Conventional Optimal Control Research Articles

ARTIFICIAL INTELLIGENCE OPTIMIZED CONTROLLER DESIGN FOR AUTOMATIC GENERATION CONTROL IN RESTRUCTURED POWER SYSTEMS

This paper presents an investigation on automatic generation control (AGC) in restructured power systems with multiple interconnected areas and multiple machines. A particle swarm optimized combined optimal fuzzy controller has been proposed. The results obtained with the proposed controller have been compared with the conventional PI controller and optimal controller to exhibit its robust performance. Furthermore, the proposed controller aims to rapidly achieve zero deviations in frequency and tie line power, thereby maintaining system synchronism. The PSO-optimized combined optimal fuzzy controller demonstrates superior performance in terms of peak transient deviation, settling periods, and dynamic oscillations compared to other controllers.

Multiscale stochastic optimal control of hysteretic structures based on wavelet transform and probability density evolution method

PurposeContemporary stochastic optimal control by synergy of the probability density evolution method (PDEM) and conventional optimal controller exhibits less capability to guarantee economical energy consumption versus control efficacy when non-stationary stochastic excitations drive hysteretic structures. In this regard, a novel multiscale stochastic optimal controller is invented based on the wavelet transform and the PDEM.Design/methodology/approachFor a representative point, a conventional control law is decomposed into sub-control laws by deploying the multiresolution analysis. Then, the sub-control laws are classified into two generic control laws using resonant and non-resonant bands. Both frequency bands are established by employing actual natural frequency(ies) of structure, making computed efforts depend on actual structural properties and time-frequency effect of non-stationary stochastic excitations. Gain matrices in both bands are then acquired by a probabilistic criterion pertaining to system second-order statistics assessment. A multi-degree-of-freedom hysteretic structure driven by non-stationary and non-Gaussian stochastic ground accelerations is numerically studied, in which three distortion scenarios describing uncertainties in structural properties are considered.FindingsTime-frequency-dependent gain matrices sophisticatedly address non-stationary stochastic excitations, providing efficient ways to independently suppress vibrations between resonant and non-resonant bands. Wavelet level, natural frequency(ies), and ratio of control forces in both bands influence the scheme’s outcomes. Presented approach outperforms existing approach in ensuring trade-off under uncertainty and randomness in system and excitations.Originality/valuePresented control law generates control efforts relying upon resonant and non-resonant bands, and deploys actual structural properties. Cost-function weights and probabilistic criterion are promisingly developed, achieving cost-effectiveness of energy demand versus controlled structural performance.

Robust optimal triple event-triggered intermittent control for uncertain input-constrained nonlinear systems

This paper investigates the concept of finite time (FT) optimal event-triggered intermittent (ETI) control for nonlinear systems with input constraints and dynamic uncertainty. Firstly, we address a key challenge faced by existing controllers, wherein the unbounded nature of the signal function renders it impractical to handle the input-constrained FT control problem. To overcome this limitation, we derive a novel lemma of semiglobal practical finite-time stability (SGPFTS) specifically for intermittent control with the additional constant terms. By leveraging the lemma and the Hamilton–Jacobi–Bellman (HJB) equation, we obtain the optimal FT guaranteed cost intermittent control law and establish FT stability criteria for uncertain nonlinear systems. Recognizing that the general HJB theory is ill-equipped to address input-constrained optimal control problems, We introduce the model predictive control (MPC) algorithm, which has been proven to be an effective online optimization method in handling robust optimal control and constrained problems. Moreover, conventional ETI optimal control methods struggle to address intermittent control for nonlinear systems with input constraints and dynamic uncertainty. To address this limitation, we propose a triple ETI Lyapunov-based MPC strategy, which not only enhances intermittent control performance but also resolves input constraints and dynamic uncertainty issues. Finally, we present two straightforward examples of uncertain nonlinear systems to demonstrate the effectiveness of the developed strategy in practice.

Stochastic Optimal Control for Multivariable Dynamical Systems Using Expectation Maximization.

Trajectory optimization is a fundamental stochastic optimal control (SOC) problem. This article deals with a trajectory optimization approach for dynamical systems subject to measurement noise that can be fitted into linear time-varying stochastic models. Exact/complete solutions to these kind of control problems have been deemed analytically intractable in literature because they come under the category of partially observable Markov decision processes (MDPs). Therefore, effective solutions with reasonable approximations are widely sought for. We propose a reformulation of stochastic control in a reinforcement learning setting. This type of formulation assimilates the benefits of conventional optimal control procedure, with the advantages of maximum likelihood approaches. Finally, an iterative trajectory optimization paradigm called as SOC-expectation maximization (SOC-EM) is put forth. This trajectory optimization procedure exhibits better performance in terms of reduction in cumulative cost-to-go which is proven both theoretically and empirically. Furthermore, we also provide novel theoretical work which is related to uniqueness of control parameter estimates. Analysis of the control covariance matrix is presented, which handles stochasticity through efficiently balancing exploration and exploitation.

The ping-pang variable amplitude limiter used in the coordinated controller of a hybrid reactive power compensation system

The hybrid reactive power compensation system, which connects different reactive power compensation devices to the same bus, will be essential equipment for future power systems. In a power grid with a high proportion of photovoltaic, wind turbines, and power electronic devices, it is significant to design a coordinated control strategy for the hybrid reactive power compensation system. In this paper, a kind of ping-pang variable amplitude limiter is used in the linear optimal controller. The ping-pang variable amplitude limiter can improve the transient stability of a hybrid reactive power compensation system. The effects of the coordinated controller are verified in simulation. Compared with the conventional linear optimal controller, the coordinated controller with the ping-pang variable amplitude limiter has a better optimization effect in large disturbance conditions.

An inverse optimal approach for distributed preview consensus tracking

This paper develops a distributed consensus control protocol that guarantees consensus tracking and global optimality with respect to a positive quadratic performance index for identical general linear multi-agent systems on an undirected graph. By using the previewable future reference signal, the consensus tracking control problem is converted into a preview control based optimal problem. The inverse optimality theory is introduced to overcome the difficulty of designing a distributed optimal controller, which is caused by the fact that the communication topology always interplays with the system dynamics and subsequently the global information is usually required in a conventional optimal controller design. First, a distributed optimal controller for tracking a reference signal with stable mode is designed. Then, an internal model based distributed optimal controller is further designed to track a time-varying reference signal. The structured quadratic performance indexes are derived for both cases, respectively, and based on which, two distributed optimal tracking control protocols are implemented to guarantee the asymptotic stability of the augmented systems only using local information. Simulation results show that an appropriate preview length can effectively improve the tracking performance.

Cleaning Schedule Optimization of Heat Exchanger Network Using Moving Window Decision-Making Algorithm

A moving window decision-making algorithm is proposed for the cleaning schedule optimization of heat exchanger network system subject to fouling in refinery crude preheat train. This algorithm is designed by incorporating the moving window scheme into a conventional multi-period optimal control problem (OCP) framework and has a distinct feature that it can efficiently handle a complex problem where a long-time horizon is considered. When compared with the conventional multi-period OCP method using fixed time horizon, our algorithm always shows an excellent performance regarding the computational time, still finding a compatible optimal solution. In our moving window decision-making algorithm, it is important to determine the optimal moving window size for the given time horizon as it significantly influences the optimization performance.

Robust Optimal Control With Inexact State Measurements and Adjustable Uncertainty Sets

The efficacy of robust optimal control with adjustable uncertainty sets is verified in several domains under the perfect state information setting. This paper investigates constrained robust optimal control for linear systems with linear cost functions subject to uncertain disturbances and state measurement errors that are both residing in adjustable uncertainty sets. We first show that the class of affine feedback policies of state measurements are equivalent to the class of affine feedback policies of estimated disturbances in terms of their conservativeness. Then, we formulate and solve a robust optimal control problem with adjustable uncertainty sets by considering the disturbance feedback policies. In contrast to the conventional robust optimal control, where uncertainty sets are fixed and known a priori, the uncertainty sets themselves are regarded as decision variables in our design. In particular, given the metrics for evaluating the optimal size/shape of the polyhedral uncertainty sets, a bilinear optimization problem is formulated to decide the optimal size/shape of uncertainty sets and a corresponding optimal control policy to robustly guarantee that the system will respect its constraints for all admissible uncertainties. In addition, we introduce a convex approximation for the proposed scheme to provide a computationally efficient inner approximation of the original problem. The proposed scheme is illustrated by numerical simulation of a building temperature control problem to demonstrate its effectiveness.

Indirect Model Predictive Control with Sparse Nonlinear Regression on Erdös-Rényi-generated Bernoulli-SIR Network Models

Epidemiological modeling is important in order to be able to predict and mitigate the consequences of epidemics. Disease transmission network models can be used to model epidemics on a detailed level, which in turn can yield better predictions, at the cost of being more difficult to analyze and control. This paper demonstrates methods that enable simple network models to be controlled with conventional indirect optimal control methods, through model simplification via Monte-Carlo simulations and sparse nonlinear regression.

Distributed coordinated control method with multiple objectives optimization algorithm for wind farms

AbstractThis paper proposes a distributed coordinated control (DCC) method. The DCC method concentrates on improving the performances of fatigue load minimization and voltage regulation of WFs. The active and reactive power outputs of the wind turbines (WTs) inside WFs are coordinated while the power flow of WF collection system and capacity of each WT are considered by using DistFlow model. With the consensus ADMM‐based framework, the WTs inside the WF are operated in fully distributed manner while meeting the requirement of the dispatch command of the transmission system operator (TSO). The WF can track the dispatch command from the TSO accurately without the coordination of central unit. Moreover, it is more scalable and lower computation‐burden than conventional centralized optimal control. A wind farm consisting of 20 WTs is used in case study to verify the effectiveness of the proposed control method.

Extended Statement of the Optimal Control Problem and Machine Learning Approach to Its Solution

Engineers strive to realize the goal of control in the best possible way based on a given quality criterion when developing control system. The well-known optimal control problem requires finding a solution as a function of time. Such a function cannot be directly used to control a real object because its application corresponds to an open-loop control system and engineers usually complete it with a feedback stabilization system. Hence, there is an obvious need to reformulate the optimal control problem so that its solution can be directly applied to real objects. The paper presents a new extended statement of the optimal control problem. An additional requirement for the control function is introduced to give the system describing the control object properties that will ensure the stability of solutions. The desired control function must provide for the optimal trajectory given the properties of the attractor in the neighbourhood. The solution to the extended optimal control problem can be directly used to control a real object. The paper presents a computational machine learning approach to solving the extended problem of optimal control based on the application of a synthesized optimal control technique. Examples of the practical solution to the stated problem are given to illustrate the efficiency of the approach, where the solution to the conventional optimal control problem is compared with the proposed extended one in the presence of perturbations in models and initial conditions.

Multi-timescale voltage control for distribution system based on multi-agent deep reinforcement learning

Nowadays a large number of distributed generators and controllable elements connecting to the distribution network have resulted in higher requirements for voltage control. Existing voltage control methods require a specific physical model and are time-consuming with the complexity increasing. To overcome these challenges, this paper proposes a multi-timescale voltage control scheme using multi-agent deep reinforcement learning (MADRL). Firstly, considering the control requirements of different timescale regulators, a multi-timescale voltage control model is formulated. Then the control variables are assigned to multiple agents, and a MADRL-based voltage control scheme is proposed, which is based on the multi-agent deep deterministic policy gradient (MADDPG) algorithm and applies Gumbel-Softmax distribution to solve discrete actions. Through centralized learning and decentralized execution, this scheme can obtain the optimal coordinated control strategy of multiple regulators adaptively and achieve the effect of distributed control. Finally, case studies are conducted on the modified IEEE-123 bus system, and the performance of the proposed method is compared with the conventional model-based optimal voltage control scheme and other DRL-based methods. The results show that the MADRL-based method possesses better performance than other methods.

Dynamic Modeling and Rule-Based Control Design for a Hybrid-Electrified Regional Aircraft

Modeling and control of hybrid-electric propulsion systems (HEPSs) is a challenging area, in particular for regional aircraft. In this research, modeling and rule-based control design for a hybrid-electrified aircraft are presented. For this purpose, real data from the ATR 42-600 as well as the modified CT7-9 turboprop engine, commercial electric machines, and battery experimental characteristics have been used to size a new version of hybrid-electric regional aircraft. Based on the dynamic modeling of HEPS, practical controllers are then designed for the turboprop engine and electric machines. It should be noted that one of the critical tasks of the control strategy for hybrid-electric propulsion is to ensure the aircraft’s safe landing. In this study, a rule-based tunable regulator is proposed to modify the conventional optimal control strategy to achieve the aircraft’s required performance over a real flight mission, in particular, to fulfill the safe landing of aircraft using the remaining battery state of charge (SOC) in the event of all-turbine failure. Finally, the results are presented to demonstrate that the proposed approach is effective for minimizing the HEPS fuel consumption, where the aircraft operational constraints, such as battery SOC and turbine overtemperature, are fulfilled at different phases of the flight mission.

Clipped DeepControl: Deep neural network two-dimensional pulse design with an amplitude constraint layer

Advanced radio-frequency pulse design used in magnetic resonance imaging has recently been demonstrated with deep learning of (convolutional) neural networks and reinforcement learning. For two-dimensionally selective radio-frequency pulses, the (convolutional) neural network pulse prediction time (a few milliseconds) was in comparison more than three orders of magnitude faster than the conventional optimal control computation. The network pulses were from the supervised training capable of compensating scan-subject dependent inhomogeneities of B0 and B1+ fields. Unfortunately, the network presented with a small percentage of pulse amplitude overshoots in the test subset, despite the optimal control pulses used in training were fully constrained. Here, we have extended the convolutional neural network with a custom-made clipping layer that completely eliminates the risk of pulse amplitude overshoots, while preserving the ability to compensate for the inhomogeneous field conditions.

Driving range evaluation based on different cabin thermal management goals of CO2 heat pumps for electric vehicles

Improving driving range is very important for electric vehicles (EVs). The use of CO2 heat pumps to replace Positive Temperature Coefficient (PTC) heaters for cabin heating is one of the most efficient choices for improving driving range in EVs. The combination of CO2 heat pumps and electric vehicles matches well with the social requirements of low-carbon, cleaner production, and sustainable development. However, heat pumps may frost under a conventional optimal discharge pressure control, resulting in a rapid drop in driving range. To solve this problem, the impact of frost on the driving range under different ambient conditions was assessed, and the failure of performance guarantee under conventional control in frost-prone conditions was deeply studied. Based on the experimental data, a heating capacity decline map was developed, and a new global performance improvement control method was proposed. Moreover, the dynamic characteristics between optimal discharge pressure control and the new control process were experimentally compared. Furthermore, a comparative analysis of driving range improvement under the global performance improvement control was carried out in three cities with typical climates. The results indicated that driving range improvement of the new method could be even as high as 10% in some conditions. Finally, the global performance improvement control method was recommended in regions with low ambient temperatures and high humidity.

Data efficient reinforcement learning and adaptive optimal perimeter control of network traffic dynamics

Existing data-driven and feedback traffic control strategies do not consider the heterogeneity of real-time data measurements. Besides, traditional reinforcement learning (RL) methods for traffic control usually converge slowly for lacking data efficiency. Moreover, conventional optimal perimeter control schemes require exact knowledge of the system dynamics and thus they would be fragile to endogenous uncertainties. To handle these challenges, this work proposes an integral reinforcement learning (IRL) based approach to learning the macroscopic traffic dynamics for adaptive optimal perimeter control. This work makes the following primary contributions to the transportation literature: (a) A continuous-time control is developed with discrete gain updates to adapt to the discrete-time sensor data. Different from the conventional RL approaches, the reinforcement interval of the proposed IRL method can be varying with respect to the real-time resolution of data measurements. Approximate optimization methods are carried out to address the curse of dimensionality of the optimal control problem with consideration on the resolution of data measurement. (b) To reduce the sampling complexity and use the available data more efficiently, the experience replay (ER) technique is introduced to the IRL algorithm. (c) The proposed method relaxes the requirement on model calibration in a “model-free” manner that enables robustness against modeling uncertainty and enhances the real-time performance via a data-driven RL algorithm. (d) The convergence of the IRL based algorithms and the stability of the controlled traffic dynamics are proven via the Lyapunov theory. The optimal control law is parameterized and then approximated by neural networks (NN), which moderates the computational complexity. Both state and input constraints are considered while no model linearization is required. Numerical examples and simulation experiments are presented to verify the effectiveness and efficiency of the proposed method.

Decentralized Data-Enabled Predictive Control for Power System Oscillation Damping

We employ a novel data-enabled predictive control (DeePC) algorithm in voltage source converter (VSC)-based high-voltage DC (HVDC) stations to perform safe and optimal wide-area control for power system oscillation damping. Conventional optimal wide-area control is model based. However, in practice, detailed and accurate parametric power system models are rarely available. In contrast, the DeePC algorithm uses only input-output data measured from the unknown system to predict the future trajectories and calculate the optimal control policy. We showcase that the DeePC algorithm can effectively attenuate interarea oscillations even in the presence of measurement noise, communication delays, nonlinear loads, and uncertain load fluctuations. We investigate the performance under different matrix structures as data-driven predictors. Furthermore, we derive a novel Min-Max DeePC algorithm to be applied independently in multiple VSC-HVDC stations to mitigate interarea oscillations, which enables decentralized and robust optimal wide-area control. Further, we discuss how to relieve the computational burden of the Min-Max DeePC by reducing the dimension of prediction uncertainty and how to leverage disturbance feedback to reduce the conservativeness of robustification. We illustrate our results with high-fidelity, nonlinear, and noisy simulations of a four-area test system.

On necessary optimality conditions and exact penalization for a constrained fractional optimal control problem

AbstractThe purpose of this article is twofold. We first develop the first‐order necessary optimality conditions for a general constrained fractional optimal control problem using calculus of variation. These conditions are of the form of fractional ordinary differential equations which reduce to the conventional Euler–Lagrange equations when the dynamical system becomes a first‐order one. Then, we prove, via the optimality conditions established, that a popular penalty method used for conventional constrained optimal control and optimization is an “exact” penalty method for the fractional control problem by showing that an optimal solution to the penalized problem satisfies the optimality conditions of the original one when the penalty parameter is sufficiently large. An example is also provided to verify the necessary optimality conditions.

PMSG Based Wind Energy Conversion System Using Intelligent MPPT with HGRSC Converter

Wind power conversion systems play a significant position in grid-coupled renewable source networks. In this paper, a permanent magnet based synchronous alternator type wind energy scheme is considered for analysis. The enhanced performance of wind power conversion could be reached by improving maximum power point tracking (MPPT) and by modernising the control circuit of the power electronic circuit. The main task is to enrich its performance level by proposing fuzzy gain scheduling (FGS) based optimal torque management for maximum power point tracking. In addition to the improved MPPT, this article analyses different topologies of direct current–direct current (DC–DC) converters such as boost converter and high-gain resonant switched capacitor converter. Comparative simulation analysis of converters with conventional optimal torque control and proposed FGS-based optimal torque control using MATLAB/simulink are presented with various wind speeds.

Vibration control of semi-active suspension by the neural network that learned the optimal preview control of MLD model

Advances in image processing technology have made it possible to measure the surface shape of the road ahead while driving. We propose a new semi-active suspension control method that considers the forward road surface shape. A vehicle model equipped with a semi-active suspension can be expressed as an MLD (Mixed Logical Dynamical) model. When the shape of the road ahead can be measured accurately, that the information on the future disturbances is available before the vehicle undergoes. In this paper, we formulate the finite time optimization problem of the MLD model in consideration of the future disturbances as a MIQP (Mixed Integer Quadratic Programming) problem in the same way as the conventional optimal control problem without future disturbance. The solution to the MIQP problem can be obtained by a commonly available solver software. However, because the MIQP problem is classified as NP-hard, it is hard to obtain the control action within the control cycle period required by the vibration control problem with general computers for vehicles. In this paper, we achieve this reduction in computational load by constructing an approximation function for the designed controller. A multilayer neural network is adopted for the approximation. The performance evaluation of the proposed control method was evaluated by a simulation. In the simulation study, the proposed method was able to achieve better ride comfort with the equivalent suspension stroke compared to the traditional MLD predictive control and the Skyhook approximation methods. Moreover, the proposed method enables to generate the control signal within the control cycle period.