Convergence of the standard RLS method andUDUTfactorisation of covariance matrix for solving the algebraic Riccati equation of the DLQR via heuristic approximate dynamic programming

Rêgo, Patrícia Helena Moraes; Neto, João Viana da Fonseca; Ferreira, Ernesto M.

doi:10.1080/00207721.2013.844283

Cited by 8 publications

(4 citation statements)

References 33 publications

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“…Portanto, a estrutura paramétrica da função de custo RLQ tem seu parâmetro θ estimado utilizando o algoritmo recursivo de mínimos quadrados (RMQ). A abordagem RMQ considerada é para viabilizar a solução on-line da equação EAR associada ao projeto de controle ótimo RLQ [53]. O algoritmo RMQ é dado por…”

Section: Implementação On-line Do Método Ipaunclassified

Optimal Control and Adaptive Learning for Stabilization of a Quadrotor-type Unmanned Aerial Vehicle via Approximate Dynamic Programming

Souza

Rêgo

Sousa

et al. 2022

RITA

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The development of an optimal controller for stabilization of a quadrotor system using an adaptive critic structure based on policy iteration schemes is proposed in this paper. This approach is inserted in the context of Approximate Dynamic Programming and it is used to solve optimal decision problems on-line, without requiring complete knowledge of the system dynamics model to be controlled. The main feature of the adaptive critic design method that allows for on-line implementation is that it solves the Bellman optimality equation in a forward-in-time fashion, whereas traditional dynamic programming requires a backward-in-time procedure. This feedback control design technique is able to tune the controller parameters on-line in the presence of variations in plant dynamics and external disturbances using data measured along the system trajectories. Computational simulation results based on a quadrotor model demonstrate the effectiveness of the proposed control scheme.

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Section: Implementação On-line Do Método Ipaunclassified

Optimal Control and Adaptive Learning for Stabilization of a Quadrotor-type Unmanned Aerial Vehicle via Approximate Dynamic Programming

Souza

Rêgo

Sousa

et al. 2022

RITA

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“…The matrix vectorization and the Kronecker product theory [13,30] contribute for an approximate solution of the HJB-Riccati equation obtained through an iterative scheme such as (P , )^, = 7( , , , )…”

Section: Rls-adhdpapproximationmentioning

confidence: 99%

“…For many traditional iterative ADP algorithms, it is necessary to build a non-linear system model and, then, execute the ADP algorithms to derive an improved control policy. In terms of RLS learning to solve the discrete-time algebraic Riccati equation (DARE), also known as HJB-Riccati equation, in optimal control problems that are solved by the Heuristic Dynamic Programming (HDP) approach, the authors [13] developed methods and algorithms based on the RLS training for the online design of the discrete-time linear-quadratic regulator (DLQR).…”

Section: Introductionmentioning

confidence: 99%

A Learning Controller Design Approach for A 3-DOF Helicopter System with Online Optimal Control

Sousa¹,

R.Lima²,

Rêgo³

et al. 2019

Computer Science &Amp; Information Technology (CS &Amp; IT )

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This paper presents the design and investigation of performance of a 3-DOF Quanser helicopter system using a learning optimal control approach that is grounded on approximate dynamic programming paradigms, specifically action-dependent heuristic dynamic programming (ADHDP). This approach results in an algorithm that is embedded in the actor-critic reinforcement learning architecture, that characterizes this design as a model-free structure. The developed methodology aims at implementing an optimal controller that acts in real-time in the plant control, using only the input and output signals and states measured along the system trajectories. The feedback control design technique is capable of an online tuning of the controller parameters according to the plant dynamics, which is subject to the model uncertainties and external disturbances. The experimental results demonstrate the desired performance of the proposed controller implemented on the 3-DOF Quanser helicopter.

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“…This study presents two ADP algorithms for multi-agent systems: the QR-solver (developed in this research) and the RLS µ -QR-HDP-DLQR (initially developed for singleagent systems), as described in [20], [21]. We compare their performances, such as convergence of the gain, by analyzing the parameter θ of the DLQR and convergence of the trajectory and desired formation.…”

Section: Introductionmentioning

confidence: 99%

HDP Algorithms for Trajectory Tracking and Formation Control of Multi-Agent Systems

2022

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A heuristic dynamic programming (HDP) algorithm for trajectory tracking and formation control of multi-agent systems (MAS) is presented in this paper. The selected HDP method allows for an online optimal control design. The multi-agent control problem is formulated as a leader-follower, where it is necessary for followers to maintain the assigned formation, while the leader follows the specified trajectory. Developed QR-Solver and RLS µ -QR-HDP-DLQR algorithms provide a new methodology to obtain the solution of the Hamilton-Jacobi-Bellman (HJB) equation. These proposed solutions are based on QR factorization to decrease the computational cost and avoid issues associated with numerical stability of conventional least squares (LS) method. The algorithms' performances such as convergence, numerical stability, and computational metrics, were experimentally evaluated for two control systems: aerial altitude control (one degree of freedom) and terrestrial robot (two degrees of freedom).

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Convergence of the standard RLS method andUDU^Tfactorisation of covariance matrix for solving the algebraic Riccati equation of the DLQR via heuristic approximate dynamic programming

Cited by 8 publications

References 33 publications

Optimal Control and Adaptive Learning for Stabilization of a Quadrotor-type Unmanned Aerial Vehicle via Approximate Dynamic Programming

Optimal Control and Adaptive Learning for Stabilization of a Quadrotor-type Unmanned Aerial Vehicle via Approximate Dynamic Programming

A Learning Controller Design Approach for A 3-DOF Helicopter System with Online Optimal Control

HDP Algorithms for Trajectory Tracking and Formation Control of Multi-Agent Systems

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