Robust Optimal Control Scheme Research Articles

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.

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.

Observer‐based robust optimal control for helicopter with uncertainties and disturbances

AbstractUnknown model uncertainties and external disturbances widely exist in helicopter dynamics and bring adverse effects on control performance. Optimal control techniques have been extensively studied for helicopters, but these methods cannot effectively handle flight control problems since they are sensitive to uncertainties and disturbances. This paper proposes an observer‐based robust optimal control scheme that enables a helicopter to fly optimally and reduce the influence of unknown model uncertainties and external disturbances. A control Lyapunov function (CLF) is firstly constructed using the backstepping method, then Sontag's formula is utilized to design an inverse optimal controller to stabilize the nominal system. Furthermore, it is stressed that the radial basis function (RBF) neural network is introduced to establish an observer with adaptive laws, approximating and compensating for the unknown model uncertainties and external disturbances to enhance the robustness of the closed‐loop system. The uniform ultimate boundedness of the closed‐loop system is ensured using the presented control approach via Lyapunov stability analysis. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control strategy.

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.

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.

Robust Inverse Optimal Control for a Boost Converter

The variability of renewable energies and their integration into the grid via power electronics demands the design of robust control algorithms. This work incorporates two techniques to ensure the stability of a boost converter through its state equations, implementing the inverse optimal control and the gain-scheduling technique for robust control settings. In such a way that, under a single adjustment, it is capable of damping different changes such as changes in the parameters, changes in the load, the input voltage, and the reference voltage. On the other hand, inverse optimal control is based on a discrete-time control Lyapunov function (CLF), and CLF candidate depends on fixed parameters that are selected to obtain the solution for inverse optimal control. Once these parameters have been found through heuristic or artificial intelligence methods, the new proposed methodology is capable of obtaining a robust optimal control scheme, without having to search for new parameters through other methods, since these are sometimes sensitive changes and many times the process of a new search is delayed. The results of the approach are simulated using Matlab, obtaining good performance of the proposed control under different operation conditions. Such simulations yielded errors of less than 1% based on the voltage reference, given the disturbances caused by changes in the input variables, system parameters, and changes in the reference. Thus, applying the new methodology, the stability of our system was preserved in all cases.

Neural Network Observers and Sensorless Robust Optimal Control for Partially Unknown PMSM With Disturbances and Saturating Voltages

This article proposes neural network (NN) based observer schemes and a sensorless robust optimal control scheme for partially unknown permanent magnet synchronous motors with disturbances and saturating voltages. First, an NN-observer scheme is designed to estimate back-electromotive force (EMF), for which the mathematical model in rotary or stationary reference frames is relaxed. The NN weight tuning law is designed via Lyapunov theory to guarantee that EMF is ultimately uniformly bounded. Second, to compensate the inexact extraction of the estimated back-EMF at any speed conditions, disturbances, and NN approximation errors, another NN-observer scheme is designed to estimate the tracking errors of rotor position and speed, for which low-pass filters and/or phase-locked loops are not needed. Third, a sensorless saturated robust optimal control scheme dealing with general disturbances and saturating voltages is designed. The scheme includes the augmented feedforward controller to transform the speed and current tracking problem into an optimal control problem. Finally, the feedback control law and worst disturbance law are obtained without estimating unknown internal dynamics. The effectiveness of the proposed schemes is tested through simulations and comparative experiments on a load drive application with a DSP board TMS320F28379D.

Design of robust control strategy in drug and virus scheduling in nonlinear process of chemovirotherapy

Since the injection of the oncolytic viruses in the virotherapy process reduces the toxicity and drug resistance inherent in the chemotherapy; chemovirotherapy as a novel combination therapy has become an efficient cancer treatment. The primary purpose of this paper is to design a robust optimal control strategy for the chemovirotherapy through which the tumor density decreases to its stable condition with limited drug and virus delivery. This desired treatment should be responsive in the presence of input disturbances and parametric uncertainties. In this regard, an ODE (Ordinary Differential Equation) mathematical model of the chemovirotherapy process presenting the connection between the avascular tumor cells, immune cells, and treatment materials is utilized. H-infinity and DK iteration controllers are designed and implemented to the uncertain model, through the continuous and discrete procedures. By comparing the closed-loop simulations, discrete injection is found to be more effective (while is also more realistic in practice). The characteristics of an optimal treatment including the treatment frequency, drug and virus dosage, and suggested start time will be determined as the final results of this research.

Robust Optimal Control for the Vehicle Suspension System With Uncertainties.

The suspension system is an important unit that affects vehicle performance, including handling stability and riding comfort. In order to improve vehicle performances, a novel robust optimal control strategy for the active suspension system in vehicles is proposed. To handle the parameter uncertainties and external random disturbances, the proposed optimal control strategy is designed by using the combination of the linear quadratic regulator (LQR) optimal control and sliding-mode control. First, by using the nominal model of the active suspension system without the uncertain parameters and the external random disturbances, an optimal control performance index is given, and the initial optimal controller is designed by using the LQR control strategy. Then, to handle the parameter uncertainties and the external disturbances, a robust optimal integral sliding-mode control strategy based on the initial optimal controller is designed, which not only can achieve the optimal control objective but also has good robustness to the uncertain parameters and external disturbances. By using the Lyapunov stability theory, stability analysis of the proposed robust optimal integral sliding-mode control strategy is performed. Finally, the collaborative simulation platform based on the Carsim and MATLAB/Simulink is developed. The simulation results illustrate the advantage of the proposed robust optimal control strategy for the suspension system.

Robust optimal control for finite-horizon zero-sum differential games via a plug-n-play event-triggered scheme

This paper proposes a robust optimal control strategy for finite-horizon two-player Zero-Sum(ZS) differential games with partially unknown dynamics by incorporating an event-triggered scheme and the critic-only adaptive dynamic programming(ADP) method. Firstly, an online identifier is designed to reconstruct unknown system dynamics based on the data-driven technique. The identifier is running in the solving process rather than as a priori part of the solution, which simplifies the system structure and decreases the computational cost. To deal with the finite-horizon constraints, a time-varying value function and a additional term are considered to such that the terminal constraint error is minimised. A critic neural network(CNN) is used to solve the event-triggered Hamilton–Jacob—Isaacs (HJI) equation under a plug-n-play structure, which reduces the redundant information transmission as well as receives all measurement information immediately. According to the Lyapunov theory, the uniformly ultimately bounded (UUB) for the event-triggered closed-loop system and the CNN weight error are demonstrated, in the meantime the asymptotic stability of the identifier weight error is proved. Finally, the application in the missile-target interception system validates the feasibility and efficacy of the proposed method.

Robust optimal control for a class of nonlinear systems with unknown disturbances based on disturbance observer and policy iteration

A robust optimal control method for a class of nonlinear systems with unknown disturbances is addressed in this paper. In this framework, adaptive dynamic programming (ADP) is presented to obtain the optimal control. On-policy learning allows the performance index function and the optimal control to be obtained iteratively. It is shown that the iterative performance index function is non-increasing. A nonlinear disturbance observer is designed to estimate external disturbances. The compensation control is used to compensate for the influence of the disturbances. It is proven that the disturbance observer error is exponentially stable, under some conditions. The properties of the nonlinear system with unknown disturbance steered by the robust optimal control input are also proven. Simulation results demonstrate the performance of the proposed robust optimal control scheme for the nonlinear system with unknown disturbance.

Risk-based online robust optimal control of air-conditioning systems for buildings requiring strict humidity control considering measurement uncertainties

The total floor area and energy consumption of buildings or spaces requiring strict temperature and humidity control have been growing rapidly worldwide. A major challenge for achieving energy-efficient control of air-conditioning systems in such applications is the measurement uncertainties underlying the systems’ online optimal control decisions under ever-changing working conditions. This paper proposes a risk-based online robust optimal control strategy for multi-zone air-conditioning systems considering component performance degradation and measurement uncertainties. A risk-based online control decision scheme, as the core of the strategy, is developed for decision-making by compromising the failure risks and energy benefits of different control modes considering uncertainties in the information used. The proposed strategy is tested and implemented in a simulation platform based on an existing pharmaceutical industrial building. The results show that the proposed strategy made the optimal online control decisions, allowing for the measurement uncertainties. Compared with a commonly used control strategy, the proposed strategy achieved approximately 20% overall energy saving in the test period.

Model Predictive Trajectory Tracking Control of Electro-Hydraulic Actuator in Legged Robot With Multi-Scale Online Estimator

This paper addresses the trajectory tracking problem for constrained high dynamic electro-hydraulic actuator in the presence of time-varying parameters, high frequency external load interference, measurement noise and some unmeasurable states. An adaptive robust optimal control scheme is proposed for the electro-hydraulic actuator in legged robot. The framework of our presented scheme is based on a linear time-varying model predictive controller (LTV-MPC) embedded with a multi-scale online estimator (MEKF). With fast- varying and slow- varying time scales, the MEKF part is used not only for measurable states filtering and unmeasurable states estimation, but also for time-varying parameters and external load interference estimation, which will be integrated into the mpc model in real time. The LTV-MPC part is a trajectory tracking controller designed by constrained MPC with an approximate high-precision real-time model and a rapidly solved cost function, which guarantees that the input and output constraints are satisfied during the receding horizon and optimal control process. Finally, with a series of highly dynamic conditions, the comparison experiment results show that the proposed controller has a simple design process, strong adaptive robust performance and trajectory tracking performance, which verifies the effectiveness of the control scheme.

Second order integral sliding mode observer and controller for a nuclear reactor

Abstract This paper presents an observer-based chattering free robust optimal control scheme to regulate the total power of a nuclear reactor. The non-linear model of nuclear reactor is linearized around a steady state operating point to obtain a linear model for which an optimal second order integral sliding mode controller is designed. A second order integral sliding mode observer is also designed to estimate the unmeasurable states. In order to avoid the chattering effect, the discontinuous input of both observer and controller are designed using the super-twisting algorithm. The proposed controller is realized by combining an optimal linear tracking controller with a second order integral sliding mode controller to ensure minimum control effort and robustness of the closed-loop system in the presence of uncertainties. The condition for the selection of gains of discontinuous control based on the super-twisting algorithm is derived using a strict Lyapunov function. Performance of the proposed observer based control scheme is demonstrated through non-linear simulation studies.

A pseudospectral method based robust-optimal attitude control strategy for spacecraft

This paper proposes an optimal integral sliding mode control (ISMC) scheme for attitude regulation of the rigid spacecraft. This control technique is capable of handling inertial matrix uncertainties as well as external disturbances. To incorporate optimality into the robust control law, the ISMC is integrated with Legendre pseudospectral method (LPSM). The minimization of the cost function and constraint handling of the spacecraft is obtained by LPSM, while the ISMC provides disturbance rejection. LPSM is chosen for its relatively high rate of convergence and its capability of solving a wide range of challenging optimal control problems. Theoretical stability analysis of closed loop system using Lyapunov theorem guarantees the convergence of attitude states. A comparative analysis between the proposed LPSM-ISMC and Chebyshev Pseudospectral Method (CPSM) based ISMC, is also presented in this paper. The effectiveness of the proposed robust-optimal control strategy is established through simulation results.

Robust Control of a Microgrid Energy Storage System Using Various Approaches

This paper presents a robust optimal control strategy for an energy storage system (ESS) of a grid-connected microgrid. The robust optimal control guarantees the highest possible economic benefit of the control schedule even under the worst case net demand prediction error conditions. Several robust optimization approaches are proposed to formulate a fast optimal control problem. The global optimum of a concise control problem can be found within a short computation time using mixed-integer linear programming. The rolling horizon controller of the energy management system periodically updates the control schedule by solving the control problem. The state of charge of an ESS is precisely calculated by the piecewise linearization technique using nonlinear efficiency maps. External working conditions such as peak control and demand response can be dynamically applied during the optimization process. The proposed strategy provides control robustness in terms of cost reduction, precise control, and external effect. Future study will focus on the development of a robust control strategy that considers both the worst and best cases of cost reduction.

Self-learning robust optimal control for continuous-time nonlinear systems with mismatched disturbances

This paper presents a novel adaptive dynamic programming(ADP)-based self-learning robust optimal control scheme for input-affine continuous-time nonlinear systems with mismatched disturbances. First, the stabilizing feedback controller for original nonlinear systems is designed by modifying the optimal control law of the auxiliary system. It is also demonstrated that this feedback controller can optimize a specified value function. Then, within the framework of ADP, a single critic network is constructed to solve the Hamilton–Jacobi–Bellman equation associated with the auxiliary system optimal control law. To update the critic network weights, an indicator function and a concurrent learning technique are employed. By using the proposed update law for the critic network, the restrictive conditions including the initial admissible control and the persistence of excitation condition are relaxed. Moreover, the stability of the closed-loop auxiliary system is guaranteed in the sense that all the signals are uniformly ultimately bounded. Finally, the applicability of the developed control strategy is illustrated through simulations for an unstable nonlinear plant and a power system.

Optimal robust control strategy of a solid oxide fuel cell system

Optimal control can ensure system safe operation with a high efficiency. However, only a few papers discuss optimal control strategies for solid oxide fuel cell (SOFC) systems. Moreover, the existed methods ignore the impact of parameter uncertainty on system instantaneous performance. In real SOFC systems, several parameters may vary with the variation of operation conditions and can not be identified exactly, such as load current. Therefore, a robust optimal control strategy is proposed, which involves three parts: a SOFC model with parameter uncertainty, a robust optimizer and robust controllers. During the model building process, boundaries of the uncertain parameter are extracted based on Monte Carlo algorithm. To achieve the maximum efficiency, a two-space particle swarm optimization approach is employed to obtain optimal operating points, which are used as the set points of the controllers. To ensure the SOFC safe operation, two feed-forward controllers and a higher-order robust sliding mode controller are presented to control fuel utilization ratio, air excess ratio and stack temperature afterwards. The results show the proposed optimal robust control method can maintain the SOFC system safe operation with a maximum efficiency under load and uncertainty variations.

Optimal synchronization of fractional-order chaotic systems subject to unknown fractional order, input nonlinearities and uncertain dynamic using type-2 fuzzy CMAC

In this paper, a new robust optimal control strategy is presented to synchronize a class of fractional-order chaotic systems with unknown fractional orders, uncertain dynamics and input nonlinearities. The dynamics of the system are estimated by an integer-order model, using proposed non-singleton type-2 fuzzy cerebellar model articulation controller (NST2-CMAC). The free parameters of NST2-CMAC are adjusted based on the adaptation laws which are derived from Lyapunov stability analysis. To show the effectiveness of the proposed method, two simulation examples are provided and the results are compared with other methods.

Data-based robust optimal control of continuous-time affine nonlinear systems with matched uncertainties

In this paper, the robust optimal control of continuous-time affine nonlinear systems with matched uncertainties is investigated by using a data-based integral policy iteration approach. It is a natural extension of the traditional optimal control design, under the framework of adaptive dynamic programming (ADP) method, to robust optimal control of nonlinear systems with matched uncertainties. In theoretical aspect, by increasing a feedback gain to the optimal controller of the nominal system, the robust controller of the matched uncertain system is obtained, which also achieves optimality with a newly well-defined cost function. When regarding the implementation, the data-based integral policy iteration algorithm is used to solve the Hamilton–Jacobi–Bellman equation corresponding to the nominal system with completely unknown dynamics information. Then, the actor-critic technique based on neural networks and least squares implementation method are employed to facilitate deriving the optimal control law iteratively, so that the closed-form expression of the robust optimal controller is available. Additionally, two simulation examples with application backgrounds are presented to illustrate the effectiveness of the established robust optimal control scheme. In summary, it is important to note that the result developed in this paper broadens the application scope of ADP-based optimal control approach to more general nonlinear systems possessing dynamical uncertainties.