Robust Optimal Control Research Articles

Robust Optimal Consensus Control for Nonlinear Multi‐agent Systems: Two Hybrid Dynamic Event‐Triggered‐Based Approach

ABSTRACTIn this paper, the dynamic event‐triggered robust optimal consensus control problem is investigated for nonlinear multi‐agent systems (MASs) with matched and mismatched disturbances via integral sliding mode (ISM) control and the adaptive dynamic programming (ADP) algorithm. First, a dynamic event‐triggered fixed‐time ISM controller is designed to guarantee that the system state converges to the predefined ISM manifold, thereby eliminating the matched disturbances. Next, the consensus control problem is transformed into an optimal control problem by constructing neighborhood error dynamics and a new modified cost function; thus, an event‐triggered‐based coupled Hamilton‐Jacobi‐Bellman equation (HJBE) is established. Then, an ADP‐based single‐critic neural network (NN) is constructed to solve coupled HJBE to obtain the event‐triggered optimal controller, in which the NN weight is updated only at the triggering instants. Through the implementation of these two dynamic event‐triggered mechanisms, resources and controller execution time can be saved. It is proved that the whole closed‐loop system signals are uniformly ultimately bounded by the Lyapunov technique. Finally, two illustrative examples verify the effectiveness and superiority of the proposed control scheme.

Developing PDE-constrained optimal control of multicomponent contamination flows in porous media

This paper develops a robust and efficient PDE-constrained optimal control model for multicomponent pollutions in porous media, which takes into account nonlinear multi-component contamination flows of groundwater. The objective of the pollution optimal control is to identify the optimal injection rates from the top part boundary of domain, which can minimize the least squares error between the concentrations that are simulated and the allowable observed concentrations at observation sites, combining with the affection of costs associated with reducing emissions at injection locations. To discrete the constrained governing system of nonlinear multi-component flows, the splitting improved upwind finite difference scheme is developed for multicomponent PDEs system involving nonlinear chemical reactions of multicomponent pollutants and the pollutant injected rates on the upper part boundary. We employ the differential evolution (DE) optimization algorithm to solve the optimization. We numerically demonstrate the effectiveness of our model by analyzing the flow simulation on a simple geometric aquifer and identifying the optimal injection rates by minimizing the concentration derivation and the abatement costs. We also investigate the simulation of the contamination flow in a more realistic-shaped aquifer, which further validates our model's robustness and efficacy. The developed PDE-constrained control model and algorithm can be applied to applications of groundwater pollution control.

Optimal fuzzy robust state feedback control for a five DOF active suspension system

Active suspension systems are integral to modern vehicles, enhancing driving comfort by addressing road irregularities and isolating the vehicle's interior from vibrations. In this research, we construct an active suspension system with five degrees of freedom (DOF) and find the best fuzzy robust state feedback controller to control it. While designing the state feedback controller, we considered the initial errors in the relative displacement and acceleration as well as their derivatives. A singleton fuzzifier, center average russification, and product inference engine are all control parameters managed by a fuzzy system. Optimization using the Sine Cosine Algorithm (SCA) is then used to determine the optimal gains for the controller that has been constructed. The technique uses two objective functions for depreciation: the body's acceleration, the relative displacement between the tire and sprung mass. Results show that the suggested active suspension system is better than that of previous studies.

Optimal quantum controls robust against detuning error

Abstract Precise control of quantum systems is one of the most important milestones for achieving practical quantum technologies, such as computation, sensing, and communication. Several factors deteriorate the control precision and thus their suppression is strongly demanded. One of the dominant factors is systematic errors, which are caused by discord between an expected parameter in control and its actual value. Error-robust control sequences, known as composite pulses, have been invented in the field of nuclear magnetic resonance (NMR). These sequences mainly focus on the suppression of errors in one-qubit control. The one-qubit control, which is the most fundamental in a wide range of quantum technologies, often suffers from detuning error. As there are many possible control sequences robust against the detuning error, it will practically be important to find ‘optimal’ robust controls with respect to several cost functions such as time required for operation, and pulse-area during the operation, which corresponds to the energy necessary for control. In this paper, we utilize the Pontryagin’s maximum principle (PMP), a tool for solving optimization problems under inequality constraints, to solve the time and pulse-area optimization problems. We analytically obtain pulse-area optimal controls robust against the detuning error. Moreover, we found that short-CORPSE, which is the shortest known composite pulse so far, is a probable candidate of the time optimal solution according to the PMP. We evaluate the performance of the pulse-area optimal robust control and the short-CORPSE, comparing with that of the direct operation.

Efficient Online Planning and Robust Optimal Control for Nonholonomic Mobile Robot in Unstructured Environments

Efficient Online Planning and Robust Optimal Control for Nonholonomic Mobile Robot in Unstructured Environments

Robust optimal control for a systematic error in the control amplitude of transmon qubits

In the era of Noisy Intermediate-Scale Quantum computing as well as in error correcting circuits, physical qubits coherence time and high fidelity gates are essential to the functioning of quantum computers. In this paper, we demonstrate theoretically and experimentally, that pulses designed by optimization can be used to counteract the loss of fidelity due to a control amplitude error of the transmon qubit. We analyze the control landscape obtained by robust optimal control and find it to depend on the error range, namely the solutions can get trapped in the basin of attraction of sub-optimal solutions. Robust controls are found for different error values and are compared to an incoherent loss of fidelity mechanism due to a finite relaxation rate. The controls are tested on the IBMQ’s qubit and found to demonstrate resilience against significant ∼10% errors.

Robust–optimal control of electromagnetic levitation system with matched and unmatched uncertainties: experimental validation

Robust–optimal control of electromagnetic levitation system with matched and unmatched uncertainties: experimental validation

Neural Network-Based Robust Guaranteed Cost Control for Image-Based Visual Servoing of Quadrotor.

In this article, a neural network (NN)-based robust guaranteed cost control design is proposed for image-based visual servoing (IBVS) control of quadrotors. According to the dynamics of three subsystems (yaw, height, and lateral subsystems) derived from the quadrotor IBVS dynamic model, the main control design is to solve the robust control problem for the time-varying lateral subsystem with angle constraints and uncertain disturbances. Considering the system dynamics, a two-loop structure is conducted. The outer loop uses the linear quadratic regulator to solve the Riccati equation for the lateral image feature system, and the inner loop adopts the optimal robust guaranteed cost control to solve the lateral velocity system. For the lateral velocity system, the optimal robust control problem is transformed to solve the modified Hamilton-Jacobi-Bellman equation of the corresponding optimal control problem utilizing adaptive dynamic programming. The implementation is accomplished with the time-varying NN and the designed estimated weight update law. In addition, the stability and effectiveness are proved by the theoretic proof and simulations.

Frequency-Domain Tuning of a Robust Optimal 2-DOF Fractional Order PID Controller for a Maglev System

Frequency-Domain Tuning of a Robust Optimal 2-DOF Fractional Order PID Controller for a Maglev System

Robustness of optimal quantum annealing protocols

Abstract Noise in quantum computing devices poses a key challenge in their realization. In this paper, we study the robustness of optimal quantum annealing protocols against coherent control errors, which are multiplicative Hamlitonian errors causing detrimental effects on current quantum devices. We show that the norm of the Hamiltonian quantifies the robustness against these errors, motivating the introduction of an additional regularization term in the cost function. We analyze the optimality conditions of the resulting robust quantum optimal control problem based on Pontryagin’s maximum principle, showing that robust protocols admit larger smooth annealing sections. This suggests that quantum annealing admits improved robustness in comparison to bang-bang solutions such as the quantum approximate optimization algorithm. Finally, we perform numerical simulations to verify our analytical results and demonstrate the improved robustness of the proposed approach.

Design of a optimal robust adaptive neural network-based fractional-order PID controller for H-bridge single-phase inverter

Adaptive Neural Network- based Fractional-order PID Control (NN-FO-PID) approach is designed for H-bridge inverter. This inverter has an LC filter to decrease the level of Total Harmonic Distortion (THD) that can affect the efficiency of the system. In addition, the reduction of THD and stability insurance of the filter are challenging performances. To fulfill this function, a fractional order proportional integrated derivative (FO-PID) controller is developed for the inverter. A few merits of the Fractional-Order notion as a useful technique include reduced sensitivity to noise and parametric fluctuation; however, for a wider range of disturbances, such as noise, this approach shows an unsuitable practical application based on its fixed gain values. Moreover, having parameters uncertainties including parametric variations, load uncertainty, supply voltage variation uplifts this challenging condition severely, and the parameters need to be adjusted once more for more dependable operations. As a result, the control parameters must be optimized once more to provide ideal operations. Here, an adaptive mechanism is proposed based on neural network structure to optimize the gains of the FO-PID controller for better performances. In real applications, this approach has some benefits, since it uses the Black-box technique, which does not necessitate a precise mathematical model of the system, resulting in a reduced computational burden, simple implementation, and reduced dependence on the model’s states. Even under extremely difficult circumstances, the artificial neural network structure effectively optimizes the FO-PID gains in real-time. This benefit can reduce the amount of THD-level for the inverter, properly. Additionally, to have a proper response in the first step condition, and trying to reduce the level of dangerous conditions, based on benefits of the ant lion optimization method, it is considered to select the initial values of the FO-PID controller gains. Here to verify the superiority of the proposed controller, PID and FO-PID controllers are offered to drive a comparison with this method, which are optimized using the PSO optimization algorithm. The analysis of simulation data shows that the suggested control strategy is appropriate for maintaining stability as well as adequately compensating for disturbances and uncertainties in the inverter. Furthermore, with the help of this controller, THD level decreased lower than 2 percent.

Optimal robust adaptive fuzzy controllers based on sliding surfaces for inverted pendulum systems

Optimal robust adaptive fuzzy controllers based on sliding surfaces for inverted pendulum systems

Optimal robust online tracking control for space manipulator in task space using off-policy reinforcement learning

This study addresses the demands for adaptability, uncertainty management, and high performance in the control of space manipulators, and the inadequacies in achieving optimal control and handling external uncertainty in task space in previous research. Based on off-policy reinforcement learning, a model-free and time-efficient method for online robust tracking control in task space is devised. To address the complexity of dynamic equations in task space, a mixed-variable approach is adopted to transform the multivariable coupled time-varying problem into a single-variable problem. Subsequently, the optimal control policy is derived with the disturbance convergence, stability, and optimality of the control method being demonstrated. This marks the first instance of achieving robust optimal tracking control in task space for space manipulators. The efficacy and superiority of the presented algorithm are validated through simulation.

Robust adaptive optimal trajectory tracking control for underactuated AUVs with position and velocity constraints in three‐dimensional space

AbstractThe safety and optimality of underactuated autonomous underwater vehicles (AUVs) during operations are essential factors to consider. In this context, a three‐dimensional robust adaptive optimal trajectory tracking control method under position and velocity constraints, unknown dynamics, and environmental disturbances is proposed. The main features of the method are: (1) The outputs of an underactuated AUV system are redefined to handle the underactuation problem. (2) The system with position and velocity constraints is transformed into an unconstrained system by a nonlinear state‐dependent transformation. (3) A critic‐identifier architecture is constructed using adaptive dynamic programming and neural networks in a backstepping framework. Specifically, critic networks and weight update laws without requiring initial stability control are designed to solve Hamilton‐Jacobi‐Bellman equations in kinematic and dynamic subsystems, and optimal virtual and actual control laws are obtained. (4) A neural network identifier is developed to estimate unknown dynamics. Disturbances are overcome by improving the cost function and solving for optimal control of the nominal dynamic subsystem. By stability analysis, tracking errors in the AUV closed‐loop system can converge to an arbitrarily small compact set of the origin, and the other signals are uniformly ultimately bounded. Simulation comparisons demonstrate the effectiveness and superiority of the proposed method.

Optimal Nonlinear Robust Sliding Mode Control of an Excitation System Based on Mixed $\mathcal{H}_{2}/\mathcal{H}_{\infty}$ Linear Matrix Inequalities

Optimal Nonlinear Robust Sliding Mode Control of an Excitation System Based on Mixed $\mathcal{H}_{2}/\mathcal{H}_{\infty}$ Linear Matrix Inequalities

A two-stage distributed robust optimal control strategy for energy collaboration in multi-regional integrated energy systems based on cooperative game

In view of the weak energy supply stability of the single regional integrated energy system (RIES), the ability to deal with uncertainties is poor. To solve the problem of equilibrium optimization among system economy, robustness and efficiency, this paper interconnects multiple RIES with different resource to form multi-RIES through peer-to-peer energy trading. The control strategy of energy interactive operation involving multiple RIES is optimized. Using the uncertainty confidence set of renewable energy to depict the uncertainty on the source side, a two-stage distributed robust optimal control model for RIES based on data-driven is proposed, and the column and constraint generation (C&CG) algorithm is adopted to significantly improve the solution efficiency. Then, a multi-RIES cooperative game model with uncertain scenarios is proposed, and according to this model, a coupled C&CG-alternating direction multiplier method (ADMM) algorithm is proposed, which realizes the privacy protection of RIES and makes the system have good convergence performance. Finally, the case analysis proves that the strategy proposed in this paper can not only realize energy coordination and complementarity among multiple RIES, but also improve the stability of the system operation and significantly reduce the dependence of the system on the distribution network.

Robust distributed Nash equilibrium solution for multi‐agent differential graphical games

AbstractThis paper studies the differential graphical games for linear multi‐agent systems with modelling uncertainties. A robust optimal control policy that seeks the distributed Nash equilibrium solution and guarantees the leader‐following consensus is designed. The weighting matrices rely on modelling uncertainties, leading to the Nash equilibrium solution, and the solution can be obtained by solving a decoupled algebraic Riccati equation. Simulation studies are finally reported to illustrate the effectiveness of proposed policy.

Infinite-time robust optimal output tracking of continuous-time linear systems using undiscounted reinforcement learning

This research paper focuses on addressing the challenge of infinite-time linear quadratic tracking control (LQT) for linear systems with parametric uncertainty. Traditional solutions to the LQT problem often involve using a discount factor to prevent the cost function from growing unbounded over time. However, this approach can introduce instability in the closed-loop system. To overcome this issue, this paper proposes an alternative approach using an undiscounted cost function that ensures the asymptotic stability of the uncertain closed-loop system. To design a control scheme without requiring precise knowledge of the system dynamics, reinforcement learning (RL) algorithms are employed. However, for systems with uncertain parameters that may lead to instability, the convergence of RL algorithms to a stabilising solution is not guaranteed. To address this limitation, a robust optimal control structure is developed using on-policy and off-policy reinforcement learning algorithms, resulting in a model-free controller. The effectiveness of the proposed robust optimal controller is validated through comparative simulations on an uncertain model of a DC–DC buck converter connected to a constant power load. These simulations demonstrate the advantages and benefits of the robust optimal controller in handling parametric uncertainty and ensuring stability in the control system.

Robust optimal control for uncertain wheeled mobile robot based on reinforcement learning: ADP approach

This paper presents a robust optimal control approach for the wheel mobile robot system, which considers the effects of external disturbances, uncertainties, and wheel slipping. The proposed method utilizes an adaptive dynamic programming (ADP) technique in conjunction with a disturbance observer. Initially, the system's state space model is formulated through the utilization of kinematic and dynamic models. Subsequently, the ADP method is employed to establish an online adaptive optimal controller, which solely relies on a single neural network for the purpose of function approximation. The utilization of the disturbance observer in conjunction with the compensation controller serves to alleviate the effects of disturbances. The Lyapunov theorem establishes the stability of the complete closed-loop system and the convergence of the weights of the neural network. The proposed approach has been shown to be effective through simulation under the effect of the disturbances and the change of the desired trajectory.

Power Regulation of a Three-Phase L-Filtered Grid-Connected Inverter Considering Uncertain Grid Impedance Using Robust Control

Uncertain grid impedance is often common in power distribution networks; therefore, it is crucial to design an efficient controller in this situation. An issue that frequently occurs is the problem of unpredictable grid impedance, which can cause voltage fluctuations, power quality problems, and potential damage to equipment. This work provides a systematic control strategy to tackle these issues by supplying well-regulated power from a DC source to an AC power grid. A linear matrix inequality (LMI)-based robust optimal control is proposed in this paper to provide stability to the inverter system without offset error at the output side. The convergence time to steady state is minimized by solving the LMI problem to maximize the eigen value of the closed-loop system with the inclusion of the uncertainty of the filter parameter and grid impedance. Furthermore, the uncertainties in this study include the potential variation of values for the filters and the grid's impedance. These uncertainties occur because the grid impedance can fluctuate fast in the event of a fault or termination of a transmission line, while the filter's impedance can also be affected by changes in operating temperature. The simulation study of this proposed control includes a comparison between wide and narrow uncertainty ranges, as well as a performance comparison under uncertain parameters. Furthermore, this approach exhibits a lower power ripple in comparison to existing PI control method.