Robust Control Theory Research Articles

Smart Structures Innovations Using Robust Control Methods

This study’s goal is to utilize robust control theory to effectively mitigate structural oscillations in smart structures. While modeling the structures, two-dimensional finite elements are used to account for system uncertainty. Advanced control methods are used to completely reduce vibration. Complete vibration suppression is achieved using advanced control techniques. In comparison to traditional control approaches, Hinfinity techniques offer the benefit of being easily adaptable to issues with multivariate systems. It is challenging to simultaneously optimize robust performance and robust stabilization. One technique that approaches the goal of achieving robust performance in mitigating structural oscillations in smart structures is H-infinity control. H-infinity control empowers control designers by enabling them to utilize traditional loop-shaping techniques on the multi-variable frequency response. This approach enhances the robustness of the control system, allowing it to better handle uncertainties and disturbances while achieving desired performance objectives. By leveraging H-infinity control, control designers can effectively shape the system’s frequency response to enhance stability, tracking performance, disturbance rejection, and overall robustness.

Earthquake Control: An Emerging Application for Robust Control. Theory and Experimental Tests

This article addresses the possibility of using robust control theory for preventing earthquakes through fluid injections in the Earth’s crust. The designed robust controllers drive aseismically a fault system to a new equilibrium point of lower energy by tracking a slow reference signal. The control design is based on a reduced-order nonlinear model able to reproduce earthquake-like instabilities. Uncertainties related to the frictional and mechanical properties of the underlying physical process and external perturbations are considered. Two types of controllers are derived. The first one is based on the sliding-mode theory and leads to local finite-time convergence of the tracking error and rejection of Lipschitz w.r.t. time perturbations. The second controller is based on linear quadratic regulator (LQR) control and presents global exponential stability of the tracking error and rejection of Lipschitz w.r.t. state perturbations. Both the controllers generate a continuous control signal, attenuating the chattering effect in the case of the sliding-mode algorithms. The developed controllers are tested extensively and compared on the basis of numerical simulations and experiments in the laboratory. The present work opens new perspectives for the application of the robust nonlinear control theory to complex geosystems, earthquakes, and sustainable energy production.

Design of Intelligent Nonlinear H2/H∞ Robust Control Strategy of Diesel Generator-Based CPSOGSA Optimization Algorithm

In today’s human society, diesel generators (DGs) are widely applied in the human energy and electricity supply system due to its technical, operational, and economic advantages. This paper proposes an intelligent nonlinear H2/H∞ robust controller based on the chaos particle swarm gravity search optimization algorithm (CPSOGSA), which controls the speed and excitation of a DG. In this method, firstly, establish the nonlinear mathematical model of the DG, and then design the nonlinear H2/H∞ robust controller based on this. The direct feedback linearization and the H2/H∞ robust control theory are combined and applied. Based on the design of the integrated controller for DG speed and excitation, the system’s performance requirements are transformed into a standard robust H2/H∞ control problem. The parameters of the proposed solution controller are optimized by using the proposed CPSOGSA. The introduction of CPSOGSA completes the design of an intelligent nonlinear H2/H∞ robust controller for DG. The simulation is implemented in MATLAB/Simulink, and the results are compared with the PID control method. The obtained results prove that the proposed method can effectively improve the dynamic accuracy of the system and the ability to suppress disturbances and improve the stability of the system.

Course keeping control for very large ship using hyperbolic tangent function based on nonlinear decoration technique

To solve the problems of difficult course keeping, high energy output, and large wear of very large ships under different sea conditions, a robust controller combining the closed-loop gain shaping algorithm and nonlinear decoration is proposed in this paper. Firstly, a linear controller is designed by using the third-order closed-loop gain shaping algorithm and takes the hyperbolic tangent function as the nonlinear decoration of the controller output, and the robustness of the system is proved by H∞ robust control theory. Secondly, taking ‘Vale Brasil’, an ore carrier with a displacement of 400,000 tons, as the test plant. The nonlinear Nomoto model and nonlinear Norrbin model were established, which were compared with the control effect from the existing controller. Thirdly, simulation experiments were carried out under normal sea state and heavy sea state to prove the effectiveness. The results indicate that the proposed control strategy can achieve the required course faster, and enhances the smoothness of rudder angle actuation compared with the existing controller. It can maintain good control ability under different sea conditions. The proposed controller has the advantages of simple parameter adjustment, better robustness, less energy consumption, and reduced rudder angle. It is more in line with engineering practice and increases ship operation benefits.

Robust Optimal Investment Strategies with Exchange Rate Risk and Default Risk

The problem of robust optimal investment with exchange rate risk and default risk is studied. We assume that investors are ambiguity averse and they have access not only to the domestic market but also to the foreign market. The corresponding Hamilton–Jacobi–Bellman (HJB) equations are first obtained through the robust stochastic optimal control theory. Then, we discuss the optimal investment problems before and after default, and the value functions and optimal investment strategies are obtained. Finally, we find that the optimal investment strategies of pre-default are affected by the intensity of default and the credit spread, and the investors cannot hold defaultable bonds in the post-default case. Numerical results also show that the exchange rate risk, default risk and ambiguity aversion have a great effect on the optimal investment strategies.

Predefined-Performance-Based Full-Process Control for Ultra-Close and High-Precision Formation Flying

The prescribed performance robust control method for the leader/follower (L/F) formation is proposed in this paper to solve the problem of spacecraft formation flying (SFF) full-process control (FPC). The objective of FPC is to establish an ultra-close formation with the constraint of collision avoidance between two spacecraft, and then to maintain the formation configuration with high-precision accuracy in a period of time. The main contribution of this paper lies in the following three aspects. Firstly, the six-degree-of-freedom (DOF) error dynamics model of SFF is developed to describe the synchronization motion of the L/F system. Secondly, the prescribed performance bound that comprehensively considers transience and transient performance is designed, which is key for the realization of collision avoidance and high-precision accuracy requirements. Finally, combing prescribed performance control and robust control theories, based on the backstepping method, the predefined performance robust controller is designed, and the tracking errors are proven to converge to the predefined performance bounds in the presence of external disturbances by using the predefined performance robust controller. Illustrative simulations are performed to verify the proposed theoretical results.

Adaptive neural network vibration suppression control of flexible joints space manipulator based on H∞ theory

Considering the control problems caused by uncertainties such as inaccurate modeling, external disturbance and joint flexibility, a neural network control method based on H∞ is proposed. By establishing the dynamic model of the free-floating space robot with flexible joints, according to its dynamic characteristics, it is split into a slow subsystem model representing the rigid characteristics and a fast subsystem model representing the flexible characteristics. Based on the H∞ robust control theory, a robust controller based on neural network is designed to realize the decoupling control of the rigid dynamic model, The designed weight adaptive learning rate can ensure the online and real-time adjustment of parameters. Based on Lyapunov theory, it is proved that the designed controller can ensure that the L2 gain of the system is less than the given index. A feedback controller based on velocity differential is designed to compensate the angle error caused by joint flexibility. The experimental simulation results verify that the proposed control method is effective and has good engineering application value.

Practical Stabilization of Switched Affine Systems: Model and Data-Driven Conditions

An important trend about data-driven systems has recently emerged motivated for practical issues, that are the difficulties to identify a model of the plant. In this direction some recent results enhanced the robust control theory to get efficient and relevant solutions. To the best of or knowledge, the existing solutions are rather limited to the linear case, and only few addresses the stabilization of nonlinear systems, which still represents a major challenge. In this work, the objective is the design of switching control law for switched affine systems, ensuring that a neighborhood of a given operating point is stable. After proposing a model-based control design, we propose a systematic method to translate a model-based condition expressed using the framework of Linear Matrix Inequalities (LMI), into a data-driven condition. This is made possible thanks to a new formulation of the existing method from the recent literature on this topic. The method is then evaluated on an academic example.

Satellite Dynamics Toolbox Library: a tool to model multi-body space systems for robust control synthesis and analysis

The level of maturity reached by robust control theory techniques nowadays contributes to a considerable minimization of the development time of an end-to-end control design of a spacecraft system. The advantage offered by this framework is twofold: all system uncertainties can be included from the very beginning of the design process; the validation and Verification (V&V) process is improved by fast detection of worst-case configurations that could escape to a classical sample-based Monte Carlo simulation campaign. Before proceeding to the control synthesis and analysis, a proper uncertain plant model has to be available in order to push these techniques to their limits of performance. In this spirit, the Satellite Dynamics Toolbox Library (SDTlib) offers many features to model a spacecraft system in a multi-body fashion on SIMULINK. Parametric models can be easily built in a Linear Fractional Transformation (LFT) form by including uncertainties and varying parameters with minimal number of repetitions. Uncertain Linear Time Invariant (LTI) and uncertain Linear Parameter-Varying (LPV) controllers can then be synthesized and analyzed in a straightforward way. The authors present in this article a tutorial, that can be downloaded at https://nextcloud.isae. fr/index.php/s/XDfRfHntejHTmmp, to show how to deal with an end-to-end robust design of a spacecraft mission and to provide to researchers a benchmark to test their own algorithms.

Linear Matrix Inequality-Based Multivariable Controller Design for Boost Cascaded Charge-Pump-Based Double-Input DC–DC Converter

An analysis and controller design of double-input dc–dc converter (DIDDC) is introduced in this article. This converter is integrated with buck and boost converters at the front-end and a charge pump on the back-end. Salient features of this topology are as follows: (i) ripple content is low in source currents, (ii) both the dc sources are connected through an inductor, which gives rise to a smooth source current waveform, (iii) both the sources supply power to load either in standalone or simultaneously together, and (iv) two control–loops (one for source current regulation, while the second one for load voltage regulation) are sufficient enough to ensure power transfer/management from dc sources to load. To ensure power management on the input dc sources while keeping a stable closed-loop converter system, a multivariable diagonal controller is designed. The first diagonal controller performs the load voltage regulation task, while the second controller regulates input of source-2 dc current. From the control point of view, the double-input single-output converter becomes a two-input two-output control problem and exhibits control–loop interactions due to the power flow from two different sources to load through common elements. The impact of off-diagonal elements’ interactions is accounted by using decouplers. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> robust control theory and linear matrix inequality (LMI) principles are adopted to design reliable controllers. The structured controller of fixed order (PID) is designed by enforcing the necessary type LMIs. To demonstrate the feasibility and effectiveness of multivariable controllers of the DIDDC, a 60/24 V to 48 V, 150 W, 50 kHz topology prototype is constructed, and the power management aspects are investigated experimentally. Load voltage regulation, source current regulation, load sharing on the input dc sources, and power management aspects of LMI-based controllers were tested extensively for all possible disturbances. In all these test cases, the closed-loop double-input converter system is stable and robust in rejecting a variety of disturbances created.

Deep Q‐learning: A robust control approach

AbstractThis work aims at constructing a bridge between robust control theory and reinforcement learning. Although, reinforcement learning has shown admirable results in complex control tasks, the agent's learning behavior is opaque. Meanwhile, system theory has several tools for analyzing and controlling dynamical systems. This article places deep Q‐learning is into a control‐oriented perspective to study its learning dynamics with well‐established techniques from robust control. An uncertain linear time‐invariant model is formulated by means of the neural tangent kernel to describe learning. This novel approach allows giving conditions for stability (convergence) of the learning and enables the analysis of the agent's behavior in frequency‐domain. The control‐oriented approach makes it possible to formulate robust controllers that inject dynamical rewards as control input in the loss function to achieve better convergence properties. Three output‐feedback controllers are synthesized: gain scheduling , dynamical , and fixed‐structure controllers. Compared to traditional deep Q‐learning techniques, which involve several heuristics, setting up the learning agent with a control‐oriented tuning methodology is more transparent and has well‐established literature. The proposed approach does not use a target network and randomized replay memory. The role of the target network is overtaken by the control input, which also exploits the temporal dependency of samples (opposed to a randomized memory buffer). Numerical simulations in different OpenAI Gym environments suggest that the controlled learning can converge faster and receive higher scores (depending on the environment) compared to the benchmark double deep Q‐learning.

The Total Low Frequency Oscillation Damping Method Based on Interline Power Flow Controller through Robust Control

The interline power flow controller (IPFC) can control the active power and reactive power of different lines in power system. To utilize the flexible control ability of IPFC and increase the damping characteristic of its controller AC system, this paper proposes a low-frequency oscillation (LFO) suppress method through IPFC. The LFO suppress method is designed by adding supplementary signals to the outer current control loop of IPFC. In addition to adding supplementary active power signals, the reactive supplementary signals are also added to related control loop, which is the total control scheme. To obtain the power system’s small signal model, the identification technology based on the PRONY algorithm is used. In addition, the robust control theory is also applied to make the controllers more adaptive. To verify the effectiveness of the proposed method, two controllers including both the active and reactive controllers are designed for in PSCAD software. Furthermore, the simulation results prove the proposed method can reach a better control effect and is also of robustness.

Automated Ground Vehicle Path-Following: A Robust Energy-to-Peak Control Approach

Due to the simultaneous existence of model uncertainties and external disturbances, designing automated ground vehicle path-following controllers is recognized as a challenging task. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> robust control methodology, as one of the accomplished strategies for controller robustification, has been commonly adopted by researchers to address the vehicle path-tracking problems. Nevertheless, despite its advantages, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> controller is only capable of limiting the total “energy” of the tracking errors. On the other hand, from a safety standpoint, constraining the “peak” of the tracking errors may carry an equal or more importance. To establish a guaranteed upper bound on the path-tracking errors, this paper proposes a novel methodology to synthesis the ground vehicle path-following controller in light of the energy-to-peak robust control theory. Additionally, to address the time-varying uncertainties presented in the tire dynamics, robust stabilization constraints based upon the small-gain theorem are also formulated into the overall controller design problem. Comparative study regarding the disturbance rejection performance between the proposed controller and the conventional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> approach is conducted via CarSim-Simulink joint simulations. Furthermore, the robustness and disturbance attenuation ability of the energy-to-peak path-tracking controller is experimentally verified on a scaled car.

A Gain-Scheduled Robust Controller for Autonomous Vehicles Path Tracking Based on LPV System With MPC and H ∞

Due to the uncertainty of vehicle model parameters, modeling errors and external disturbances, the performance of path tracking control system is poor, especially under high velocity and large curvature extreme conditions. To address this issue, this paper presents a novel gain-scheduled robust control strategy based on linear parameter varying system with model predictive control (MPC) and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> . Firstly, fully considering the influence of the time-varying characteristics of vehicle velocity and tire cornering stiffness on the path tracking system model, a novel linear parameter varying system model is built for path tracking control of autonomous vehicle. Then, a path tracking robust controller is designed based on gain-scheduled approach, and the linear matrix inequality (LMI) is applied to solve optimization problem, in which MPC and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> robust control theory are applied to the controller design process. Finally, the simulation experiments have verified that the proposed novel robust control strategy can improve the path tracking accuracy and ensure the vehicle lateral and roll stability, especially under high velocity and large curvature extreme conditions. Meanwhile, the proposed robust controller shows superiority to suppress the parameters uncertainty, modeling error and external disturbance.

Robustness analysis and training of recurrent neural networks using dissipativity theory

Abstract Neural networks are widely applied in control applications, yet providing safety guarantees for neural networks is challenging due to their highly nonlinear nature. We provide a comprehensive introduction to the analysis of recurrent neural networks (RNNs) using robust control and dissipativity theory. Specifically, we consider H 2 {\mathcal{H}_{2}} -performance and the ℓ 2 {\ell _{2}} -gain to quantify the robustness of dynamic RNNs with respect to input perturbations. First, we analyze the robustness of RNNs using the proposed robustness certificates and then, we present linear matrix inequality constraints to be used in training of RNNs to enforce robustness. Finally, we illustrate in a numerical example that the proposed approach enhances the robustness of RNNs.

The Unified Supplementary Damping Method Based on Voltage-Soured Converter High-Voltage Direct Current Transmission Through Robust Control

The VSC-HVDC system can damp the inter-area low-frequency oscillation effectively. To enhance the ability of the VSC-HVDC supplementary control, this article proposes a unified low-frequency oscillation controller design using the robustness theory. The unified control strategy uses both the active power control and reactive power control loop of the VSC to expand the supplementary control dimensions. To design the controller, the TLS-ESPRIT identification method is used to obtain the system small signal model and the oscillation characteristic. Based on the model identified out, the linear matrix inequality method based robust control theory is applied for the controller design, and the robust controllers for active power control and reactive power control loop are both designed to improve the control effect. Finally, the simulation results show that the controller can reach better control effect and the robustness can also be guaranteed.

Output-Based Event-Triggered Cooperative Robust Regulation for Constrained Heterogeneous Multiagent Systems.

The output-based event-triggered cooperative output regulation problem is addressed for constrained linear heterogeneous multiagent system in this article. In light of the robust control theory, H∞ leader-following consensus with respect to exogenous signals, including both disturbance to be rejected and reference state of leader to be tracked, is guaranteed. Meanwhile, the system performance alleviates degradation through a model recovery anti-windup technique while encountering input saturation. Furthermore, the follower's self-state observer, the leader-state observer, and the anti-windup auxiliary system are integrated into a comprehensive system, and a unified event-triggering mechanism of full states is addressed. A fixed lower bound of sampled interval is adopted such that the frequency of data transmission gets reduced and no Zeno-behavior happens. Both the input and output of the follower's controller and anti-windup compensator hold constant, respectively, during the event-triggered intervals such that the resulting output-based event-triggered controller can be directly implemented in a digital platform. Finally, a simulation example is provided to illustrate the effectiveness.

Optimized Takagi–Sugeno Fuzzy Mixed H2/H∞ Robust Controller Design Based on CPSOGSA Optimization Algorithm for Hydraulic Turbine Governing System

The hydraulic turbine governing system (HTGS) is a complex nonlinear system that regulates the rotational speed and power of a hydro-generator set. In this work, an incremental form of an HTGS nonlinear model was established and the Takagi–Sugeno (T-S) fuzzy linearization and mixed H2/H∞ robust control theory was applied to the design of an HTGS controller. A T-S fuzzy H2/H∞ controller for an HTGS based on modified hybrid particle swarm optimization and gravitational search algorithm integrated with chaotic maps (CPSOGSA) is proposed in this paper. The T-S fuzzy model of an HTGS that integrates multiple-state space equations was established by linearizing numerous equilibrium points. The linear matrix inequality (LMI) toolbox in MATLAB was used to solve the mixed H2/H∞ feedback coefficients using the CPSOGSA intelligent algorithm to optimize the weighting matrix in the process so that each mixed H2/H∞ feedback coefficients in the fuzzy control were optimized under the constraints to improve the performance of the controller. The simulation results show that this method allows the HTGS to perform well in suppressing system frequency deviations. In addition, the robustness of the method to system parameter variations is also verified.

Risk-averse autonomous systems: A brief history and recent developments from the perspective of optimal control

We present an historical overview about the connections between the analysis of risk and the control of autonomous systems. We offer two main contributions. Our first contribution is to propose three overlapping paradigms to classify the vast body of literature: the worst-case, risk-neutral, and risk-averse paradigms. We consider an appropriate assessment for the risk of an autonomous system to depend on the application at hand. In contrast, it is typical to assess risk using an expectation, variance, or probability alone. Our second contribution is to unify the concepts of risk and autonomous systems. We achieve this by connecting approaches for quantifying and optimizing the risk that arises from a system's behavior across academic fields. The survey is highly multidisciplinary. We include research from the communities of reinforcement learning, stochastic and robust control theory, operations research, and formal verification. We describe both model-based and model-free methods, with emphasis on the former. Lastly, we highlight fruitful areas for further research. A key direction is to blend risk-averse model-based and model-free methods to enhance the real-time adaptive capabilities of systems to improve human and environmental welfare.

Robust observable control of open and closed quantum systems

In recent work, we introduced the asymptotic theory of quantum robust control, which enables control of moments of quantum observables and gates in the presence of Hamiltonian uncertainty or field noise. In this paper, we extend this theory of quantum robust control to encompass two of the most important generalizations: robust control of arbitrary quantum observables and robust control of quantum systems sustaining environmental decoherence. In addition, we present deterministic Pareto optimization algorithms that can be applied in conjunction with either asymptotic or leading order measures of robustness. This enables robust control of any observable in quantum systems with any initial density matrix, and for which the entropy can change arbitrarily during the time evolution. Methods for robust optimal control of open quantum systems are presented that maximize the expected value of a quantum control objective while minimizing the expected environmentally induced decoherence.