Robust Optimal Control Research Articles

Qopt: An Experiment-Oriented Software Package for Qubit Simulation and Quantum Optimal Control

Realistic modeling of qubit systems including noise and constraints imposed by control hardware is required for performance prediction and control optimization of quantum processors. We introduce qopt, a software framework for simulating qubit dynamics and robust quantum optimal control considering common experimental situations. To this end, we model open and closed qubit systems with a focus on the simulation of realistic noise characteristics and experimental constraints. Specifically, the influence of noise can be calculated using Monte Carlo methods, effective master equations or with the efficient filter function formalism, which enables the investigation and mitigation of autocorrelated noise. In addition, limitations of control electronics, including finite bandwidth effects as well as nonlinear transfer functions and drive-dependent noise, can be considered. The calculation of gradients based on analytic results is implemented to facilitate the efficient optimization of control pulses. The software easily interfaces with QuTiP, is published under an open-source license, is well tested, and features a detailed documentation.

Robust Optimal Control Design for Performance Enhancement of PWM Voltage Source Inverter.

PWM (pulse-width modulation) voltage source inverters are used in a wide range of AC power systems where the output voltage must be controlled to follow a sinusoidal reference waveform. In order to achieve precision and fast-tracking control, restrictive sliding mode control (RSMC) provides a fast system state convergence time. However, the RSMC still suffers from the chattering problem, which leads to high harmonic distortion and slow response of the inverter output state. Furthermore, the load of the inverter may be severe load changing and the control parameters become difficult to adjust, worsening the adaptability to achieve the desired control of the inverter output. In this paper, a robust optimal control design comprised of an enhanced restrictive sliding mode control (ERSMC) and density particle swarm optimization (DPSO) algorithm is proposed, and then applied to PWM voltage source inverters. The ERSMC not only has finite time convergence but also provides chatter elimination. The DPSO is highly adaptable for acquiring the control parameters of the ERSMC and finding the best solution in the global domain. The proposed controller is realized for the actual PWM voltage source inverter controlled by a TI DSP-based development platform, so that the inverter output voltage has fast dynamic response and satisfactory steady-state behavior despite high load changing and non-linear disturbances.

Fundamental Framework to Plan 4D Robust Descent Trajectories for Uncertainties in Weather Prediction

Aircraft trajectory planning is affected by various uncertainties. Among them, those in weather prediction have a large impact on the aircraft dynamics. Trajectory planning that assumes a deterministic weather scenario can cause significant performance degradation and constraint violation if the actual weather conditions are significantly different from the assumed ones. The present study proposes a fundamental framework to plan four-dimensional optimal descent trajectories that are robust against uncertainties in weather-prediction data. To model the nature of the uncertainties, we utilize the Global Ensemble Forecast System, which provides a set of weather scenarios, also referred to as members. A robust trajectory planning problem is constructed based on the robust optimal control theory, which simultaneously considers a set of trajectories for each of the weather scenarios while minimizing the expected value of the overall operational costs. We validate the proposed planning algorithm with a numerical simulation, assuming an arrival route to Leipzig/Halle Airport in Germany. Comparison between the robust and the inappropriately-controlled trajectories shows the proposed robust planning strategy can prevent deteriorated costs and infeasible trajectories that violate operational constraints. The simulation results also confirm that the planning can deal with a wide range of cost-index and required-time-of-arrival settings, which help the operators to determine the best values for these parameters. The framework we propose is in a generic form, and therefore it can be applied to a wide range of scenario settings.

Optimal robust control with cooperative game theory for lower limb exoskeleton robot

For achieving trajectory tracking issue of the lower limb exoskeleton robot, a novel optimal robust control with cooperative game theory is proposed. The uncertainties are considered (possible time-varying, bounded and fast), and the fuzzy set theory is creatively adopted to describe the boundary. From the view of analytical mechanics, the trajectory tracking is treated as the constraints control problem, including holonomic and nonholonomic constraints, which need to satisfy the conditions of human motion. Combining the robust control and optimal design, optimal robust control is formulated to satisfy both performances guaranteeing and optimal. The Pareto optimal solution is obtained to guarantee the minimum control cost. In the simulation, the adaptive robust control is chosen as a comparison. The existence of Pareto optimality and the effectiveness of optimal robust control have been verified via simulation results.

Robust bi-objective optimal control of tungiasis diseases

Tungiasis, a neglected seasonal disease, leads to long-term injury and life threats to humans in developing countries. In this paper, we investigate the optimal control of tungiasis disease with an uncertain parameter, where both epidemic prevention and economic concerns are considered. Based on the life cycle of jiggers and propagation process of the disease, a human-jigger parasite model with control schemes for humans and jiggers is established. The effect of controls on the control reproduction number is discussed. A robust bi-objective optimal control problem is proposed, in which the accumulated number of infected humans and control cost, and their sensitivities to the uncertain parameter are all in the vector objective. Since the objective vector contains non-standard sensitivity terms, it is difficult to solve this problem using conventional optimization techniques. By introducing an auxiliary initial value system, we transform this problem into a standard form. Furthermore, a numerical method which combines a modified normal boundary intersection scheme with the interior point scheme is constructed. Finally, numerical simulations for different seasons are carried out using actual data of humans and jiggers in Nigeria. From all results, we conclude that enhancing the jigger adulticiding effort can significantly reduce the control reproduction number; the intervention control measures should be carried out in time, especially in the dry season; the obtained Pareto points can provide decision-makers with a trade-off between the two goals and choose an appropriate policy to implement.

State estimation-based robust optimal control of influenza epidemics in an interactive human society

This paper presents a state estimation-based robust optimal control strategy for influenza epidemics in an interactive human society in the presence of modeling uncertainties. Interactive society is influenced by random entrance of individuals from other human societies whose effects can be modeled as a non-Gaussian noise. Since only the number of exposed and infected humans can be measured, the states of the influenza epidemics are first estimated by an extended maximum correntropy Kalman filter (EMCKF) to provide a robust state estimation in the presence of the non-Gaussian noise. An online quadratic program (QP) optimization is then synthesized subject to a robust control Lyapunov function (RCLF) to minimize susceptible and infected humans, while minimizing and bounding the rates of vaccination and antiviral treatment. The main contribution of this work is twofold. First, the joint QP-RCLF-EMCKF strategy meets multiple design specifications such as state estimation, tracking, pointwise control optimality, and robustness to parameter uncertainty and state estimation errors that have not been achieved simultaneously in previous studies. Second, the uniform ultimate boundedness (UUB)/convergence of all error trajectories is guaranteed by using a Lyapunov stability argument. Simulation results show that the proposed approach achieves appropriate tracking and state estimation performance with good robustness.

Fuzzy approach‐based optimal robust control for permanent magnet synchronous motor with experimental validation

AbstractThis paper presents an optimal robust control for a permanent magnet synchronous motor (PMSM) with uncertainties and external disturbances which can be described by fuzzy approach. The fuzzy approach based on fuzzy set theory is distinguish from probability theory or fuzzy logic theory. Firstly, a dynamical model of the PMSM with uncertainties is established using a fuzzy approach. Then, a robust controller with an optimizable parameter is designed for PMSM to handle the uncertainties. The stability of the proposed control is proven using the Lyapunov theory. Furthermore, the controller gain is optimized by minimizing performance index, which contains the control performance and cost. Finally, the numerical simulations and experimental results are presented to validate the effectiveness of the proposed control with an optimal parameter.

Dual Beetle Antennae Search system for optimal planning and robust control of 5-link biped robots

In this paper, we presented an optimization-based control framework for the trajectory planning and the stable control of multiple non-linear systems, i.e., 5-link Biped Robot, inverted pendulum, and acrobot using the BAS (Beetle Antennae Search) algorithm with PID (Proportional–Integral–Derivative) controller. Traditional approaches treat path planning and stable control of the system as a separate problem, or multiple controls are employed to achieve both goals. Therefore, these approaches are complex, computationally, and time-wise expensive. The addition of disturbance to the system makes the control further intricate. In this paper, we proposed an optimization-based approach for the path planning and stable control of the non-linear systems by employing a hybrid controller, which includes BAS and PID. We devised a switching mechanism, where BAS will first perform the trajectory optimization through feedforward control. In the second phase, a disturbance is introduced in the system, and BAS is used to optimize the K values of PID for the control stability. In the simulation, we applied this technique on three non-linear systems, i.e., 5-link Biped Robot, inverted pendulum, and acrobot, and promising results are obtained. In addition we performed a comparison of dual Beetle Antennae Search algorithm with known swarm algorithms, i.e. PSO (Particle Swarm Optimization) and GA (Genetic Algorithm). The results showed that BAS and PSO are comparable. For example, in inverted pendulum the objective function converges to 7.566×10−4 and 0.029 by BAS and PSO respectively. Likewise, in 5-link Biped Robot the objective function converges to 0.0250 and 0.0351 by BAS and PSO respectively. In addition, the number of function evaluations in case of BAS increases linearly, i.e., 3 times of the iterations. However, the function evaluations increase exponentially in case of PSO and GA.

Variable gain gradient descent-based reinforcement learning for robust optimal tracking control of uncertain nonlinear system with input constraints

In recent times, a variety of reinforcement learning (RL) algorithms have been proposed for optimal tracking problem of continuous time nonlinear systems with input constraints. Most of these algorithms are based on the notion of uniform ultimate boundedness (UUB) stability, in which normally higher learning rates are avoided in order to restrict oscillations in state error to smaller values. However, this comes at the cost of higher convergence time of critic neural network weights. This paper addresses that problem by proposing a novel tuning law containing a variable gain gradient descent for critic neural network that can adjust the learning rate based on Hamilton–Jacobi–Bellman (HJB) approximation error. By allowing high learning rate the proposed variable gain gradient descent tuning law could improve the convergence time of critic neural network weights. Simultaneously, it also results in tighter residual set, on which trajectories of augmented system converge to, leading to smaller oscillations in state error. A tighter bound for UUB stability of the proposed update mechanism is proved. Numerical studies are then furnished to validate the variable gain gradient descent-based update law presented in this paper on a continuous time nonlinear system.

Robust adaptive PI control of wave energy converters with uncertain dynamics

There exist several approaches to design the optimal control strategy to harvest wave energy with a point absorber. However they are generally based on the assumption that the WEC and the PTO dynamics are well-known. In the practical WEC control implementation, this is generally not the case. The objective of this paper is to design a robust optimal control strategy that can take into account the uncertain WEC and PTO dynamics. Our choice is a robust adaptive PI control law. The proposed controller is validated and compared through simulation for irregular sea states.

Grey relation analysis of natural frequency and semi-active robust optimal control of a multi-dimensional isolator based on parallel mechanism and magneto-rheological damper

For isolating multi-dimensional vibrations experienced by precise facilities carried on a vehicle, a novel isolator is proposed based on 2-RPC/2-SPC parallel mechanism with magneto-rheological dampers. Kinematics and dynamics of the isolator are analyzed by geometrics and the Lagrange method. Grey relation analysis approach is conducted to determine the contributions of geometric parameters on natural frequency conveniently. Through analysis, the first order natural frequency of the isolator is affected by the length of the fixed platform most significantly. Due to manufacturing and assembling errors which could not be avoided in the isolator, robust optimal control algorithm is conducted to ensure control effect and robustness of the isolator at the same time. The gain of robust optimal control algorithm is obtained by deducing and solving linear matrix inequality. Compared to passive control, velocity root mean square values of robust optimal semi-active control decreased obviously in horizontal, longitudinal, vertical, and roll directions.

Empowering Optimal Control with Machine Learning: A Perspective from Model Predictive Control

Solving complex optimal control problems have confronted computational challenges for a long time. Recent advances in machine learning have provided us with new opportunities to address these challenges. This paper takes model predictive control, a popular optimal control method, as the primary example to survey recent progress that leverages machine learning techniques to empower optimal control solvers. We also discuss some of the main challenges encountered when applying machine learning to develop more robust optimal control algorithms.

A Fully Distributed Robust Optimal Control Approach for Air-Conditioning Systems Considering Uncertainties of Communication Link in Iot-Enabled Building Automation Systems

A Fully Distributed Robust Optimal Control Approach for Air-Conditioning Systems Considering Uncertainties of Communication Link in Iot-Enabled Building Automation Systems

Robust Optimal Control of Connected Automated Vehicles Considering Dynamic Platoon Size in Mixed Traffic Environment

Robust Optimal Control of Connected Automated Vehicles Considering Dynamic Platoon Size in Mixed Traffic Environment

Data-Driven Distributionally Robust MPC for Constrained Stochastic Systems

In this letter we introduce a novel approach to distributionally robust optimal control that supports online learning of the ambiguity set, while guaranteeing recursive feasibility. We introduce conic representable risk, which is useful to derive tractable reformulations of distributionally robust optimization problems. Specifically, to illustrate the techniques introduced, we utilize risk measures constructed based on data-driven ambiguity sets, constraining the second moment of the random disturbance. In the optimal control setting, such moment-based risk measures lead to tractable optimal controllers when combined with affine disturbance feedback. Assumptions on the constraints are given that guarantee recursive feasibility. The resulting control scheme acts as a robust controller when little data is available and converges to the certainty equivalent controller when a large sample count implies high confidence in the estimated second moment. This is illustrated in a numerical experiment.

Active Vibration Control of Railway Vehicle Car Body by Secondary Suspension Actuators and Piezoelectric Actuators

Active vibration suppression of high-speed electric multiple unit (EMU) car bodies was studied by the combined use of secondary suspension actuators and piezoelectric actuators. A vertical dynamics model was established considering secondary suspension actuators and piezoelectric actuators. The positions of the piezoelectric actuators and sensors were optimized using <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">2</sub> 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> norms. The feedback controller was designed using a robust optimal control method. The effects of the vibration devices and active control methods on the vehicle dynamic performance were simulated using MATLAB. The dynamic performance differences among the passive suspension vehicle, secondary vertical actuator installation vehicle, and active vibration control vehicle were compared and analyzed. The results show that the piezoelectric actuators and piezoelectric sensors were arranged at distances of 7.15, 12.25, and 17.35 meters from the left end of the car body, and the normalized <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">2</sub> 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> norms of the first and second order elastic modes of the car body were the largest, which can be used as piezoelectric actuators and sensor placement positions. Secondary suspension actuators can reduce rigid car body vibrations, and piezoelectric actuators can reduce elastic vibration. The higher the speed, the better is the acceleration suspension effect. When the vehicle speeds were 200 km∙h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> and 350 km∙h <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> , the vehicle vibration acceleration decreased by 10% and 18%, respectively. Compared with the passive suspension system, the active vibration suspension system with a robust controller can reduce the rigid and elastic vibrations of the vehicle and improve ride comfort.

Optimal Robust Control Based on Partial Derivative Plant Approximation for Frequency Support Using Multiple DC Microgrids

In this paper, an uncertainty-based optimal control framework is proposed for the Hybrid Energy Storage System (HESS) which allows for improved frequency regulation of a distributed micro-grid. The control architecture updates the penalty factor of the controller quality function automatically and provides policy to the HESS which consists of battery and ultra-capacitor banks. The HESS supports a Photo-Voltaic Distributed Energy Resource (PVDER) during grid dynamics in the presence of frequency oscillations by managing the DC link voltage. The penalty factor update is based on the sensitivity of the battery and ultra-capacitor power contribution to the frequency change and is dynamically changing. These changing gains and penalty factors optimize the HESS output. The approach is generalized by making it compliant for extensions that include assimilation of affine, stochastic, linear time-variant, and trajectory following non-linear systems. A modified IEEE 123 bus distribution system is used as a test system to validate the proposed architecture and provide a quantitative comparison with the conventional frequency-droop approach. It has been observed that the proposed architecture provides around 50\% improvement frequency regulation when compared to optimal control.

Robust Optimal Design and Control of a Maneuvering Morphing Airfoil

This paper presents a new approach to optimizing the design of a morphing airfoil for an unmanned aerial vehicle (UAV) by accounting for the range of possible flight trajectories that the UAV is required to be able to fly. A morphing mechanism and control system for the airfoil are simultaneously optimized to maximize how well the UAV can follow different flight trajectories. To solve the resulting concurrent optimization problem, a new solution approach incorporating robust optimization (a method for optimization under uncertainty) is proposed, which accounts for a continuous range of possible flight trajectories. This method determines the set of “worst-case” trajectories and finds a design that is optimal under them (thus ensuring better performance under any other trajectory). Results are presented comparing the robust design found using the proposed approach against designs that have only been optimized for one specific trajectory. The results show the robust design found using the proposed approach has significantly better performance over the set of worst-case trajectories than designs optimized for a single flight trajectory, guaranteeing a bound on its performance under any randomly sampled trajectory.

Enhanced Sliding Mode Control for a Nonlinear Active Suspension Full Car Model

This paper delivers findings on optimal robust control studies of nonlinear full car models. A nonlinear active suspension full car model is used, which considers the dynamic of a hydraulic actuator. The investigation on the benefit of using Sliding Mode Control (SMC) structure for the effective trade-off between road handling. The design of SMC in the chassis/internal subsystem is enhanced by modifying a sliding surface based on Proportional-Integral-Derivatives (PID) with the utilization of particle swarm optimization (PSO) algorithm in obtaining the best optimum value of control parameters. The switching control is designed through the Lyapunov function, which includes the boundedness of uncertainties in sprung masses that can guarantee the stability of the control design. The responses of the proposed controller have improved the disturbance rejection up to 60% as compared to the conventional SMC controller design and shown the high robustness to resist the effect of varying the parameter with minimal output deviations. The study proved that the proposed SMC scheme offers an overall effective performance in full car active suspension control to perform a better ride comfort as well as the road handling ability while maintaining a restriction of suspension travel. An intensive computer simulation (MATLAB Simulink) has been carried out to evaluate the effectiveness of the proposed control algorithm under various road surface conditions.

Robust optimal control of connected and automated vehicle platoons through improved particle swarm optimization

This paper addresses the robust optimal control problem for connected and automated vehicle platoons subject simultaneously to uncertain parasitic actuation lag and input delays. First, by adopting the constant time headway policy (CTHP) for spacing, the intervehicular spacing error propagation transfer function is derived between adjacent vehicles downstream under a decentralized control law. Second, the Hurwitz stability region for the derived spacing error propagation transfer function is obtained in a unified stability analysis framework for the time headway and controller gains by utilizing the signature conditions for real polynomials. The robust optimal control problem is formulated as a min–max optimization problem, and then an improved multi-agent based particle swarm optimization algorithm is developed to seek the optimal values of the design parameters in the derived stability region such that a weighted objective function is minimized. Finally, simulation experiments are performed on a numerical example to illustrate the effectiveness of the proposed design approach.