Coupled State-Dependent Riccati Equation Control for Continuous Time Nonlinear Mechatronics Systems

This paper considers a novel coupled state-dependent Riccati equation (SDRE) approach for systematically designing nonlinear quadratic regulator (NLQR) and H∞ control of mechatronics systems. The state-dependent feedback control solutions can be obtained by solving a pair of coupled SDREs, guaranteeing nonlinear quadratic optimality with inherent stability property in combination with robust L2 type of disturbance reduction. The derivation of this control strategy is based on Nash's game theory. Both finite and infinite horizon control problems are discussed. An under-actuated robotic system, Furuta rotary pendulum, is used to examine the effectiveness and robustness of this novel nonlinear control approach.

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The Generalized State Dependent Riccati Equation Control of Continuous Time Nonlinear Systems

Volume 4A: Dynamics, Vibration, and Control ◽

10.1115/imece2014-37817 ◽

2014 ◽

Author(s):

Xin Wang ◽

James Long ◽

Wangping Sun ◽

Wen Lian

Keyword(s):

Nonlinear Systems ◽

Riccati Equation ◽

Continuous Time ◽

Performance Criteria ◽

Effective Control ◽

Control Approach ◽

State Dependent ◽

Nonlinear Mechanical ◽

Nonlinear Mechanical System ◽

Generalized State

This paper presents a novel Generalized State Dependent Riccati Equation control approach with the purpose of providing a more effective control design framework for continuous time nonlinear systems to achieve a mixed Nonlinear Quadratic Regulator and H∞ control performance criteria. By solving the Generalized State Dependent Riccati Equation, the optimal control solution is found to achieve mixed performance objectives guaranteeing nonlinear quadratic optimality with inherent stability property in combination with H∞ type of disturbance reduction. An efficient computational algorithm is given to find the solution to the Generalized State Dependent Riccati Equation. The efficacy of the proposed technique is used to design the control system for inverted pendulum, an under-actuated nonlinear mechanical system.

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Algorithms to Solve StochasticH2/H∞Control with State-Dependent Noise

Mathematical Problems in Engineering ◽

10.1155/2014/205967 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9

Author(s):

Ming Gao ◽

Changdi Fu ◽

Weihai Zhang

Keyword(s):

Discrete Time ◽

Continuous Time ◽

Stochastic Systems ◽

Infinite Horizon ◽

Control Problems ◽

Numerical Examples ◽

State Dependent

This paper is concerned with the algorithms which solveH2/H∞control problems of stochastic systems with state-dependent noise. Firstly, the algorithms for the finite and infinite horizonH2/H∞control of discrete-time stochastic systems are reviewed and studied. Secondly, two algorithms are proposed for the finite and infinite horizonH2/H∞control of continuous-time stochastic systems, respectively. Finally, several numerical examples are presented to show the effectiveness of the algorithms.

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