Optimal Control Of Systems Research Articles

Design of Optimal FOPI Controller for Two-Area Time-Delayed Load Frequency Control System with Demand Response

Design of Optimal FOPI Controller for Two-Area Time-Delayed Load Frequency Control System with Demand Response

Modeling and optimal control of nonlinear fractional order chaotic system of factors affecting money laundering: genetic algorithms and particle swarm optimization

ABSTRACT The purpose of this article is to model and optimally control the non-linear chaotic system of the fractional order of factors affecting money laundering. The model of factors affecting money laundering was expressed as a system of fractional order differential equation. Due to the presence of chaos in this model, optimal control was provided for it. For optimal control of the chaos in the proposed model, particle swarm optimization algorithm and genetic algorithm were used. The implementation and simulation of this research was done by coding in MATLAB software. The results of the research show that the optimal control applied to the model can control the factors affecting money laundering. When the controller is applied from scratch, the results of the genetic algorithm method are excellent. All the results obtained for the particle swarm optimization method show that this method is also very successful and the results are very close to the genetic algorithm method. Due to the necessity of conducting this research, it can be mentioned that money laundering as an economic crime has a significant negative impact on the economic growth and development of countries.

Optimal Formation Control of Second-Order Heterogeneous Multiagent Systems Using Adaptive Predefined-Time Strategy

Optimal Formation Control of Second-Order Heterogeneous Multiagent Systems Using Adaptive Predefined-Time Strategy

Inverse Optimal Adaptive Control of Canonical Nonlinear Systems With Dynamic Uncertainties and Its Application to Industrial Robots

Inverse Optimal Adaptive Control of Canonical Nonlinear Systems With Dynamic Uncertainties and Its Application to Industrial Robots

Optimal proportional-integral speed control for closed-loop engine timing system

In internal combustion engines, adjusting the air-fuel ratio is essential to control the speed and minimize the burnt fuel. The throttle opening is the actuator to control the air-fuel. A better design for the used/conventional controller can give a better response without additional cost. In this work, the proposed controller gains of the proportional-integral (PI) controller are tuned to enhance the speed in constant and variable drive cycle modes. The tuning process is conducted based on two of the most efficient performance indices used in this field. The performance indices are integral absolute error (IAE) and integral time absolute error (ITAE). The optimization problem is solved using three reliable stochastic optimization algorithms to ensure mature convergence of the solutions, to avoid local optima solutions, and to ensure effective shrinking of the search space. The optimization algorithms are teaching-learning-based optimization (TLBO), particle swarm optimization (PSO), and genetic algorithm (GA). Different simulations are conducted to validate the results. The results are compared with conventional tuning methods regarding the system's time response.

Optimal Consensus Control for Multi-Agent Systems With Unknown Dynamics and States of Leader: A Distributed KREM Learning Method

Optimal Consensus Control for Multi-Agent Systems With Unknown Dynamics and States of Leader: A Distributed KREM Learning Method

Actor–Critic-Based Predefined-Time Fuzzy Adaptive Optimal Control for Uncertain Nonlinear Systems With Input Saturation

Actor–Critic-Based Predefined-Time Fuzzy Adaptive Optimal Control for Uncertain Nonlinear Systems With Input Saturation

Intelligent optimal control of nonlinear diabetic population dynamics system using a genetic algorithm

Diabetes is a chronic disease affecting millions of people worldwide. Several studies have been carried out to control the diabetes problem, involving both linear and non-linear models. However, the complexity of linear models makes it impossible to describe the diabetic population dynamic in depth. To capture more detail about this dynamic, non-linear terms were introduced into the mathematical models, resulting in more complicated models strongly consistent with reality (capable of re-producing observable data). The most commonly used methods for control estimation are Pantryagain’s maximum principle and Gumel’s numerical method. However, these methods lead to a costly strategy regarding material and human resources; in addition, diabetologists cannot use the formulas implemented by the proposed controls. In this paper, the authors propose a straightforward and well-performing strategy based on non-linear models and genetic algorithms (GA) that consists of three steps: 1) discretization of the considered non-linear model using classical numerical methods (trapezoidal rule and Euler–Cauchy algorithm); 2) estimation of the optimal control, in several points, based on GA with appropriate fitness function and suitable genetic operators (mutation, crossover, and selection); 3) construction of the optimal control using an interpolation model (splines). The results show that the use of the GA for non-linear models was successfully solved, resulting in a control approach that shows a significant decrease in the number of diabetes cases and diabetics with complications. Remarkably, this result is achieved using less than 70% of available resources.

Online Pareto optimal control of mean-field stochastic multi-player systems using policy iteration

Online Pareto optimal control of mean-field stochastic multi-player systems using policy iteration

Optimal control of a heat pump-based energy system for space heating and hot water provision in buildings: Results from a field test

This paper presents and discusses results from a field test that uses model predictive control (MPC) to optimise the operation of a multi-source heat pump-based energy system for space heating and hot water provision in a building. The objective of the optimisation is to minimise the electricity consumption of the heat pump using flexibility from the heat sources, the space heating and domestic hot water tanks while ensuring end-user comfort and system constraints. The field test was performed in the context of the RES4BUILD project. The integrated system consists of photovoltaic-thermal (PVT) collectors, an advanced vapour-compression multi-source heat pump and water buffer tanks for space heating and hot water needs. The heat pump utilises a solar buffer, a borehole thermal energy storage (BTES) and air as heat sources. The solar buffer is supplied with heat from the PVT collectors. The optimal operation of the system is obtained by monitoring and controlling the interactions between the different system components using MPC, taking into account the weather and heat load forecasts. Results have shown that MPC has a potential and added value for the optimal operation of multi-source heat pumps in real-life while considering system constraints and user behaviour to ensure thermal comfort. However, significant effort and expert knowledge are needed to develop the sufficiently accurate system models required by this control approach. The outcomes and conclusions of this work are therefore a basis for further development of such control approaches to improve their replicability and feasibility on a large scale, considering the diverse nature of energy system components in buildings.

Reinforcement learning for optimal control of linear impulsive systems with periodic impulses

This paper focuses on the finite- and infinite-horizon optimal control problems of linear impulsive systems with periodic impulses under the quadratic performance index. Necessary and sufficient conditions for the optimal impulsive system are derived in terms of hybrid Riccati equations by utilizing the variational method and the collocation method combined with a time-varying Lyapunov function. Different from the existing model-based impulsive control schemes, three reinforcement learning (RL)-based algorithms are proposed to solve the optimal impulsive controller and hybrid controller for the impulsive system without the exact knowledge of the system dynamics. The asymptotical stability of the impulsive control system and the convergence of the RL-based algorithms are proved rigorously. Finally, a numerical simulation illustrates the effectiveness of the proposed control methods.

Optimal supervisory control of discrete event systems for cyclic tasks

In this paper, we investigate the problem of optimal supervisory control for cyclic tasks in the context of discrete-event systems (DES). We consider the completion of each single task as the visit of a marked state, and overall control objective is to complete tasks cyclically in the sense that marked states are visited infinitely often. Following the standard optimal supervisory control framework, two types of costs, disable cost and occurrence cost, are considered. However, instead of considering the standard accumulated total cost or the average cost per event, we consider the measure for the control performance using the average cost per task. We show that such an optimality measure is more suitable for tasks that need to be completed cyclically. Our goal is to design a live and non-blocking supervisor such that the average cost per task in the worst-case is minimized. To solve the problem, we propose a game-theoretical approach by converting the optimal control problem as a two-player graph game. Structural properties of the converted game are discussed. In particular, we show that this game can be solved by a set of mean payoff decision problems, for which effective algorithms exist. Our problem can be considered as a special instance of the general ratio-game in the literature. However, by exploring new structural property for this problem, we achieve superior computational efficiency when compared to the conventional solution designed for more general problem formulations. Illustrative examples are provided to demonstrate the proposed algorithm.

Hierarchical approximate optimal interaction control of human-centered modular robot manipulator systems: A Stackelberg differential game-based approach

A Stackelberg game-based approximate optimal interaction control approach is presented for human-centered modular robot manipulator (MRM) systems. Joint torque feedback (JTF) technique is utilized to form the MRM dynamic model. The major objective of optimal control with human–robot collaboration (HRC) is transformed into approximating Stackelberg equilibrium by adopting Stackelberg game governed between the human and the MRM that are regarded as players with different hierarchical level in interaction process. On the basis of the adaptive dynamic programming (ADP), the approximate optimal interaction control policy with HRC task is developed via critic neural network (NN)-based Stackelberg game manner for addressing Hamilton–Jacobian (HJ) equations. The position tracking error is ultimately uniformly bounded (UUB) according to the Lyapunov theory. Experiment results demonstrate the effectiveness of the proposed method.

Well‐posedness of quantum stochastic differential equations driven by fermion Brownian motion in noncommutative Lp‐space

This paper is concerned with quantum stochastic differential equations driven by the fermion field in noncommutative space for . First, we investigate the existence and uniqueness of ‐solutions of quantum stochastic differential equations in an infinite time horizon by using the noncommutative Burkholder–Gundy inequality given by Pisier and Xu and the noncommutative generalized Minkowski inequality. Then, we investigate the stability, self‐adjointness, and Markov properties of ‐solutions and analyze the error of numerical schemes of quantum stochastic differential equations. The results of this paper can be utilized for investigating the optimal control of quantum stochastic systems with infinite dimensions.

Physics-Informed Representation and Learning: Control and Risk Quantification

Optimal and safety-critical control are fundamental problems for stochastic systems, and are widely considered in real-world scenarios such as robotic manipulation and autonomous driving. In this paper, we consider the problem of efficiently finding optimal and safe control for high-dimensional systems. Specifically, we propose to use dimensionality reduction techniques from a comparison theorem for stochastic differential equations together with a generalizable physics-informed neural network to estimate the optimal value function and the safety probability of the system. The proposed framework results in substantial sample efficiency improvement compared to existing methods. We further develop an autoencoder-like neural network to automatically identify the low-dimensional features in the system to enhance the ease of design for system integration. We also provide experiments and quantitative analysis to validate the efficacy of the proposed method. Source code is available at https://github.com/jacobwang925/path-integral-PINN.

Robustness improvement of optimal control in terms of RBFNN with empirical model reduction and transfer learning

This paper proposes a method to compute solutions of optimal controls for dynamic systems in terms of radial basis function neural networks (RBFNN) with Gaussian neurons. The RBFNN is used to compute the value function from Hamilton–Jacobi–Bellman equation with the policy iteration. The concept of dominant system is introduced to create initial coefficients of the neural networks to stabilise unstable systems and guarantee the convergence of policy iteration. Model reduction and transfer learning techniques are introduced to improve robustness of RBFNN optimal control, and reduce computational time. Numerical and experimental results show that the resulting optimal control has excellent control performance in stabilisation and trajectory tracking, and much-improved robustness to disturbances and model uncertainties even when the system responses move to a domain of the state space that is larger than the domain where the neural networks are trained.

Extended state-based finite-time fuzzy optimal recoil control for nonlinear drilling riser systems after emergency disconnection

To guarantee the safety and reliability of drilling riser after emergency disconnection, it is significant to investigate and refrain recoil response of the riser. This paper deals with the problem of Takagi–Sugeno (T-S) fuzzy recoil dynamic modeling and optimal recoil control of nonlinear deepwater drilling riser systems subject to friction resistance of fluid discharge and platform heave motion. First, a nonlinear recoil control model of coupled riser-tensioner is proposed by taking the nonlinear top tension of tensioner into account. Then, a T-S fuzzy dynamic model of the riser-tensioner system is established to approximate the original nonlinear one by using fuzzy modeling scheme. Third, an augmented T-S fuzzy model of riser system is proposed, where the linear exosystem model of friction resistance and platform heave motion is utilized. Fourth, a finite-time fuzzy optimal recoil controller is designed to suppress the recoil response of the riser, the existence and design algorithm of the fuzzy optimal recoil controller are derived. Simulation results demonstrate that the nonlinear recoil model is more accurate than the existing linear one to describe the recoil characteristics of the riser, and the fuzzy optimal recoil controllers are effective to reduce recoil responses and guarantee the safety of the riser significantly.

Optimal operation and control of hybrid power systems with stochastic renewables and FACTS devices: An intelligent multi-objective optimization approach

This paper delves into the increasingly complex domain of Optimal Power Flow (OPF) within modern power systems, enhanced by the integration of unpredictable renewable energy sources. The research originally integrates stochastic photovoltaic and wind energy sources, along with a suite of Flexible AC Transmission System (FACTS) components – including thyristor-controlled series compensators, static VAR compensators, and thyristor-controlled phase shifters. The primary objective is to solve the OPF problem by reducing generation costs while accommodating the variable nature of renewable energy sources and load demands. This study prioritizes the examination of both constant and fluctuating load requirements. The inherent variability of PV and wind energy, along with load demand, is captured through the modelling of probability density functions. This approach enables a more detailed optimization process, incorporating not just the cost of thermal energy generation but also the scheduling costs of renewable sources and associated penalty costs. Moreover, the study examines the strategic placement and sizing of FACTS components, an aspect essential in minimizing the overall cost of power production. Employing both single- and multi-objective optimization algorithms, the research addresses the OPF problem in a modified IEEE-30 bus system through various case studies. The application of the recently developed flow direction algorithm, including its multi-objective variant with an ε-based constraint-handling mechanism to OPF problem is the primary contributions of this work. The results, benchmarked against several advanced metaheuristic algorithms, reveal the proposed algorithm's superior performance. This comprehensive study not only underscores the potential of integrating renewable energy sources into the grid but also highlights the efficacy of intelligent optimization strategies in managing the complexities of modern power systems.

Combining hybrid metaheuristic algorithms and reinforcement learning to improve the optimal control of nonlinear continuous-time systems with input constraints

This paper proposes an innovative method for achieving optimal tracking control in nonlinear continuous-time systems with input constraints. The method combines reinforcement learning and hybrid metaheuristics to enhance the controller’s performance. Specifically, a hybrid metaheuristic algorithm is employed to optimize the hyperparameters of a critic neural network, which serves as the system’s controller. The proposed approach is evaluated through extensive simulation studies on a nonlinear system with input constraints. Results demonstrate its superiority over traditional control techniques in terms of accuracy, timeliness, and stability. Notably, the approach effectively eliminates overshoot and steady-state error while providing precise and prompt tracking and showcasing remarkable robustness against model uncertainties. By synergistically integrating reinforcement learning and hybrid metaheuristics, this approach represents a significant advancement in enhancing the control performance of complex nonlinear systems. The simulation studies confirm superiority of the proposed approach over existing techniques, offering a promising solution for achieving optimal tracking control in nonlinear systems with input constraints. This approach holds potential for a wide range of applications, including robotics, aerospace, and manufacturing, where precise and prompt tracking control is critical.

Optimal control for both forward and backward discrete-time systems

Forward discrete-time systems use past information to update the current state, while backward discrete-time systems use future information to update the current state. This study focuses on optimal control problems within the context of forward and backward discrete-time systems. We begin by investigating a general optimal control problem for both forward and backward discrete-time systems. Leveraging the inherent properties of these systems and the Bellman optimality principle, we derive recursive equations as a means to solve such optimal control problems. Using these recursive equations, we obtain analytical expressions for both the optimal controls and optimal values of bang–bang and linear quadratic optimal control problems. Finally, we present a numerical example and an industrial wastewater treatment problem to illustrate and demonstrate our findings.