Nonlinear Optimization Approach Research Articles

Nonlinear optimal control for triangular tethered multi-satellite formations

Triangular satellite constellations are created by three satellites which are linked through tethers. Such formations serve distributed observation space missions or the creation of high-density satellite communication networks over high-frequency bands. In a tethered multi-satellite system consisting of three-satellites in triangular formation the associated dynamic model exhibits strong nonlinearities. Stabilization and precise positioning of the multi-satellite constellation is a nontrivial task and the solution of the associated nonlinear control problem is an elaborated procedure. In this article a novel nonlinear optimal control method is applied to the above-noted model the tethered multi-satellite system in triangular formation. First, the state-space model of the triangular tethered multi-satellite formation undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the tethered satellites a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution of the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of setpoints under moderate variations of the control inputs and a minimum dispersion of energy when changing the position of the satellites in their triangular tethered formation.

Wasserstein-penalized Entropy closure: A use case for stochastic particle methods

We introduce a framework for generating samples of a distribution given a finite number of its moments, targeted at particle-based solutions of kinetic equations and rarefied gas flow simulations. Our model, referred to as the Wasserstein-Entropy distribution (WE), couples a physically-motivated Wasserstein penalty term to the traditional maximum-entropy distribution (MED) function, which serves to regularize the latter. The penalty term becomes negligible near the local equilibrium, reducing the proposed model to the MED, known to reproduce the hydrodynamic limit. However, in contrast to the standard MED, the proposed WE closure can cover the entire physically realizable moment space, including the so-called Junk line. We also propose an efficient Monte Carlo algorithm for generating samples of the unknown distribution which is expected to outperform traditional non-linear optimization approaches used to solve the MED problem. Numerical tests demonstrate that given moments up to the heat flux—that is, information equivalent to that contained in the Chapman-Enskog distribution—the proposed methodology provides a reliable closure in the collision-dominated and early transition regimes. Applications to greater rarefaction demand information from higher-order moments, which can be incorporated within the proposed closure.

Generalized geometric pore size distribution code GPSD-3D for periodic systems composed of monodisperse spheres

The generalized geometric pore size distribution P(r;rp|rc) as function of pore radius r, probe sphere radius rp, and coating thickness rc for a periodic two-dimensional system composed of circles (GPSD-2D) had been defined recently. For rp=rc=0 it reduces to the widely accepted pore radius distribution P(r) introduced by Gelb and Gubbins. The three-dimensional counterpart GPSD-3D for periodic systems composed of spheres is implemented here using an efficient Voronoi-based semi-analytic strategy that offers significant advantages compared with both a grid-based implementation and constrained nonlinear optimization with respect to speed, precision and memory requirements. Moreover, GPSD-3D is fully parallelized using OpenMP. Program summaryProgram title:GPSD-3DCPC library link to program files:https://doi.org/10.17632/ntcr87fgr5.1Developers repository link:https://github.com/mkmat/CODE-GPSD-3DLicensing provisions: MITProgramming languages:fortran, c++, perlNature of problem: Calculation of a set of pore radii for a user-provided configuration of (material) spheres contained in a periodic three-dimensional, rectangular box. This set depends on the user-specified radius rp of a probe sphere, and a user-specified hypothetical coating thickness rc of the material spheres. The variable size of the set, and thus the resolution of the resulting generalized geometric pore size distribution increases linearly with computing time.Solution method: Analytic calculation of pore radii from the Voronoi faces for the case of monodisperse systems, constrained nonlinear optimization or grid-based approach for polydisperse systems.Additional comments: This code requires a c++ compiler such as g++, a OpenMP-supporting fortran compiler such as gfortran, perl, and the voro++ library. Download links will be automatically provided during installation of GPSD-3D.

MiPhDUO: microwave imaging via physics-informed deep unrolled optimization

Microwave imaging (MWI) is a non-invasive technique that can identify unknown scatterer objects’ features while offering advantages such as low cost and portable devices with respect to other imaging methods. However, MWI faces challenges in solving the underlying inverse scattering problem, which involves recovering target properties from its scattered fields. Existing methods include linearized and non-linear optimization approaches, but they have limitations respectively in terms of range of validity and computational complexity (in view of the possible occurrence of ‘false solutions’). In recent years, learning-based approaches have emerged as they can allow real-time imaging but usually lack generalizability and a direct connection to the underlying physics. This paper proposes a physics-informed approach that combines convolutional neural networks with physics-based calculations. It is based on a few cascaded operations, making use of the gradient of the relevant cost function, and successively improving the estimation of the unknown target. The proposed approach is assessed using simulated as well as experimental Fresnel data. The results show that the integration of physics with deep learning can contribute to improve reconstruction accuracy, generalizability, and computational efficiency in MWI.

Two-frame wavefront reconstruction method with nonlinear optimization for Ronchi lateral shearing interferometry

Ronchi lateral shearing interferometry is widely applied in wavefront measurement of advanced lithography tools. In Ronchi lateral shearing interferometry, higher-order diffraction beam interference is a common challenge, currently mitigated by introducing more phase shifts, resulting in extended measurement times and added errors. In this study, we propose a nonlinear optimization approach that combines a 2-frame phase-shifting algorithm to suppress the influence of high diffraction orders, reducing the required number of phase shifts by more than 75%. We formulate a numerical model that aligns with the interferometry, construct a highly robust error function, and enable high-precision wavefront reconstruction by optimizing Zernike coefficients. The accuracy and robustness of the proposed method are verified through simulations and experiments.

Toward Interpretable-AI Policies Using Evolutionary Nonlinear Decision Trees for Discrete-Action Systems.

Black-box artificial intelligence (AI) induction methods such as deep reinforcement learning (DRL) are increasingly being used to find optimal policies for a given control task. Although policies represented using a black-box AI are capable of efficiently executing the underlying control task and achieving optimal closed-loop performance-controlling the agent from the initial time step until the successful termination of an episode, the developed control rules are often complex and neither interpretable nor explainable. In this article, we use a recently proposed nonlinear decision-tree (NLDT) approach to find a hierarchical set of control rules in an attempt to maximize the open-loop performance for approximating and explaining the pretrained black-box DRL (oracle) agent using the labeled state-action dataset. Recent advances in nonlinear optimization approaches using evolutionary computation facilitate finding a hierarchical set of nonlinear control rules as a function of state variables using a computationally fast bilevel optimization procedure at each node of the proposed NLDT. In addition, we propose a reoptimization procedure for enhancing the closed-loop performance of an already derived NLDT. We evaluate our proposed methodologies (open- and closed-loop NLDTs) on different control problems having multiple discrete actions. In all these problems, our proposed approach is able to find relatively simple and interpretable rules involving one to four nonlinear terms per rule, while simultaneously achieving on par closed-loop performance when compared to a trained black-box DRL agent. A postprocessing approach for simplifying the NLDT is also suggested. The obtained results are inspiring as they suggest the replacement of complicated black-box DRL policies involving thousands of parameters (making them noninterpretable) with relatively simple interpretable policies. The results are encouraging and motivating to pursue further applications of proposed approach in solving more complex control tasks.

A nonlinear optimal control approach for unmanned surface vessels

A nonlinear optimal control approach for unmanned surface vessels

Surface profile measurement using nonlinear optimization approach in diffraction phase microscopy

Nanoscale measurement of surface profile has important application in the field of non-destructive surface testing and evaluation. We propose a nonlinear optimization based phase retrieval approach in diffraction phase microscopy for nanoscale surface profile measurement. The proposed approach relies on minimizing an objective function derived from the interferogram signal and the application of total variation regularization. The performance of the method is demonstrated via numerical simulations for processing interferograms affected by sharp phase variations, noise and non-uniform amplitude fluctuations. In addition, the practical application of the method is validated for nanoscale surface topography by processing experimental interferograms obtained in diffraction phase microscopy.

Tailored Dispersion and Nonlinear Effects in Flint Glass Honeycomb PCF for Optical Communication

This paper describes a highly nonlinear flint glass-based honeycomb photonic crystal fiber (FGH-PCF) with a wavelength of 1550 nm. The PCF’s distinctive honeycomb lattice structure, combined with the nonlinear capabilities of flint glass, enables a wide range of nonlinear optical applications. To adjust the PCF's dispersion and nonlinear effects, numerical simulations and optimization approaches were used. To achieve maximum performance, fabrication procedures were carefully regulated. Dispersion values of −436.6 ps/(nm.km) for x polarization and −448.1 ps/(nm.km) for y polarization were verified by experimental characterization. The PCF displayed low confinement losses of 2.289 dB/cm (x polarization) and 4.935 dB/cm (y polarization), as well as birefringence of 2.202×10-3. The PCF measured 558.8 and 547.9 W-1 km-1 for x and y polarization, respectively, indicating a high nonlinear coefficient. The highly nonlinear FGH-PCF shows promising potential for nonlinear optical applications such as four-wave mixing, supercontinuum generation, frequency conversion, and parametric amplification. This research paves the way for compact and efficient nonlinear devices in modern optical communication systems and other cutting-edge technologies.

A zeroing neural network model for form-finding problems: A nonlinear optimization approach

How to establish a simple and efficient nonlinear optimization problem form-finding model in noise environments is the main concern of this paper, thereby, a sequential quadratic programming form-finding (SQP) approach via a noise-tolerant zeroing neural network (NTZNN) is presented to solve the proposed problem. First, the rank of force density matrix is selected as optimization objective due to its crucial physical property. In addition, linear relations between the force density vectors and force density matrix are selected as the constraint conditions, which can ensure the tensegrity mechanism in a stable status. Furthermore, the simulations are shown that the presented SQP-NTZNN algorithm has superiority with anti-noise performance and computation efficiency, which by comparing the computational rate in the same noise environment with the novel form-finding algorithm. Eventually, the form-finding simulations under different initial conditions are formed to verify the importance of the constrained conditions, it can prove the high efficiency of the proposed nonlinear constrained optimization model which is transformed from the form-finding problem.

A robust state-dependent Riccati equation controller with parameter uncertainty and matched disturbance

The state-dependent Riccati equation (SDRE) unveils a nonlinear optimal control approach; the method is sensitive to uncertainty and disturbance that provokes the necessity of precise modeling and omitting disturbance from the model and environment which is occasionally impossible. In this paper, a robust state-dependent Riccati equation is introduced using only the pure SDRE itself. Lyapunov’s second method for stability analysis is used to extract two tuning rules for weighting matrices of the robust approach for handling both matched disturbance and parametric uncertainty. A fourth-order differential equation is simulated to show the effectiveness of the suggested method and the results were compared with conventional SDRE. The robust version could handle the matched disturbance with a steady-state shift from the equilibrium point where the conventional SDRE failed. Additionally, a comparison and detailed analysis have been performed between the proposed design and sliding mode control.

Using the Orthogonal Conditional Nonlinear Optimal Perturbations Approach to Address the Uncertainties of Tropical Cyclone Track Forecasts Generated by the WRF Model

Abstract The orthogonal conditional nonlinear optimal perturbations (O-CNOPs) approach for measuring initial uncertainties is applied to the Weather Research and Forecasting (WRF) Model to provide skillful forecasts of tropical cyclone (TC) tracks. The hindcasts for 10 TCs selected from 2005 to 2020 show that the ensembles generated by the O-CNOPs have a greater probability of capturing the true TC tracks, and the corresponding ensemble forecasts significantly outperform the forecasts made by the singular vectors, bred vectors, and random perturbations in terms of both deterministic and probabilistic skills. In particular, for two unusual TCs, Megi (2010) and Tembin (2012), the ensembles generated by the O-CNOPs successfully reproduce the sharp northward-turning track in the former and the counterclockwise loop track in the latter, while the ensembles generated by the other methods fail to do so. Moreover, additional attempts are performed on the real-time forecasts of TCs In-Fa (2021) and Hinnamnor (2022), and it is shown that O-CNOPs are very useful for improving the accuracy of real-time TC track forecasts. Therefore, O-CNOPs, together with the WRF Model, could provide a new platform for the ensemble forecasting of TC tracks with much higher skill.

Nonlinear optimal control for permanent magnet synchronous spherical motors

PurposePermanent magnet synchronous spherical motors can have wide use in robotics and industrial automation. They enable three-DOF omnidirectional motion of their rotor. They are suitable for several applications, such as actuation in robotics, traction in electric vehicles and use in several automation systems. Unlike conventional synchronous motors, permanent magnet synchronous spherical motors consist of a fixed inner shell, which is the stator, and a rotating outer shell, which is the rotor. Their dynamic model is multivariable and strongly nonlinear. The treatment of the associated control problem is important.Design/methodology/approachIn this paper, the multivariable dynamic model of permanent magnet synchronous spherical motors is analysed, and a nonlinear optimal (H-infinity) control method is developed for it. Differential flatness properties are proven for the spherical motors’ state-space model. Next, the motors’ state-space description undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instance around a time-varying operating point, which is defined by the present value of the motors’ state vector and by the last sampled value of the control input vector. For the approximately linearized model of the permanent magnet synchronous spherical motors, a stabilizing H-infinity feedback controller is designed. To compute the controller’s gains, an algebraic Riccati equation has to be repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. Finally, the performance of the nonlinear optimal control method is compared against a flatness-based control approach implemented in successive loops.FindingsDue to the nonlinear and multivariable structure of the state-space model of spherical motors, the solution of the associated nonlinear control problem is a nontrivial task. In this paper, a novel nonlinear optimal (H-infinity) control approach is proposed for the dynamic model of permanent magnet synchronous spherical motors. The method is based on approximate linearization of the motor’s state-space model with the use of first-order Taylor series expansion and the computation of the associated Jacobian matrices. Furthermore, the paper has introduced a different solution to the nonlinear control problem of the permanent magnet synchronous spherical motor, which is based on flatness-based control implemented in successive loops.Research limitations/implicationsThe presented control approaches do not exhibit any limitations, but on the contrary, they have specific advantages. In comparison to global linearization-based control schemes (such as Lie-algebra-based control), they do not make use of complicated changes of state variables (diffeomorphisms) and transformations of the system's state-space description. The computed control inputs are applied directly to the initial nonlinear state-space model of the permanent magnet spherical motor without the intervention of inverse transformations and thus without coming against the risk of singularities.Practical implicationsThe motion control problem of spherical motors is nontrivial because of the complicated nonlinear and multivariable dynamics of these electric machines. So far, there have been several attempts to apply nonlinear feedback control to permanent magnet-synchronous spherical motors. However, due to the model’s complexity, few results exist about the associated nonlinear optimal control problem. The proposed nonlinear control methods for permanent magnet synchronous spherical motors make more efficient, precise and reliable the use of such motors in robotics, electric traction and several automation systems.Social implicationsThe treated research topic is central for robotic and industrial automation. Permanent magnet synchronous spherical motors are suitable for several applications, such as actuation in robotics, traction in electric vehicles and use in several automation systems. The solution of the control problem for the nonlinear dynamic model of permanent magnet synchronous spherical motors has many industrial applications and therefore contributes to economic growth and development.Originality/valueThe proposed nonlinear optimal control method is novel compared to past attempts to solve the optimal control problem for nonlinear dynamical systems. Unlike past approaches, in the new nonlinear optimal control method, linearization is performed around a temporary operating point, which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector and not at points that belong to the desirable trajectory (setpoints). Besides, the Riccati equation which is used for computing the feedback gains of the controller is new, and so is the global stability proof for this control method. Compared to nonlinear model predictive control, which is a popular approach for treating the optimal control problem in industry, the new nonlinear optimal (H-infinity) control scheme is of proven global stability, and the convergence of its iterative search for the optimum does not depend on initial conditions and trials with multiple sets of controller parameters. It is also noteworthy that the nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state dependent Riccati equations (SDRE). The SDRE approaches can be applied only to dynamical systems which can be transformed into the linear parameter varying form. Besides, the nonlinear optimal control method performs better than nonlinear optimal control schemes, which use approximation of the solution of the Hamilton–Jacobi–Bellman equation by Galerkin series expansions. Furthermore, the second control method proposed in this paper, which is flatness-based control in successive loops, is also novel and demonstrates substantial contribution to nonlinear control for robotics and industrial automation.

Real-world implementation and evaluation of a Model Predictive Control framework in an office space

In this work, Model Predictive Control (MPC) is experimentally implemented on a Heating, Ventilation and Air Conditioning (HVAC) system of a large-scale office space. As controller model, a physics-based Modelica building model is calibrated based on historic data pursuing an iterative, nonlinear optimization approach. For the calibration period with a horizon of seven weeks, the calibrated model exhibits a high model accuracy with a Root Mean Square Error (RMSE) of 0.49 °C between the measured and estimated room temperature. The MPC toolchain includes modules for state estimation and forecasts of disturbances quantities (such as outdoor temperature, solar radiation including calculation of the direct and diffuse fraction, supply temperatures and occupancy). The MPC execution comprises the operation of heating based on radiators and floor heating (via regulation of valve openings) as well as shading of three Venetian blind systems (via regulation of vertical position and slat inclination angle). The experiment is conducted during a heating period with a duration of three weeks from October 21 to November 11, 2022. The heating actuators are controlled considering their typical dynamics and take into account the night setback during unoccupied office periods. User acceptance of the automated shading control is included through additional cost function terms for the shading operation. The field test reveals the predictive control capabilities of the proposed MPC toolchain in a real-life scenario, demonstrating energy-efficient building operation and total average discomfort of 0.53 Kh/d. The MPC formulation provides flexibility regarding adjustability of the control towards energy efficiency, thermal comfort, daylight transmission and non-oscillating shading control. Finally, the disturbance forecast accuracies for outdoor temperature and the solar radiation quantities are evaluated and the MPC control performance is compared against a conventional control approach.

A nonlinear optimal control approach for autonomous reentry space vehicles

Nonlinear control for autonomous reentry space vehicles has been a topic of intensive research during the last years in the area of aerospace science and technology. The associated dynamic model is obtained by expressing position variables and orientation angles of the space vehicle in different coordinate frames, namely an earth-fixed, an earth rotating and a body fixed frame. In this article, a nonlinear optimal control approach is proposed for the dynamic model of reentry space vehicles. It is proven that the longitudinal motion dynamic model of reentry space vehicles is differentially flat and a flatness-based controller is designed about it. Next, in the nonlinear optimal control approach, the dynamic model of the reentry space vehicle undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the reentry space vehicle a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs and a minimum dispersion of energy.

A NON-LINEAR OPTIMISATION APPROACH TO IN-PIT HAUL ROAD DESIGN

Truck haul costs, as one of the predominant operational costs for mining and quarrying operations, are known to be heavily dependent on the design parameters of haul roads. Furthermore, in-pit haul road design parameters determine the pit limits and therefore, the potential feasibility of the mining operation. Thus, when in search of an optimal solution in terms of in-pit haul roads, one should primarily consider the location of the in-pit haul road, its design features and the deriving operational costs regarding extraction and haul costs. A suitable objective function in this case may be the undiscounted profit for the ultimate pit design. However, for each considered scenario, truck and excavator operational costs can be calculated using simulation techniques for better accuracy. Furthermore, finding an optimal solution requires the execution of a reliable and efficient algorithm, depending on the shape of the objective function. Hence, a non-linear optimisation approach was proposed in this paper for solving the in-pit haul road optimisation problem, based on a simulation of the materials allocation, which was used for calculating the objective function. Design parameters were assumed to be predetermined, while the only variable used for finding an optimal solution was the location of the in-pit haul road inside the pit contour. In addition, two 1-D algorithms were compared for finding the optimal solution (Search with accelerated step size and 1-D Simplex method). Furthermore, two regression models are proposed (Multiple Linear Regression – MLR and Non-Linear Regression - NLR), which could identify the more feasible region for the in-pit haul road location and reduce the number of iterations required for convergence.

Design optimization to minimize wake of wide-body transport aircraft

A cutting-edge sustainable airplane can improve performance and enhance profitability are the most significant future concerns for the aviation industry. This research aims to analyse and assess aircraft performance of mid-size transport aircraft through retrofit designs. An optimal design was employed using a non-linear optimization approach under two cases fuselage alone (case 1) and a combination of fuselage-wing-empennage (case 2). These two retrofit concepts were evaluated and compared with the baseline A310–200 aircraft. To compute the objective function for various cases, non-linear solver was used from MATLAB optimization tool box. Additionally, the parametric studies of aerodynamics, structural and operational performance analysis are carried out by using Advanced Aircraft Analysis (AAA) 5.0 software. Sensitivity analyses are performed to assess the overall effectiveness of the optimal design. The key findings of this paper obtained the following parameters as Maximum take-off Weight, empty weight, fuel weight, parasite drag coefficient, rate of climb, take-off distance and landing distance are improved by 0.36%, 26.02%, 10.12%, 4.48%, 27.24%, 13.13% and 9.2% respectively. At the end, the paper provides a clear statement on the managerial perceptions and future insights for the upcoming challenges towards sustainable design.

Numerical approach based on particle swarm technique for optimization of nonlinear buried pipeline on tensionless foundation

This work aims to contribute to the development of numerical approach for optimization of buried pipeline by using finite element (FE) method and particle swarm optimization (PSO), considering static analysis and material hardening. The buried pipeline is discretized by finite element approach, constituted by Euler-Bernoulli three nodes beam element, while the soil-structure interaction is modeled by Winker-type tensionless foundation. Moreover, the tensionless foundation is discretized by spring element in the numerical model. The material nonlinearity behavior is analyzed by Von Mises isotropic hardening model. In the numerical approach, this model is solved by stress increment procedure. Furthermore, the critical loading and optimum wall thickness, that leads to optimized condition, are determined using swarm techniques. The cost function is formulated using evaluated stress and target stress, more, the calculated error is minimized by using swarm techniques for single-variable and two-variable optimization. Several applications are carried out by considering several soil conditions, boundary conditions and loading types. As a novelty, the soil random stiffness is included in the numerical model, where the optimum wall thickness and critical loading are evaluated considering material nonlinearity. The performance of finite element particle swarm technique is also compared to finite element genetic algorithms technique. The results demonstrate the effectiveness of proposed numerical approach for nonlinear buried pipeline optimization.

Predictive control and coordination for energy community flexibility with electric vehicles, heat pumps and thermal energy storage

Electrification of private transportation and residential heating is a potential action to decrease significantly carbon emissions. However, the lack of coordination of such emerging loads can increase stress on the power distribution grid. To this end, this paper proposes a two-stage energy management strategy, to enhance the flexibility of energy communities. First, an optimization algorithm-based model predictive control (MPC) is developed for home energy management systems (HEMS) to schedule electric vehicles (EVs) for charging and discharging in cooperation with heat pump and thermal energy storages. The objective is to reduce electricity bills and EV battery degradation costs while maintaining thermal demand. Second, the predictive coordination based on the nonlinear AC optimal power flow approach is applied to enhance the grid flexibility under a community energy management system scheme. To validate the performance of the proposed method, we develop a co-simulation framework by implementing the optimization algorithm and simulation scenarios in a Python Environment and modelling the electricity grid in the PowerFactory-DIgSILENT, which are linked together. Extensive numerical simulations are carried out under the active demand response program-based hourly electricity pricing and different weather data in Sweden. The results show that the proposed method can reduce operating costs and enhance the energy flexibility of the energy community. Moreover, it can decrease the stress on the community power grid and prevent load-shedding events compared to the non-predictive coordinated method.

A nonlinear optimal control approach for multi-DOF redundant robotic manipulators

A nonlinear optimal (H-infinity) control approach is proposed for the dynamic model of multi-DOF redundant robotic manipulators. Because of the complicated kinematics and dynamics and the high dimensionality of the state-space model of such robots, the related control problem is of elevated difficulty. In the present article, a three-link planar robotic manipulator it considered. The article’s approach relies first on approximate linearization of the state-space model of the redundant robotic manipulator, according to first-order Taylor series expansion and the computation of the related Jacobian matrices. For the approximately linearized model of the manipulator, a stabilizing H-infinity feedback controller is designed. To compute the controller’s gains an algebraic Riccati equation is solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. The proposed control method retains the advantages of typical optimal control, that is fast and accurate tracking of the reference setpoints under moderate variations of the control inputs.