limited budgets and cannot purchase all the land necessary to perfectly preserve biodiversity, and human activities are uncertain, so exact developments are unpredictable. We propose a multistage, robust optimization problem with a data-driven hierarchical-structured uncertainty set which captures the endogenous nature of the binary (0-1) human land use uncertain parameters to help COs choose land parcels to purchase to minimize the worst-case human impact on biodiversity. In the proposed approach, the problem is formulated as a game between COs, which choose parcels to protect with limited budgets, and the human development, which will maximize the loss to the unprotected parcels. We leverage the cellular automata model to simulate the development based on climate data, land characteristics, and human land use data. We use the simulation to build data-driven uncertainty sets. We demonstrate that an equivalent formulation of the problem can be obtained that presents exogenous uncertainty only and where uncertain parameters only appear in the objective. We leverage this reformulation to propose a conservative $K$-adaptability reformulation of our problem that can be solved routinely by off-the-shelf solvers likemore »