João Viana da Fonseca Neto

On the Convergence of DLQR Control System Design and Recurrences of Riccati and Lyapunov in Dynamic Programming Strategies

The convergence evaluation of the discrete linear quadratic regulator (DLQR) to map the Z-stable plane, is the main target of this research that is oriented to the development of tuning method for multivariable systems. The tuning procedures is based on strategies to select the weighting matrices and dynamic programming. The solutions of DLQR are presented, since Bellman formulations until Riccati and Lyapunov recurrences and are based on the Generalized Policy Iteration, Policy Iteration and Value Iteration. The algorithms and the proposed heuristic method are developed from Riccati and Lyapunov recurrences and are implemented to map the closed loop dynamic eingen values in the Z plane. A fourth order model is used to evaluate the convergence and its ability to map the plan Z by selection of the weighting matrices of Optimal Control.

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

The main focus of this article is to present a proposal to solve, via UDUT factorisation, the convergence and numerical stability problems that are related to the covariance matrix ill-conditioning of the recursive least squares (RLS) approach for online approximations of the algebraic Riccati equation (ARE) solution associated with the discrete linear quadratic regulator (DLQR) problem formulated in the actor–critic reinforcement learning and approximate dynamic programming context. The parameterisations of the Bellman equation, utility function and dynamic system as well as the algebra of Kronecker product assemble a framework for the solution of the DLQR problem. The condition number and the positivity parameter of the covariance matrix are associated with statistical metrics for evaluating the approximation performance of the ARE solution via RLS-based estimators. The performance of RLS approximators is also evaluated in terms of consistence and polarisation when associated with reinforcement learning methods. The used methodology contemplates realisations of online designs for DLQR controllers that is evaluated in a multivariable dynamic system model.

QR-Duality Tuning of Standard Kalman Filters Oriented to Rocket Velocity Indirect Measurement

The development of a tuning procedure for standard Kalman filter algorithm based on Q and R matrices duality principle is the main issue of this article. The tuning procedure is based on heuristics that are guided by the influence of Q and R matrices on the Kalman gain selections, as these matrices variations are driven by the QR-duality principle. An analysis of the filter performance is carried out by decreasing or increasing the filter bandwidth, the tuning objective aims to build optimal gains sets that map an aerospace vehicle behavior. Taking into account the rocket stages, some discussions about practical aspects of dynamic systems models simulation are presented in the sense of displacement, velocity and acceleration state space variables.

Estimators Based on Non-squares Loss Functions to Approximate HJB-Riccati Equation Solution for DLQR Design via HDP

This paper is concerned with the development of online algorithms for approximate solutions of the Hamilton-Jacobi-Bellman (HJB) equation. In the discrete linear quadratic regulator (DLQR) control system design, the HJB equation is the discrete algebraic Riccati (DARE) equation. Due to the problem of dimensionality curse, this equation is approximated via heuristic dynamic programming (HDP). The proposed methodology is based on a familiy of non-squares approximators for critic adaptive solution of the DARE associated to the DLQR problem, referred to in this work as HJB-Riccati equation, which is characterized as a parameterization of the HJB equation. The proposed method is evaluated in a multivariable dynamic system of 4th order with two inputs and it is compared with standard recursive least square algorithm.

Online Optimal DLQR-DFIG Control System Design via Recursive Least-Square Approach and State Heuristic Dynamic Programming for Approximate Solution of the HJB Equation

Our aim in this paper is to present a novel method for online optimal control system design via state heuristic dynamic programming (HDP) to approximate the solution of the Hamilton-Jacobi-Bellman (HJB) equation by means of the recursive least-square (RLS) approach. Because the randomness nature associated to primary energy sources, the control of eolic and solar energy systems demands methods and technics that are suitable with the high degree of the environment uncertainties. The reinforcement learning (RL) and approximate dynamic programming (ADP) approaches furnish the key ideas and the mathematical formulations to develop optimal control system methods and strategies for alternative energy systems. We are proposing a online design method to establish control strategies for the the main unit of a eolic system that is the doubly fed induction generator (DFIG). The performance of proposed method is evaluated via computational experiments for discrete time HDP algorithms that map eigenstructure assignments in the stable Z-plane.

Hybrid Support System for Decision Making Based on MLP-ANN, IED and SCADA for Disturbances Analysis of Electrical Power Distribution Transformers

The operation and maintenance of the power system require attention, precise diagnostics on failure and agility on system recovery. In addition, each operation needs to be carefully planned and executed, once errors can be fatal. To improve the operation and maintenance tasks, in this article is presented the proposal of a support system for decision making units based on artificial neural network (ANN), intelligent electronic devices (IED), supervisory control and data acquisition (SCADA) system for disturbances analysis of electrical power distribution transformers. The intelligent system is hybrid in the sense that it performs on-line tasks in real time for data acquisition systems via IED and off-line tasks are performed for analysis of disturbances in electrical power distribution transformers. The hybrid decision making support system (HDMSS) has built a MLP-ANN engine for classifying patterns and providing support for decisions. The MLP-ANN engine is evaluated for fault detection in distribution transformer of electrical power substation. The proposed method was evaluated using real data collected directly from IED, such as: digital relays. The on-line simulations results show the effectiveness and the feasibility of the proposed system based on artificial neural network.

Dissolved oxygen PWM control and oxygen uptake rate estimation using Kalman Filter in activated sludge systems

The measurement and utilization of the oxygen uptake rate (OUR), or respiration rate, is very important in biological wastewater treatment process. It provides information about the biological activity and can indicate the presence of the toxic elements able to corrupt the system. An alternative to the lack of OUR sensors is to use computer codes as software sensors for the estimation of respirometric activity, based on dissolved oxygen (DO) measurements. In this paper the OUR is estimated using Kalman Filter as a software sensor and the DO concentration is controlled by aerators of on-off type triggered by pulse wide modulation. Simulation and experimental estimations are performed on a bench scale aerobic reactor.

Convergence Analysis using non-squares estimators to approximate the solution of HJB-Riccati equation for the design DLQR via HDP

The proposed methodology is based on development of online algorithms for approximate solutions of the Hamilton-Jacobi-Bellman (HJB) equation through a family of non-squares approximators for critic adaptive solution of the Discrete Algebraic Riccati Equation (DARE), associated with the problem of Discrete Linear Quadratic Regulator (DLQR). The proposed method is evaluated in a multivariable dynamic system of 4th order with two inputs and it is compared with standard recursive least square algorithm.

A Framework for Modeling, Digital Control Design and Simulations of Dynamic

A digital system design framework, based on fuzzy logic controllers and virtual instrumentation, are the main issues presented in this article. An algorithm oriented for real time applications is the core of the fuzzy control and its performance is evaluated in a computational (MATLABr and LabV IEWr) platforms. The (CTBoard/NI-Elvis) hardware platform is used to implement the fuzzy position and velocity controls of a DC servomotor. The results are compared with the traditional PID control simulations in computational and hardware platforms. The algorithms performance are also evaluated in terms of portability and runtime for real world applications.

Parametric ARX Modeling of the Electrolytic Smelter Pot

The Anode effect that occurs in electrolytic smelter pot is responsible for gases such as PFCs. These gases contributeto the greenhouse effect, and in addition jeopardizes its productive capacity. From the voltage (output) and current(input) signals and based on Systems Identification Theory, the ARX models of the electrolytic smelter pot are built torepresent the steady state operation and the anode effect occurrence. After the simulations based on real anode effectsignal and algebraic properties of the transfer functions some models are validated based on the time response speed ofconvergence. The selected transfer functions of the electrolytic smelter pot are used to perform the steady staterepresentation and are oriented to predict the anode effect by the increasing of voltage. Therefore, this paper showsour latest investigation on parametric ARX models that represent the behavior of the plant in the neighborhood of itsinstability operation point.