We consider -free numbers over Beatty sequences. New results are given. In particular, for a fixed irrational number of finite type and any constant , we can show that where is the set of positive -free integers and the implied constant depends only on and This improves previous results. The main new ingredient of our idea is employing double exponential sums of the type
This paper addresses the problems of robust fault estimation and fault-tolerant control for Takagi-Sugeno (T-S) fuzzy systems with time delays and unknown sensor faults. A fuzzy augmented state and fault observer is designed to achieve the system state and sensor fault estimates simultaneously. Furthermore, based on the information of on-line fault estimates, an observer-based dynamic output feedback fault-tolerant controller is developed to compensate for the effect of faults by stabilizing the...
In this paper we construct a minimizing sequence for the problem (1). In particular, we show that for any subsolution of the Hamilton-Jacobi equation there exists a minimizing sequence weakly convergent to this subsolution. The variational problem (1) arises from the theory of computer vision equations.
This paper considers a parametric approach for quasi-linear systems by using dynamic compensator and multi-objective optimization. Based on the solutions of generalized Sylvester equations, we establish the more general parametric forms of dynamic compensator and the left and right closed-loop eigenvector matrices, and give two groups of arbitrary parameters. By using the parametric approach, the closed-loop system is converted into a linear constant one with a desired eigenstructure. Meanwhile,...
A smoothing sample average approximation (SAA) method based on the log-exponential function is proposed for solving a stochastic mathematical program with complementarity constraints (SMPCC) considered by Birbil et al. (S. I. Birbil, G. Gürkan, O. Listes: Solving stochastic mathematical programs with complementarity constraints using simulation, Math. Oper. Res. 31 (2006), 739–760). It is demonstrated that, under suitable conditions, the optimal solution of the smoothed SAA problem converges almost...
Observer design for ODE-PDE cascades is studied where the finite-dimension ODE is a globally Lipschitz nonlinear system, while the PDE part is a pair of counter-convecting transport dynamics. One major difficulty is that the state observation only rely on the PDE state at the terminal boundary, the connection point between the ODE and the PDE blocs is not accessible to measure. Combining the backstepping infinite-dimensional transformation with the high gain observer technology, the state of the...
A class of functional equations with nonlinear iterates is discussed on the unit circle . By lifting maps on and maps on the torus to Euclidean spaces and extending their restrictions to a compact interval or cube, we prove existence, uniqueness and stability for their continuous solutions.
Design of model following control system (MFCS) for nonlinear system with time delays and disturbances is discussed. In this paper, the method of MFCS will be extended to nonlinear system with time delays. We set the nonlinear part of the controlled object as , and show the bounded of internal states by separating the nonlinear part into . Some preliminary numerical simulations are provided to demonstrate the effectiveness of the proposed method.
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