The Maximal Solution and Comparison Theorems for the Periodic Discrete-Time Riccati Equation

2016 ◽  
Vol 6 (4) ◽  
pp. 416-433
Author(s):  
Xiao-Shan Chen
Keyword(s):  
Riccati Equation ◽  
Discrete Time ◽  
Maximal Solution ◽  
Comparison Theorems ◽  
Periodic Case

AbstractProperties and comparison theorems for the maximal solution of the periodic discrete-time Riccati equation are supplemented by an extension of some earlier results and analysis, for the discrete-time Riccati equation to the periodic case.

H 2-H∞ Control of Discrete Time Nonlinear Systems Using the SDRE Approach

2011 ◽  
Author(s):  
Xin Wang ◽  
Edwin E. Yaz ◽  
Susan C. Schneider ◽  
Yvonne I. Yaz
Keyword(s):  
Riccati Equation ◽  
Discrete Time ◽  
Steady State Solution ◽  
State Feedback Control ◽  
Disturbance Attenuation ◽  
Performance Criteria ◽  
Linear Matrix ◽  
Time Step ◽  
Control Approach ◽  
The Difference

A novel H2–H∞ State Dependent Riccati Equation control approach is presented for providing a generalized control framework to discrete time nonlinear system. By solving a generalized Riccati Equation at each time step, the nonlinear state feedback control solution is found to satisfy mixed performance criteria guaranteeing quadratic optimality with inherent stability property in combination with H∞ type of disturbance attenuation. Two numerical techniques to compute the solution of the resulting Riccati equation are presented: The first one is based on finding the steady state solution of the difference equation at every step and the second one is based on finding the minimum solution of a linear matrix inequality. The effectiveness of the proposed techniques is demonstrated by simulations involving the control of an inverted pendulum on a cart, a benchmark mechanical system.

Discrete Time-Coupled State-Dependent Riccati Equation Control of Nonlinear Mechatronic Systems

2020 ◽  
Vol 142 (8) ◽  
Author(s):  
Xin Wang
Keyword(s):  
Riccati Equation ◽  
Discrete Time ◽  
Disturbance Attenuation ◽  
Infinite Time ◽  
Mechatronic Systems ◽  
Feedback Controllers ◽  
Control Laws ◽  
State Dependent ◽  
Time Optimal ◽  
Nonlinear Plant

Abstract A discrete-time-coupled state-dependent Riccati equation (CSDRE) control strategy is structured in this paper for synthesizing state feedback controllers satisfying the combined nonlinear quadratic regulator (NLQR) and H∞ robust control performance objectives. Under smoothness assumptions, the nonlinear plant dynamics can be formulated into state-dependent coefficient form through direct parameterization. By solving a pair of coupled state-dependent Riccati equations, the optimal stabilizing solutions can achieve inherent stability, nonlinear quadratic optimality, and H∞ disturbance attenuation performance. The established two-player Nash's game theory is utilized for developing both of the finite and infinite time optimal control laws. Furuta swing-up pendulum, a representative nonholonomic underactuated nonlinear system, is stabilized in real-time for validating the robustness and potential of proposed approach in mechatronics applications.

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