Robust Optimal Control Research Articles

Robust Constrained Multi-Objective Guidance of Supersonic Transport Landing Using Evolutionary Algorithm and Polynomial Chaos

Landing of supersonic transport (SST) suffers from a large uncertainty due to its highly sensitive aerodynamic properties in the subsonic domain, as well as the wind gusts around runways. At the vehicle design stage, a landing trajectory optimization under wind uncertainty in a multi-objective solution space is desired to explore the possible trade-off in its key flight performance metrics. The proposed algorithm solves this robust constrained multi-objective optimal control problem by integrating non-intrusive polynomial chaos expansion into a constrained evolutionary algorithm. The computationally tractable optimization is made possible through the conversion of a probabilistic problem into an equivalent deterministic representation while maintaining a form of the multi-objective problem. The generated guidance trajectories achieve a significant reduction of the uncertainty in their terminal states with a marginal modification in the control history of the deterministic solutions, validating the importance of the consideration of robustness in trajectory optimization.

Automatic scenario generation for efficient solution of robust optimal control problems

AbstractExisting methods for nonlinear robust control often use scenario‐based approaches to formulate the control problem as large nonlinear optimization problems. The optimization problems are challenging to solve due to their size, especially if the control problems include time‐varying uncertainty. This paper draws from local reduction methods used in semi‐infinite optimization to solve robust optimal control problems with parametric and time‐varying uncertainty. By iteratively adding interim worst‐case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. We show that the local reduction method for optimal control problems consists of solving a series of simplified optimal control problems to find worst‐case constraint violations. In particular, we present examples where local reduction methods find worst‐case scenarios that are not on the boundary of the uncertainty set. We also provide bounds on the error if local solvers are used. The proposed approach is illustrated with two case studies with parametric and additive time‐varying uncertainty. In the first case study, the number of scenarios obtained from local reduction is 101, smaller than in the case when all extreme scenarios are considered. In the second case study, the number of scenarios obtained from the local reduction is two compared to 512 extreme scenarios. Our approach was able to satisfy the constraints both for parametric uncertainty and time‐varying disturbances, whereas approaches from literature either violated the constraints or became computationally expensive.

Optimal robust control of nonlinear systems: inter-sample optimisation in sampled-data control

A methodology is presented for the design and implementation of robust controllers that optimise inter-sample performance for a broad range of nonlinear systems operated within a sampled-data environment. The methodology applies to nonlinear continuous-time systems described by state equations, and it allows for modelling uncertainties and constraints on maximal control effort. It is shown that there exist optimal robust state-feedback controllers that minimise inter-sample tracking errors for such systems, as long as an appropriate controllability requirement is met. A relatively simple design and implementation procedure for such controllers is described.

A High Robust Optimal Nonlinear Control with MPPT Speed for Wind Energy Conversion System (WECS) Based on Doubly Fed Induction Generator (DFIG)

As part of efforts to improve wind energy production using a doubly fed induction generator (DFIG), this paper presents modeling with power maximization through control of speed (MPPT) and control of stator active and reactive power for doubly fed induction generator. The quality of the generated energy and the performance of wind energy conversion systems (WECS) based on DFIG are affected by uncertainties and external disturbances. Therefore, the system requires high-performance control under the nonlinearity influence and the applied external disturbances. This work provides a new contribution and approach that combines nonlinear control (Backstepping) and optimal control (LQR). Backstepping control has been applied to give a good performance using nonlinear strategy and stability condition, but its main drawback is that it is relatively robust for sudden changes in wind speed or any external disturbances as well as it is sensitive against the uncertainties, which may lead to a chattering and an instability as well as overshoot or undershoot. To overcome the problems mentioned above the optimal control (LQR) has been applied to address this drawback in nonlinear control. Furthermore, it, the hybrid approach of Backstepping and LQR control resulting a robust control under the hardest scenarios during the wind system operating as well as provides a good performance in terms of chattering, stability and other performance characteristics which help to produce a high-quality energy. Overall, integrating LQR control with Backstepping can lead to a more powerful, flexible, and efficient control system with improved performance and reduced computational complexity.

Model-free predictive current control of Syn-RM based on time delay estimation approach

Abstract This paper investigates an optimal model-free control design for a synchronous reluctance motor (Syn-RM) with unknown nonlinear dynamic functions, parameter variations, and disturbances. The idea is to combine a predictive control with a time-delay estimation technique (TDE) in order to successfully deal with the system’s uncertainties and make the Syn-RM control scheme easy to implement in real-time. This model-free control strategy comprises two cascade control loops namely outer and inner loops. The outer loop is designed for the mechanical part of Syn-RM to ensure the convergence of the speed dynamics by using a proportional-integral controller while the inner loop is developed to control the uncertain dynamics of currents via an optimal robust controller. In the proposed current loop, the predictive control is enhanced by the inclusion of ultra-local model theory where dynamic functions and disturbances are estimated by instantaneous input-output measurements of the Syn-RM using the TDE approach. Moreover, a particle swarm optimization (PSO) algorithm is also proposed to find the optimal design parameters to improve the dynamic performances of the closed-loop control system. Numerical validation tests of the proposed TDE-based model-free predictive current control (TDE-MFPCC) method are performed in the simulation environment of the Syn-RM system, and the results show the robustness and the effectiveness of the proposed TDE-MFPCC compared to the conventional model-based PCC.

Cooperative-theoretic optimal adaptive robust control for fuzzy multiple manipulator systems

This article presents the study of the trajectory tracking issue of multiple manipulators from the viewpoint of servo constraint-following. First, on the framework of Udwadia-Kalaba (U-K) theory, the tasks of (holonomic or nonholonomic) trajectory tracking control are transformed into a series of servo constraints, and a nominal control is presented to realize the servo constraint-following for the system without uncertainty. Second, consider that there exists the time-varying uncertainty in the system, which is bounded and characterized by the fuzzy set theory. An adaptive robust control (ARC) is presented to achieve tracking errors uniform boundedness (UB) and uniform ultimate boundedness (UUB). Third, cooperative game theory is employed to obtain the dual optimal control parameters of the presented controller, and the mathematical derivation is performed to verify that there exists the Pareto optimal solution. Finally, simulation results show the effectiveness of the proposed control for the trajectory tracking control of multiple manipulators.

Reinforcement learning-based robust optimal tracking control for disturbed nonlinear systems

Reinforcement learning-based robust optimal tracking control for disturbed nonlinear systems

Robust optimal asset-liability management with mispricing and stochastic factor market dynamics

This paper investigates a robust optimal asset-liability management problem under an expected utility maximization criterion. More specifically, the manager is concerned about the potential model uncertainty and aims to seek the robust optimal investment strategies. We incorporate an uncontrollable random liability described by a generalized drifted Brownian motion. Also, the manager has access to an incomplete financial market consisting of a risk-free asset, a market index with potentially path-dependent, time-varying risk premium and volatility, and a pair of mispriced stocks. The market dynamics are assumed to rely on an affine-form, square-root factor process and the price error is modeled by a co-integrated system. We adopt a backward stochastic differential equation approach hinging on the martingale optimality principle to solve this non-Markovian robust control problem. Closed-form expressions for the robust optimal investment strategies, the probability perturbation process under the well-defined worst-case scenario and the corresponding value function are derived. The admissibility of the robust optimal controls is verified under some technical conditions. Finally, we perform some numerical examples to illustrate the effects of model parameters on the robust investment strategies and draw some economic interpretations from these results.

The Equivalence Conditions of Optimal Feedback Control-Strategy Operators for Zero-Sum Linear Quadratic Stochastic Differential Game with Random Coefficients

From the previous work, when solving the LQ optimal control problem with random coefficients (SLQ, for short), it is remarkably shown that the solution of the backward stochastic Riccati equations is not regular enough to guarantee the robustness of the feedback control. As a generalization of SLQ, interesting questions are, “how about the situation in the differential game?”, “will the same phenomenon appear in SLQ?”. This paper will provide the answers. In this paper, we consider a closed-loop two-person zero-sum LQ stochastic differential game with random coefficients (SDG, for short) and generalize the results of Lü–Wang–Zhang into the stochastic differential game case. Under some regularity assumptions, we establish the equivalence between the existence of the robust optimal feedback control strategy operators and the solvability of the corresponding backward stochastic Riccati equations, which leads to the existence of the closed-loop saddle points. On the other hand, the problem is not closed-loop solvable if the solution of the corresponding backward stochastic Riccati equations does not have the needed regularity.

Integrated optimal control of distributed in-wheel motor drive electric vehicle in consideration of the stability and economy

From the perspective of handling stability and economy, this paper brings forward an integrated optimal control scheme of distributed in-wheel motor drive electric vehicles (IWMDEV). A linear quadratic regulator (LQR) controller is presented according to nominal model and ideal motions firstly. To tackle the uncertain parameters and random disturbance, a novel robust optimal (RO) control strategy is further proposed to design the top level controller by employing the combination of optimal control and high order sliding mode control. By virtue of the integral and terminal sliding mode surface, the resulting robust optimal control method can not only achieve better performance, but also converge in finite time without chattering phenomenon. As for the bottom level controller, an optimal algorithm is developed to determine the weights for each term in objective function of torque allocation dynamically and coordinate the relationship between driving safety and energy-saving performance timely. Finally, joint simulations are carried out. In comparison with LQR control strategy, the results demonstrate that the proposed control scheme could ensure the robustness and effectiveness in the presence of parametric perturbation and external disturbance. Moreover, the torque allocation algorithm, which considers both handling stability and energy consumption, proves to be an effectual approach.

Safe Reinforcement Learning-Based Robust Approximate Optimal Control for Hypersonic Flight Vehicles

In this paper, a safe reinforcement learning-based robust approximate optimal controller (SRL-RAOC) is proposed with the framework of actor-critic for hypersonic flight vehicles. First, we develop a system transformation based on barrier function, which transforms the issue of full-state safety constraints into an unconstrained optimization problem. Next, the safe reinforcement learning algorithm is employed to design the approximate optimal controller under an online actor-critic framework. Further, a robustifying term is presented to compensate for the neural network approximation errors introduced by the actor-critic framework. Hereafter, the stability analysis of the closed-loop system is accomplished by utilizing the Lyapunov technique, which shows that SRL-RAOC can guarantee that the equilibrium point is asymptotically stable. Moreover, the control input obtained by SRL-RAOC is demonstrated to be close to the optimal control input within a small bound. Finally, a numerical example is provided to demonstrate the effectiveness of SRL-RAOC.

Toward an optimal twisting-sliding mode control of a three-phase PMSM for electric vehicles

This paper deals with an optimal twisting sliding mode controller (OT-SMC) for the operation of a three phase permanent magnet synchronous machine (PMSM) in an electric vehicle (EV). In order to drive these vehicles, optimal performance is needed with robust control against real-time disturbances such as the variable load torque, uncertainties such as the parameters variation and speed variations between medium, low, and high speed as well as good performance characteristics for enhanced drive quality and longer battery time. Several conventional techniques have been applied to PMSM but they suffer from the problem of uncertainties and disturbances due to the PI regulator. A hybrid approach comprising of a robust nonlinear and optimal controller to achieve these objectives is attempted for driving electrical vehicles. This advanced hybrid controller obtained after the merger of sliding mode control (SMC) and a linear quadratic controller (LQR) is found to outperform existing controllers due to their superb performance characteristics. Furthermore, SMC is designed based on the exponential reaching law for the twisting sliding mode control (T-SMC) in order to ensure stability of the system while reducing the chattering, accelerating the rate of convergence with higher accuracy of the control performance, and the LQR is developed using the steady-state error method (N-LQR) in order to obtaining better performance characteristics. In addition, the hybridization between a twisting SMC and an optimal LQR is characterized by stabilizing and minimizing the oscillations in the permanent regime thus optimizing the system’s performance. Extensive simulation results illustrate the effectiveness and validity of the proposed control for achieving the highest performance of the PMSM.

Robust optimal control of nonlinear fractional systems

Parameter uncertainty is inevitably found in almost every system and, if is ignored, it could jeopardize the effectiveness of control method. Motivated by this issue, we consider a robust optimal control problem governed by a nonlinear fractional system with uncertain parameters, where the system sensitivity with respect to the uncertain parameters is explicitly included in the cost functional. For this problem, we first prove that the system sensitivity can be expressed as the solution of an auxiliary fractional system. Then, we propose a numerical scheme for discretizing both the original and auxiliary fractional systems, resulting in a finite-dimensional optimization problem. Furthermore, a numerical solution algorithm based on gradients of the cost functional is developed for the resulting optimization problem. Finally, numerical results for two example problems are given to demonstrate the validity and applicability of the proposed algorithm.

A robust optimal distributed control design for simultaneous voltage regulation and current sharing in DC microgrid

AbstractIn this article, a robust optimal distributed controller is designed for achieving average voltage regulation and current sharing in a DC microgrid. Each distributed generation unit (DGU) consists of a DC‐DC buck converter that supplies a local constant current load. The proposed controller only utilises output currents of converters and the possible maximum error values in estimation of series resistance in the RLC filter used in each DGU. The proposed controller is formed such that the possible estimation error is considered as an uncertain parameter. In addition to obtaining two main objectives, average voltage regulation, and current sharing, a robust control problem is solved through an optimal control technique to calculate controller parameters such that the stability of the grid is guaranteed. The stability of the closed loop system with parametric uncertainty is proved through Lyapunov analysis. The closed loop system with the suggested controller is tested by simulations and through different scenarios to reveal the reliable and satisfactory performance of the proposed robust optimal control structure.

Instant decompression‐induced swell drying of banana: Machine learning and swarm intelligence embedded modeling and process optimization

AbstractA novel approach of instant decompression‐induced swell drying also known as instant controlled pressure drop‐hot air dried (ICPD‐HAD) process was applied for the process performance and quality enhancement of dried banana slices. Using a hybrid approach of particle swarm embedded methodology, the process parameters treatment pressure (TP), treatment time (TT), and duration of decompressed State (DDS) were optimized for various responses including drying time (DT), browning index (BI), rehydration ratio (RR), and total antioxidant activity (TAA). The optimized process conditions were found to be 0.1 MPa of TP, 25 s of TT, and 12 s of DDS for a minimum DT of 225 min and, maximum BI, RR, and TAA, of 6.20%, 3.40%, and 98.78% respectively. The results also demonstrated that the dried banana samples produced by the ICPD‐HAD method exhibited superior quality in terms of minimal DT and BI and maximum TAA and RR compared to those produced by the vacuum and hot air drying techniques. Microstructural investigation demonstrating the superiority of ICPD‐induced samples provided additional evidence for the minimum DT requirement. Furthermore, the use of an artificial neural network was employed to investigate the drying kinetics of the novel instant decompression‐induced swell drying process. With R2 greater than 0.99 and a minimum mean square error (MSE) of 0.000131, the 2‐4‐1 artificial neural network (ANN) architecture performed admirably as a means of optimal simulation and robust control of the drying process.Practical applicationsInstant decompression‐induced swell drying also known as ICPD‐HAD process is a novel approach for the drying of banana sample with enhanced process performance and quality attires. It is common for banana drying to cause loss of total antioxidant activity and other important functional properties like color and texture. This issue can be solved and process performance can be enhanced with less energy use by employing an innovative swell drying technique triggered by instant decompression. Therefore, the dried banana samples made using this cutting‐edge technique will be advantageous from a health point of view. This method can be used by the food manufacturing sector to produce dried bananas of a higher quality and greater consumer acceptance.

Neural network based robust optimal energy control of pulse width modulation‐inverter fed motor driving pump

AbstractThis paper revisits loss model control (LMC) of the 3‐phase induction motor (IM) and presents a robust LMC algorithm for medium‐sized pump drives. Compared with other power loss reduction algorithms for IM, the presented one has the advantages of fast and smooth flux adaptation, high accuracy, and versatile implementation. An improved loss‐model for IM drive has been developed. The model considers the surplus power loss caused by inverter voltage harmonics and magnetic saturation using closed‐form equations. Further, the resistance‐temperature change is considered by a first‐order thermal model. To determine the optimal flux level that achieves maximum drive efficiency, an artificial neural network (ANN) controller is synthesised and trained offline. The voltage and speed control loops are connecting via the stator frequency to avoid the possibility of excessive magnetization. Beside, the obtained thermal information enhances motor protection and control. These together have the potential of making the proposed algorithm robust and reliable. The system reliability is investigated and assessed in terms of energy saving using ramp start/stop. Theoretical analysis, computer simulations, and experimental studies are performed on 5.5 kW variable speed water pump using the proposed control. The test results are provided and discussed to validate the effectiveness.

Adaptive Dynamic Programming-Based Event-Triggered Robust Control for Multiplayer Nonzero-Sum Games With Unknown Dynamics1-4mmPlease verify and confirm the term "Multi-Player" has been changed to "Multiplayer" in the title of this article.

In this article, the event-triggered robust control of unknown multiplayer nonlinear systems with constrained inputs and uncertainties is investigated by using adaptive dynamic programming. To relax the requirement of system dynamics, a neural network-based identifier is constructed by using the system input-output data. Subsequently, by designing a nonquadratic value function, which contains the bounded functions, the system states, and the control inputs of all players, the event-triggered robust stabilization problem is converted into an event-triggered constrained optimal control problem. To obtain the approximate solution of the event-triggered Hamilton-Jacobi (HJ) equation, a critic network for each player is established with a novel weight updating law to relax the persistence of excitation condition based on the experience replay technique. Furthermore, according to the Lyapunov stability theorem, the present event-triggered robust optimal control ensures the multiplayer system to be uniformly ultimately bounded. Finally, two simulation examples are employed to show the effectiveness of the present method.

Dynamic Event-Triggered-Based Integral Reinforcement Learning Algorithm for Frequency Control of Microgrid With Stochastic Uncertainty

The intermittency of renewable energy and the uncertainty of load put forward higher robustness requirements for the frequency recovery of microgrid (MG). The energy storage equipment provides an idea for frequency control because of its fast response and strong controllability. In this paper, an on-line adaptive frequency control method is proposed to control the governor and energy storage to realize the frequency recovery of MG under stochastic uncertainty. First, the MG system with external disturbances is constructed as a zero-sum differential game model to obtain a robust optimal control scheme. Then, considering the system parameter uncertainty, an improved integral reinforcement learning (IRL) algorithm is designed, in which the reinforcement signal contains a non-quadratic function to solve the energy storage control constraints. Furthermore, a novel dynamic event-triggered control (DETC) is developed to reduce control update times of energy storage. The dynamic variable in DETC coupled with static trigger includes not only the past triggering information but also the disturbances. DETC has a larger trigger threshold than static event-triggered control (SETC). Meanwhile, the proposed algorithm is implemented by an action-critic network structure, in which the action network of energy storage is updated aperiodically. Finally, simulation results show that the proposed control algorithm can realize the frequency recovery of MG, and it has good robustness compared with other algorithms.

Hybrid evolutionary robust optimization-based optimal control for time-delay nonlinear systems

Optimal controls receive much attention owing to their remarkable performance for nonlinear systems. However, unknown time-delay disturbances in the optimal control process make it difficult to find high-quality optimal set points. To address this problem, a hybrid evolutionary robust optimization-based optimal control (HERO-OC) method is proposed to reduce the negative effect of time-delay disturbances and enhance the performance of optimal set points. First, a data-driven time-delay disturbance observer (DTDO), based on fuzzy neural networks, is designed to describe the time-delay disturbances of optimal objectives. Then, the expressions and intervals of time-delay disturbances can be estimated to improve the accuracy of optimal objectives. Second, a hybrid evolutionary robust optimization (HERO) algorithm, which combines an expectation robust optimization strategy with a min–max evolutionary robust optimization strategy, is proposed to solve optimal set points. Then, the average robustness and conservative of robustness optimal set points can be improved. Third, an adaptive time-delay controller using Lyapunov–Krasovskii functionals is proposed to track optimal set points. Then, control accuracy is improved while ensuring control stability. Finally, the superior performance of HERO-OC is compared with some novel optimal control methods in a second-order nonlinear system and a wastewater treatment process.

Multidimensional-Taylor-network-based robust optimal tracking control for MIMO nonlinear discrete-time systems

In practical engineering, system control is indispensable. However, due to the influence of model uncertainty, speed unavailability, input nonlinearity (such as actuator dead zone/fault), and multi-input coupling, the control results are not satisfactory. In this paper, a robust optimal tracking control strategy is proposed for a class of nonlinear multi-input-multi-output discrete-time systems with unknown uncertainties. This control strategy is to minimize the cost function in the process of uncertainty processing and stabilize the closed-loop system by establishing an adaptive controlling approach based on a combination of actor MTN and critic MTN based on the Multi-dimensional Taylor Network (MTN). By using the approximation property of MTN, the optimal control signal is generated by action MTN, which is used to approach the controller, and the cost function is approximated by critic MTN, which is tuned online because the cost function cannot be obtained in hands-on experience. By designing a new cost function, the amount of calculation in the control process is reduced, and the adaptive critic design control idea is integrated into the controller design to deal with the uncertainty of the system. The simulation results verify the effectiveness of the control strategy proposed in the essay.