Robust Control Approach Research Articles

H-Infinity Control of a Six-Legged Robot in Lifting Mode

The present work aims at elaborating an efficient robust control approach of a six-legged robot in the lifting phase movement with the presence of nonlinearities, internal and external disturbances. A dynamic model of the legged robot is derived using the Newton-Euler formalism. Furthermore, an identification method is used to determine the system’s behavior by considering the joint variables at low, medium and high velocities. The variations between the obtained models in the different velocity margins are considered as nonlinearities and dynamic uncertainties, and are represented by the multiplicative uncertainty configuration. The H-infinity mixed-sensitivity method is applied in order to achieve a good performance and robust stability against external disturbances and the internal uncertainties represented by the unmodeled dynamics, the sensor noise, and the restrictions on the actuators control weight. In order to verify the capability of this controller to achieve the system stability and performances against the different disturbances, the small gain theorem method and robust stability and performance margin plots are used. The simulation results show that the control algorithm proposed in this paper can effectively achieve the robust stability and the hexapod robot performances.

A Robust Fault-Tolerant Predictive Control for Discrete-Time Linear Systems Subject to Sensor and Actuator Faults.

In this paper, a robust fault-tolerant model predictive control (RFTPC) approach is proposed for discrete-time linear systems subject to sensor and actuator faults, disturbances, and input constraints. In this approach, a virtual observer is first considered to improve the observation accuracy as well as reduce fault effects on the system. Then, a real observer is established based on the proposed virtual observer, since the performance of virtual observers is limited due to the presence of unmeasurable information in the system. Based on the estimated information obtained by the observers, a robust fault-tolerant model predictive control is synthesized and used to control discrete-time systems subject to sensor and actuator faults, disturbances, and input constraints. Additionally, an optimized cost function is employed in the RFTPC design to guarantee robust stability as well as the rejection of bounded disturbances for the discrete-time system with sensor and actuator faults. Furthermore, a linear matrix inequality (LMI) approach is used to propose sufficient stability conditions that ensure and guarantee the robust stability of the whole closed-loop system composed of the states and the estimation error of the system dynamics. As a result, the entire control problem is formulated as an LMI problem, and the gains of both observer and robust fault-tolerant model predictive controller are obtained by solving the linear matrix inequalities (LMIs). Finally, the efficiency of the proposed RFTPC controller is tested by simulating a numerical example where the simulation results demonstrate the applicability of the proposed method in dealing with linear systems subject to faults in both actuators and sensors.

A family of logarithmic hyperbolic cosine spline nonlinear adaptive filters

Spline nonlinear adaptive filters are well known for their ability to efficiently model nonlinear systems while having low computational complexity. However, the performance of traditional spline adaptive filter degrades in the presence of impulsive disturbances. For improving the performance of spline adaptive filters in impulsive noise scenarios, a logarithmic hyperbolic cosine spline adaptive filter is proposed in this paper. To improve the convergence rate while maintaining low steady-state error, a variable parameter approach for the logarithmic hyperbolic cosine spline adaptive filter is also proposed. In addition, a robust nonlinear active noise control approach is also designed based on the proposed logarithmic hyperbolic cosine spline adaptive filter. The computational complexity of the proposed algorithms is studied and two approximate versions of the logarithmic hyperbolic cosine spline adaptive filter are proposed to decrease computational cost without degrading performance. Bound on learning rates are also derived to ensure the stability of the proposed adaptive systems. The simulation studies conducted, demonstrate the enhanced performance achieved by the proposed algorithms.

Handling Stability Advancement With 4WS and DYC Coordinated Control: A Gain-Scheduled Robust Control Approach

This paper focuses on the stability control algorithm for four-wheel independent steering (4WIS) and four-wheel independent drive (4WID) electric vehicle (EV) with the coordinated control of four-wheel steering (4WS) and direct yaw-moment control (DYC) techniques. In order to design an adaptive gain-scheduled robust controller for stability control, linear parameter-varying (LPV) system and H∞ optimal control theory are applied. The polytopic model is proposed to build the LPV system for 4WIS-4WID EV. Taking structured uncertainties and sensor noise into consideration, gain-scheduled robust controller is designed and worked out using linear matrix inequality (LMI). To verify the performance of the adaptive gain-scheduled robust controller, fishhook maneuver and sinusoidal steering maneuver are carried out based on hardware-in-the-loop (HIL) tests. Test results indicate that the adaptive gain-scheduled robust controller can improve vehicle's handling stability especially in extreme conditions. Meanwhile, the designed controller shows strong robustness to suppress system parametric perturbation.

Robust constrained trajectory tracking control for a PVTOL aircraft subject to external disturbances

This paper addresses the trajectory tracking control problem of a planar vertical take-off and landing (PVTOL) aircraft in the presence of position constraints and external disturbances. A novel robust constrained control approach is proposed by incorporating the barrier Lyapunov function (BLF) and nonlinear damping items within the framework of dynamic surface control design. The dynamic surface control is used to avoid the ‘explosion of terms’ problem of the traditional backstepping control. The tan-type BLF is utilised to preserve the position tracking errors always within the predefined position constraints. The nonlinear damping items are applied to handle the effect of external disturbances. The uniform ultimate boundedness of the resulting closed-loop system is rigorously proved through the Lyapunov’s direct method. A distinct feature of the proposed control approach is that it is a general methodology for the trajectory tracking control of PVTOL aircraft with or without position constraints. Both theoretical analysis and numerical simulations illustrate the effectiveness and benefits of the proposed control approach.

A Novel Robust Control Method for Motion Control of Uncertain Single-Link Flexible-Joint Manipulator

Single-link flexible-joint manipulator (FJM) is a kind of time-varying nonlinear system with underactuated characteristics. This paper takes the uncertain single-link FJM (USLFJM) as the object, and presents a novel robust control approach based on equivalent input disturbance (EID) method for motion control (i.e., position control and trajectory tracking control) of the USLFJM. Based on the uncertain dynamic model and desired target of this system, an error system is constructed. The error system is considered as a linear system with a nonlinear virtual disturbance. The motion control objective of the USLFJM can be realized by globally asymptotically stabilizing this linear system and compensating the influence of the nonlinear virtual disturbance. Then, an EID-based control system is designed to realize this control objective. Only position measurements are utilized in this paper, and the stability of the control system is proved. The simulation results are presented to illustrate the validity and the robustness of the proposed control method.

Time-Varying Tube-Based Output Feedback Robust MPC for T–S Fuzzy Systems

For Takagi–Sugeno fuzzy systems subject to inexact membership functions, bounded disturbances, and noises, an output feedback robust model predictive control (RMPC) approach with time-varying robust tubes is investigated. The membership functions errors are bounded within convex sets via the properties of zonotopes and interval matrices. An offline table stores a series of structures that include nested robust positive invariant sets with the corresponding nominal feedback controller gains, ancillary controller gains, and observer gains. According to bounds of real-time estimation error sets, the time-varying structures in the offlined table are searched. Then, the output feedback RMPC problem with time-varying tightened constraints on inputs and states is optimized to stabilize the nominal system. The output feedback RMPC approach can not only update bounds of the estimation errors and uncertain terms resulting from inexact membership functions, but also reduce the computational burden. The proposed RMPC algorithm with recursive feasibility guarantees the robust stability of the controlled systems.

An Improved Robust Predictive Control Approach Based on Generalized 3rd Order S-PARAFAC Volterra Model Applied to a 2-DoF Helicopter System

This paper proposes a generalized robust predictive control approach based on 3rd order S-PARAFAC Volterra Model. The main idea is to use the predictive control law based on the latter model with taking into account the parameter and operation uncertainties resulting from the measurement noise and the robust identification technique named Unknown But Bounded Error (UBBE). One of the advantages is the convexity of the objective function with respect to the parameter uncertainty set. The min-max optimization problem becomes thus simpler, by minimizing the objective function in the worst-case only over the set of uncertain models. This work proposes a new generalized nonlinear robust control algorithm dedicated for uncertain processes. In this algorithm we optimize a quadratic criterion and take into account the physical and geometrical constraints due to parameter uncertainties. The performances of this work are illustrated and validated on a benchmark as a continuous stirred-tank reactor system (CSTR) and on an experimental 2-DoF helicopter system.

Robust self-tuning regressive adaptive controller design for a DC–DC BUCK converter

This paper demonstrates Robust Adaptive Control (RAC) approach using a technique for system identification applied to a Buck (step-down) converter by PWM (Pulse width modulation) in the presence of input voltage variations, load variations, parametric variations and high variance noises. Maintaining stability margins and closed-loop regulation within a pre-determined range of operating condition is the main objective behind designing feedback loops. The proposed control technique omits the need for mathematical model of the system by using a black-box identification procedure. Due to the various disturbing factors on a DC–DC converter, Minimum Degree Pole Placement (MDPP) scheme is proposed as an adaptive control technique, which is optimized with an Improved Exponential Regressive Least identification (IERLS) algorithm. Additionally, to hinder the impact and the uncertainty caused by high variance noise, a robust identification algorithm is introduced. Finally, capability of the proposed method is examined in different operating conditions through simulations and experimental results.

Relative Position Model Predictive Control of Double Cube Test-Masses Drag-Free Satellite with Extended Sliding Mode Observer

The drag-free satellites, being space-borne ultrahigh precise measurement platforms, have played irreplaceable roles in a great number of space science missions such as navigation, earth science, fundamental physics, and astrophysics. Most of these missions have to be performed based on the satellites placed with double cube test-masses, which makes the satellite layout and control strategy be more complex. This paper investigates the orbit keeping control problem of a class of low Earth orbit drag-free satellites with double cube test masses. A disturbance observer-based composite control method is proposed, which consists of an extended sliding mode observer and the tube-based robust model predictive control approach. In this design, the observer is proposed to estimate the relative position and velocity of the satellite and the external space disturbance force. A tube-based robust model predictive control scheme is then developed to stabilize the satellite orbit control systems in the presence of actuator saturation, state constraints, and additive stochastic noises. Finally, a simulation example is presented to demonstrate the efficacy and superiority of the proposed orbit control method.

Non-linear Control of Grid Tied Solar Photovoltaic System Considering Uncertainties

This work proposes a robust and efficient control approach for grid-connected solar photovoltaic (PV) systems considering non-linear and uncertain behaviour. The proposed controller is consisting of a super twisting algorithm-based second-order sliding mode control. The main objective to design this controller is to achieve maximum power transfer from the solar PV system in addition to control the DC link voltage and the current injected into the grid. Uncertainties in solar PV system output are considered as the input conditions changes. The proposed controller has been tested for various test cases and performance analysis carried out. The proposed system performs very well under transient conditions and gives very fast response. Performances of the proposed controller are also verified experimentally with the help of hardware implementation under different scenarios. The developed system performs accurately to meet the objective and as well as maintain the standards defined by IEEE.

Robust visual servoing control for quadrotors landing on a moving target

In this paper, a robust visual servoing control approach is proposed to address the landing problem for quadrotors on a moving platform. A vision system is implemented to estimate the position and velocity of the quadrotor. A robust cascade controller is proposed by following backstepping-like fundamentals and robust compensating theory. The effects of time-varying uncertainties, including parameter uncertainties and external disturbances, and time-varying delays resulted from image acquisition, image processing, and sensor measurement delays can be restrained. Experimental results using a quadrotor to land on a ground moving target illustrate the effectiveness of the proposed approach.

A robust optimal control approach in the weighted Sobolev space for underactuated mechanical systems

This paper proposes new robust nonlinear optimal control formulations in the weighted Sobolev space, here called nonlinear W2 and W∞ controllers, to handle with two classes of underactuated mechanical systems: the reduced ones with a reduced number of DOF; and the entire underactuated mechanical systems with input coupling. The optimal control problems are formulated via dynamic programming and particular solutions are presented for the resulting Hamilton–Jacobi equations with the corresponding stability analysis. Also, the concepts of Wm,p,σ-stability and Wm,p,σ-gain for a general class of systems are established, with the demonstration for the particular case of study. The novel W2 and W∞ controllers are synthesized for an unmanned aerial vehicle benchmark. The results demonstrate that these controllers provide better transient performance with faster response against external disturbances in comparison with a classic nonlinear H∞ controller, in addition to have a simple design.

Polynomial networks based adaptive attitude tracking control for NSVs with input constraints and stochastic noises

This paper proposes a backstepping technique and Multi-dimensional Taylor Polynomial Networks (MTPN) based adaptive attitude tracking control strategy for Near Space Vehicles (NSVs) subjected to input constraints and stochastic input noises. Firstly, considering the control input has stochastic noises, and the attitude motion dynamical model of the NSVs is actually modeled as the Multi-Input Multi-Output (MIMO) stochastic nonlinear system form. Furthermore, the MTPN is used to estimate the unknown system uncertainties, and an auxiliary system is designed to compensate the influence of the saturation control input. Then, by using backstepping method and the output of the auxiliary system, a MTPN-based robust adaptive attitude control approach is proposed for the NSVs with saturation input nonlinearity, stochastic input noises, and system uncertainties. Stochastic Lyapunov stability theory is utilized to analysis the stability in the sense of probability of the entire closed-loop system. Additionally, by selecting appropriate parameters, the tracking errors will converge to a small neighborhood with a tunable radius. Finally, the numerical simulation results of the NSVs attitude motion show the satisfactory flight control performance under the proposed tracking control strategy.

Nonlinear output path following control using a two-loop robust model predictive control approach

In this paper, output tracking of a geometric path for a nonlinear uncertain system with input and state constraints is considered. We propose an enhanced two-loop model predictive control approach for output tracking of a nonlinear uncertain system. Additionally, we propose an optimal version of output path following control problem to improve the controller synthesis. Satisfaction of the dynamical constraints of a system such as velocity, acceleration and jerk limitations is added to the problem introducing a new augmented system. The recursive feasibility of the proposed method is demonstrated, and its robust stability is guaranteed such that relaxation on the terminal constraint and penalty are achieved. To validate the theoretical benefits of the proposed controller, it is simulated on a SCARA robot manipulator and the results are compared with a two-loop model predictive controller successfully.

Doubly fed induction generators to enhance inter-area damping based on a Robust controller: {{varvec{H}}}_{2}/{{varvec{H}}}_{infty } Control

In this study, an auxiliary damping controller based on a robust controller considering the active and reactive power control loops for a doubly-fed induction generator for wind farms is proposed. The presented controller is able to improve the inter-area oscillation damping. In addition, the proposed controller applies only one accessible local signal as the input; however, it can improve the inter-area oscillation damping and, consequently the system stability for the various working conditions and uncertainties. The oscillatory modes of the system are appointed using the linear analysis. Then, the controller’s parameters are determined using the robust control approaches ({H}_{infty }/{H}_{2}) with the pole placement and linear matrix inequality method. The results of the modal analysis and time-domain simulations confirm that the controller develops the inter-area oscillation damping under the various working conditions and uncertainties.

A Robust Control Approach to Event-Triggered Networked Control Systems With Time-Varying Delays

A robust control approach is proposed to solve the asymptotic stabilization problem of networked control systems, where the data transmission is mediated by a triggering function, and is subject to time-varying transmission delays. We show that the triggering mechanism and the delay effects could be regarded as uncertain components interconnected with a stable linear time-invariant system. We then use two operators to describe the uncertainties, and find the corresponding integral quadratic constraints of the operators. The stability of the networked control system is analyzed from a robust control point of view. Beyond the stability analysis, a co-design algorithm is devised to design the control gain and detection parameters jointly to maximize the inter-event interval as well as the maximum allowable time-delay. Theoretically, the proposed scheme guarantees that out-of-order packet delivery does not happen. The robust control framework allows the algorithm developed for time-varying delays to be applied to the constant delay and the delay free cases. Finally, the theoretical results are demonstrated and verified by numerical simulations.

The Covid-19 Pandemic and its Impact on the Performance of Firms: An Analysis Based on World Bank Microdata

:This study analyzes the impact on the sales of firms during the outbreak of the COVID-19 pandemic, based on microdata made available by the World Bank through the Enterprise Surveys platform, when the Covid-19 Enterprise Survey Follow-Up was conducted. The study performed a comparison of two linear regression techniques: (1) ordinary least squares with dummy variables, better understanding the average effect of the regressors on the dependent variable and; (2) quantile regression, making it possible to better identify heterogeneous effects in the sample. Controlling potential effects of heteroscedasticity to the quantile regression model, a recent and more robust control approach was employed, through the contributions of Parente and Santos Silva (2016). The intra-cluster estimator allows to obtain non-biased estimates of standard error of the parameters, presenting a more reliable result in relation to the traditional approach of Koenker and Bassett (1978). The results suggest that factors such as access to credit, government subsidies, remote work and hiring temporary workers have heterogeneous effects between firms. Permanent and full-time employees had a greater impact on firms with lower sales growth, signaling a downward trend over conditional quantiles. Government subsidies had a decreasing effect, indicating greater impact on firms with less growth (significant in the 50% and 75% quantiles). Licensed workers affected negatively in all quantiles, but with a greater impact on growth in lower quantiles, that is, in firms with less growth (significant at 1%). The actions of governments promote a "deliberate disconnection" that inevitably results in a socioeconomic crisis, unprecedented in history. These "indirect" effects of the pandemic have already been duly documented in the financial market (TOPCU and GULAL 2020). Although expectations about the potential consequences of social isolation policies have been negatively reflected, other evidence points to positive results, depending on the behavior of the public authority, acting in a transparent manner. From this analyze, it is observed that the orientation of public policies to mitigate the adverse effects of the COVID-19 pandemic should not be guided in a uniform manner. This guidance allows better control of the adverse effects of the pandemic, aiming at a better allocation of resources and a greater return in terms of social well-being.

Policy Iteration and Event-Triggered Robust Adaptive Dynamic Programming for Large-Scale Systems

Abstract In this paper, an event-triggered robust optimal control approach is proposed for large-scale systems with both parametric and dynamic uncertainties through robust adaptive dynamic programming, policy iteration, and small-gain techniques. By using the input and output data, the unmeasurable states are reconstructed instead of constructing a Luenberger observer. Starting from an admissible control policy, an event-based feedback control policy is learned to save the communication resources and reduce the number of control updates. The closed-loop stability and the convergence of the proposed algorithm are analyzed by using Lyapunov and small-gain techniques. A practical example of multimachine power systems with governor controllers is given to demonstrate the effectiveness of the proposed method.

Robust Model Predictive Control for Takagi-Sugeno Model With Bounded Disturbances—Pólya Approach

This paper proposes a general robust model predictive control (MPC) approach for the constrained Takagi-Sugeno (T-S) fuzzy model with additive bounded disturbances. We adopt the homogeneous polynomially parameter-dependent (HPP) Lyapunov matrix with the arbitrary complexity degree and the corresponding HPP control law for the controller design. By applying the Polya’s theorem and the extended nonquadratic boundedness property, a systematic approach to construct a set of sufficient conditions for assessing robust stability described by parameter-dependent linear matrix inequalities (LMIs) is established. The proposed approach is an improvement over existing approaches in terms of control performance and stabilizable model range. Numerical examples are provided to show the effectiveness of the proposed robust MPC approach.