Integrals of Motion for Discrete-Time Optimal Control Problems

用于离散时间线性时不变系统状态估计的全阶比例积分观测器设计

Design of full order proportional-integral observer for the state estimation of discrete-time linear time-invariant systems

本文针对离散时间线性时不变系统的状态估计问题，基于实矩阵与多项式矩阵性质，建立了全阶比例积分观测器存在的显式充要条件，并给出观测器构造的简单步骤。

Low-Gain Stability of Projected Integral Control for Input-Constrained Discrete-Time Nonlinear Systems

We consider the problem of zeroing an error output of a nonlinear discrete-time system in the presence of constant exogenous disturbances, subject to hard convex constraints on the input signal. The design specification is formulated as a variational inequality, and we adapt a forward-backward splitting algorithm to act as an integral controller which ensures that the input constraints are met at each time step. We establish a low-gain stability result for the closed-loop system when the plant is exponentially stable, generalizing previously known results for integral control of discrete-time …

离散空间上基于条件聚合的Choquet积分

Conditional aggregation-based Choquet integral on discrete space

本文推导了基于新型生存函数的广义Choquet积分计算公式，并在背包问题和住宿选择中验证其效用，同时给出了不同参数下生存函数重合的充要条件，关联决策中备选方案的不可比性。

负虚系统的离散时间积分共振控制：在高速纳米定位器中的应用

Discrete-time Integral Resonant Control of Negative Imaginary Systems: Application to a High-speed Nanopositioner

针对负虚系统，提出离散时间积分共振控制方法，证明其步进超前负虚特性，可实现零阶保持采样负虚系统的渐近稳定，并通过FPGA硬件实验验证了其在高速纳米定位器上的高效阻尼效果。

LQR based improved discrete PID controller design via optimum selection of weighting matrices using fractional order integral performance index

The continuous and discrete time Linear Quadratic Regulator (LQR) theory has been used in this paper for the design of optimal analog and discrete PID controllers respectively. The PID controller gains are formulated as the optimal state-feedback gains, corresponding to the standard quadratic cost function involving the state variables and the controller effort. A real coded Genetic Algorithm (GA) has been used next to optimally find out the weighting matrices, associated with the respective optimal state-feedback regulator design while minimizing another time domain integral performance index…

Integrality of Subgradients and Biconjugates of Integrally Convex Functions

Integrally convex functions constitute a fundamental function class in discrete convex analysis. This paper shows that an integer-valued integrally convex function admits an integral subgradient and that the integral biconjugate of an integer-valued integrally convex function coincides with itself. The proof is based on the Fourier-Motzkin elimination. The latter result provides a unified proof of integral biconjugacy for various classes of integer-valued discrete convex functions, including L-convex, M-convex, L$_{2}$-convex, M$_{2}$-convex, BS-convex, and UJ-convex functions as well as multi…