TY - JOUR

T1 - Regulation with Guaranteed Convergence Rate for Continuous-Time Systems with Completely Unknown Dynamics in the Presence of Disturbance

AU - Rahdarian, Ali

AU - Zadeh, Danial Sadrian

AU - Shamaghdari, Saeed

AU - Moshiri, Behzad

AU - Montazeri, Allahyar

PY - 2022/11/28

Y1 - 2022/11/28

N2 - This paper presents the design of a novel H ∞ -based control framework for state regulation of continuous-time linear systems with completely unknown dynamics. The proposed method solves the regulation problem with the desired convergence rate and simultaneously seeks to attenuate the adverse effect of disturbance on the system. The H ∞ regulation problem assumes a cost function that considers regulation with a guaranteed rate of convergence as well as disturbance attenuation. The problem is then turned into a two-player zero-sum game optimization problem that can be solved by solving the associated algebraic Riccati equation (ARE), which provides a model-based solution. To solve this problem in a model-free way, a novel integral reinforcement learning (IRL) algorithm is designed to learn the solution online without requiring any prior knowledge of the system dynamics. It is shown that the model-free method (i.e., IRL-based method) provides the same solution as the model-based method (i.e., ARE). The effectiveness of the proposed method is ascertained through simulation examples; it is shown that the proposed method effectively addresses the problem for both stable and unstable systems.

AB - This paper presents the design of a novel H ∞ -based control framework for state regulation of continuous-time linear systems with completely unknown dynamics. The proposed method solves the regulation problem with the desired convergence rate and simultaneously seeks to attenuate the adverse effect of disturbance on the system. The H ∞ regulation problem assumes a cost function that considers regulation with a guaranteed rate of convergence as well as disturbance attenuation. The problem is then turned into a two-player zero-sum game optimization problem that can be solved by solving the associated algebraic Riccati equation (ARE), which provides a model-based solution. To solve this problem in a model-free way, a novel integral reinforcement learning (IRL) algorithm is designed to learn the solution online without requiring any prior knowledge of the system dynamics. It is shown that the model-free method (i.e., IRL-based method) provides the same solution as the model-based method (i.e., ARE). The effectiveness of the proposed method is ascertained through simulation examples; it is shown that the proposed method effectively addresses the problem for both stable and unstable systems.

KW - General Engineering

KW - General Materials Science

KW - General Computer Science

KW - Electrical and Electronic Engineering

U2 - 10.1109/access.2022.3208058

DO - 10.1109/access.2022.3208058

M3 - Journal article

VL - 10

SP - 122376

EP - 122386

JO - IEEE Access

JF - IEEE Access

SN - 2169-3536

ER -