A multiobjective optimization approach for linear quadratic Gaussian/loop transfer recovery design

Abstract

SummaryThis article bestows the linear quadratic Gaussian (LQG)/Loop Transfer Recovery (LTR) optimal controller design for a perturbed linear system having insufficient information about systems states through a multiobjective optimization approach. A Kalman filter observer is required to estimate the unknown states at the output from the noisy data. However, the main downside of the LQG controller's is that its robustness cannot be guaranteed because it consists of linear quadratic regulator (LQR) and Kalman observer, and due to observer incorporation within the LQR framework results in loss of robustness which is undesirable. Therefore, it is necessary to recover the robustness by tuning the controller which further plays havoc with system performance and control effort for certain plants. The present work addresses the investigation of the trade‐off between multiobjective indexes (formulated on the basis of robustness, optimal control, and performances) through three multiobjective optimization algorithms as NSGA‐II, multiobjective simulated annealing and multiobjective particle swarm optimization. The tuned parameters meet the competitive multiobjective performance indexes that are verified through simulation results. The Pareto front with multiple solutions helps to design a robust controller depending on the weightage given to the respective performance indexes. Simulation results reveal that the proposed multiobjective control strategy helps in recovering the characteristics of LQG/LTR.

Fractional‐order filter‐based enhanced full state feedback control design with multi‐objective formulation using grey wolf optimization algorithm

“…The MOOP formulation and its solution can be obtained in the following three ways: The multi‐objective problems consisting of two or more conflicting performance indices generates a set of non‐dominated solutions by making trade‐offs between objective functions. These nondominated solutions can be obtained in the form of Pareto optimal fronts 22,24 The one way to formulate the conflicting vector valued problem is to normalize the vector along the y ‐axis, which represent the common y ‐axis's of the optimization problem $$$ {F}_{\mathrm{opt}.}$…”

“…Discrete PID based on the LQR with fractional order integral performance index (PI) and real coded genetic algorithm (GA) optimized weighting matrices 23 . A novel LQG/LQR controller design based on multi‐objective formulation has been proposed, in which the problem was formulated and solved by making trade‐off between multiple objectives in time as well as frequency domain 24 . In most of the research with multi‐objective formulation, the results have been obtained with a meta‐heuristic optimization algorithm to get the optimal solution 25 .…”

“…23 A novel LQG/LQR controller design based on multi-objective formulation has been proposed, in which the problem was formulated and solved by making trade-off between multiple objectives in time as well as frequency domain. 24 In most of the research with multi-objective formulation, the results have been obtained with a meta-heuristic optimization algorithm to get the optimal solution. 25 The important meta-heuristics are classified as: physics-based, evolutionary, and swarm intelligence (SI) algorithms.…”

Discrete‐time state‐feedback control of polytopic LPV systems

“…It is worth mentioning that such formulation may be useful to handle Linear Quadratic Gaussian (LQG) problems and its variations. 31,32 Many works in the literature establish the connection between the classical LQG problem and a dual version of the generalized ℋ 2 control problem. 33 Furthermore, using implications of the poly-quadratic concept, an improved LMI-based condition for quadratic ℋ 2 control synthesis is also provided.…”

Adjusting LQG with Noise Signals, PID Controller for Acrobot System

“…It is necessary to develop algorithms [15][16][17][18][19] so that they are more in line with today's trend. Based on [20][21][22][23], the author applied algorithms [20][21][22][23] for robot models. e author used modern algorithms such as neural control, adaptive fuzzy control, and sliding fuzzy control to control the model [24][25][26][27], and efficiency levels of the above control methods are presented in detail.…”