Static output feedback stabilization of discrete time linear time invariant systems based on approximate dynamic programming

Abstract

This study proposes a method for the static output feedback (SOF) stabilization of discrete time linear time invariant (LTI) systems by using a low number of sensors. The problem is investigated in two parts. First, the optimal sensor placement is formulated as a quadratic mixed integer problem that minimizes the required input energy to steer the output to a desired value. Then, the SOF stabilization, which is one of the most fundamental problems in the control research, is investigated. The SOF gain is calculated as a projected solution of the Hamilton-Jacobi-Bellman (HJB) equation for discrete time LTI system. The proposed method is compared with several examples from the literature.

Overlapping Decentralized Guaranteed Cost Control Method for Discrete-Time Systems of Building Structures with Uncertain Parameters under Earthquake Action

“…Definition 1. For system (10) and the performance index (13), if there is a matrix G and a positive definite symmetric matrix P such that for all nonzero Z(k) and all uncertain matrices satisfying equation ( 12), we have…”

“…e control law u(k) � GZ(k) is called a quadratic guaranteed cost control law with a performance matrix P for system (10).…”

“…Proof: According to Definition 1, there exists a quadratic guaranteed cost control law u(k) � GZ(k) for system (10). A matrix inequality holds if and only if there exists a matrix G and a symmetric matrix P > 0 such that for the allowed uncertain matrix F, the following matrix inequality holds:…”

“…Kemerli et al [9] proposed the design and implementation of the discretetime sliding mode controller with a hybrid control strategy according to Gao's reaching law and variable rate reaching law and conducted simulated experiments with a 5-story building under seismic excitation; the results show that better results were achieved in terms of controller energy consumption and structural response compared to Gao's controller. Demir et al [10] studied a method to stabilize the static output feedback (SOF) of a discrete-time linear timeinvariant (LTI) system by using a small number of sensors. Gómez et al [11] discussed the active control of building structures subjected to tridirectional earthquake excitation, for which there is no available mathematical model, the discrete-time hysteretic nonlinear model was developed, and use the pole-placement design to control the building structure in bidirectional with vertical and torsional effects.…”