We investigate the solvability of the reverse Stackelberg game. Here, a leader player acts first by presenting a leader function that maps the follower decision space into the leader decision space. Subsequently, the follower acts by determining his optimal decision variable. Such a game setting can be adopted within a multi-level optimization approach for large-scale control problems like road...

We present a novel framework for characterizing signals in images using techniques from computational algebraic topology. This technique is general enough for dealing with noisy multivariate data including geometric noise. The main tool is persistent homology which can be encoded in persistence diagrams. These diagrams visually show how the number of connected components of the sublevel sets of...

The problem of computing bounds on the region-of-attraction for systems with polynomial vector fields is considered. Invariant subsets of the region-of-attraction are characterized as sublevel sets of Lyapunov functions. Finite-dimensional polynomial parametrizations for Lyapunov functions are used. A methodology utilizing information from simulations to generate Lyapunov function candidates sa...

We study a surprising phenomenon related to the representation of a cloud of data points using polynomials. We start with the previously unnoticed empirical observation that, given a collection (a cloud) of data points, the sublevel sets of a certain distinguished polynomial capture the shape of the cloud very accurately. This distinguished polynomial is a sum-of-squares (SOS) derived in a simp...

It often results in sublevel grey full rank square matrix to become non-feasible solution square matrix when there are null-strategy variables and redundancy constraints in the grey matrix solving method of grey matrix game. We can not directly find the optimum grey game solutions in the non-feasible solution square matrix. However, we define concepts of nullstrategy variables and redundancy co...

We consider the problem of deciding whether the persistent homology group of a simplicial pair (K, L) can be realized as the homology H∗(X) of some complex X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded in R3. As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on S3 within a given tolerance constraint. This prob...

Based on the engineering background of Meishan iron mine with sublevel caving (SLC) method, in this work, we adopted method for identifying shape mined orebody (the original location blasted slice), which analyzed and determined reasonable stope structure parameters. In field test, markers were arranged slice, was measured by situ tests, reliable data achieved. The obtained through test when wi...

This paper considers the optimization landscape of linear dynamic output feedback control with $\mathcal{H}_\infty$ robustness constraints. We consider feasible set all stabilizing full-order dynamical controllers that satisfy an additional constraint. show this $\mathcal{H}_\infty$-constrained has at most two path-connected components are diffeomorphic under a mapping defined by similarity tra...

This paper is based on the open pit to underground mining practice of Daye Iron Mine. The influence mechanism between high-steep slope and non-pillar sublevel caving method is studied by using physical model test. Firstly, engineering geological properties of the choosing typical research section is analysed and generalized. Secondly, the system of open pit to underground mining is developing a...