Optimal Control Applications and Methods最新文献

{"title":"Proximal policy optimization learning based control of congested freeway traffic","authors":"Shurong Mo, Nailong Wu, Jie Qi, Anqi Pan, Zhiguang Feng, Huaicheng Yan, Yueying Wang","doi":"10.1002/oca.3068","DOIUrl":"https://doi.org/10.1002/oca.3068","url":null,"abstract":"Abstract In this paper, a delay compensation feedback controller based on reinforcement learning is proposed to adjust the time interval of the adaptive cruise control (ACC) vehicle agents in the traffic congestion by introducing the proximal policy optimization (PPO) scheme. The high‐speed traffic flow is characterized by a two‐by‐two Aw Rasle Zhang nonlinear first‐order partial differential equations (PDEs). Unlike the backstepping delay compensation control, 23 the PPO controller proposed in this paper consists of the current traffic flow velocity, the current traffic flow density and the previous one step control input. Since the system dynamics of the traffic flow are difficult to be expressed mathematically, the control gains of the three feedback can be determined via learning from the interaction between the PPO and the digital simulator of the traffic system. The performance of Lyapunov control, backstepping control and PPO control are compared with numerical simulation. The results demonstrate that PPO control is superior to Lyapunov control in terms of the convergence rate and control efforts for the traffic system without delay. As for the traffic system with unstable input delay value, the performance of PPO controller is also equivalent to that of backstepping controller. Besides, PPO is more robust than backstepping controller when the parameter is sensitive to Gaussian noise.","PeriodicalId":105945,"journal":{"name":"Optimal Control Applications and Methods","volume":"20 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135166093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A shape parameter insensitive CRBFs‐collocation for solving nonlinear optimal control problems","authors":"Ahmed E. Seleit, Tarek A. Elgohary","doi":"10.1002/oca.3063","DOIUrl":"https://doi.org/10.1002/oca.3063","url":null,"abstract":"Abstract In this work, we introduce a Coupled Radial Basis Functions collocation ( CRBFs‐Coll ) approach for solving optimal control problems. CRBFs are real‐valued Radial Basis Functions (RBFs) augmented with a conical spline. They show insensitivity to the shape parameter resulting in robust behavior in function approximation. The method is applied to classical nonlinear optimal control problems: Zermelo's problem, a Duffing oscillator with various boundary conditions, and a nonlinear pendulum on a cart problem. The nonlinear optimal control problem is solved by deriving the necessary conditions for optimality followed by collocation using CRBFs as basis functions for approximating the two‐point boundary value problem (TPBVP). The resulting system of nonlinear algebraic equations (NAEs) is then solved using a standard solver. Unlike existing methods that rely on nodal distributions that are denser at the boundaries to obtain a solution, the present CRBFs‐Coll approach is capable of solving the optimal control problem on uniform nodes without the need for interpolation. The present CRBFs‐Coll approach is shown to be simple to implement and provides accurate results over an equidistant nodal distribution while maintaining a continuous representation of the control and states.","PeriodicalId":105945,"journal":{"name":"Optimal Control Applications and Methods","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136212950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stochastic maximum principle for moving average control system","authors":"Yuhang Li, Yuecai Han, Yanwei Gao","doi":"10.1002/oca.3059","DOIUrl":"https://doi.org/10.1002/oca.3059","url":null,"abstract":"Abstract In this paper, we consider the stochastic optimal control problem for moving average control system. The corresponding moving average stochastic differential equation is a kind of integral differential equations. We prove the existence and uniqueness of the solution of the moving average stochastic differential equations. We obtain the stochastic maximum principle of the moving average optimal control system by introducing a kind of generalized anticipated backward stochastic differential equations. We prove the existence and uniqueness of the solution of this adjoint equation, which is singular at 0. As an application, the linear quadratic moving average control problem is investigated to illustrate the main results.","PeriodicalId":105945,"journal":{"name":"Optimal Control Applications and Methods","volume":"215 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135254325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Massively parallelizable proximal algorithms for large‐scale stochastic optimal control problems","authors":"Ajay K. Sampathirao, Panagiotis Patrinos, Alberto Bemporad, Pantelis Sopasakis","doi":"10.1002/oca.3054","DOIUrl":"https://doi.org/10.1002/oca.3054","url":null,"abstract":"Abstract Scenario‐based stochastic optimal control problems suffer from the curse of dimensionality as they can easily grow to six and seven figure sizes. First‐order methods are suitable as they can deal with such large‐scale problems, but may perform poorly and fail to converge within a reasonable number of iterations. To achieve a fast rate of convergence and high solution speeds, in this article, we propose the use of two proximal quasi‐Newtonian limited‐memory algorithms— minfbe applied to the dual problem and the Newton‐type alternating minimization algorithm ( nama )—which can be massively parallelized on lockstep hardware such as graphics processing units. In particular, we use minfbe and nama to solve scenario‐based stochastic optimal control problems with affine dynamics, convex quadratic cost functions (with the stage cost functions being strongly convex in the control variable) and joint state‐input convex constraints. We demonstrate the performance of these methods, in terms of convergence speed and parallelizability, on large‐scale problems involving millions of variables.","PeriodicalId":105945,"journal":{"name":"Optimal Control Applications and Methods","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135648456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An enhanced arithmetic optimization algorithm for optimal control of reactive power","authors":"Shuvam Sahay, Ramanaiah Upputuri, Pooja Kumari, Niranjan Kumar","doi":"10.1002/oca.3061","DOIUrl":"https://doi.org/10.1002/oca.3061","url":null,"abstract":"Abstract In this article, an enhanced arithmetic optimization algorithm (EAOA) is utilized to resolve the optimal reactive power dispatch problem (ORPD) of power plants, which is a non‐linear, non‐smooth, complex optimization problem. Typically, it is formulated as a constrained optimal power flow problem. This paper utilizes the gamma distribution to generate initial random solutions, which improves the accuracy of the arithmetic optimization algorithm (AOA). The original mode of deviation of math optimizer accelerated (MOA) is replaced with the improved pattern of change in the prey's energy in Harris Hawk Optimization (HHO), which creates a superior balance between the exploration and exploitation of AOA. This paper implements logarithmic and exponential operators in place of division and multiplication operators, which improves the exploration ability of AOA and also utilizes the gamma distribution in the generation of random numbers, which are essential for the selection of operators in both search phase which enlarges the search area and improves the global optimum solution. A parametric analysis is performed on 10 benchmark functions for nine possible values before selecting the algorithm's initial parameters. A comparative statistical analysis along with Friedman's test is carried out on 23 benchmark functions to test the overall performance as compared to Sine‐Cosine Algorithm (SCA), Swarm‐Salp Algorithm, Grey Wolf Optimization (GWO), and basic Arithmetic Optimization Algorithm (AOA). EAOA is applied to the IEEE 57 bus system for optimal reactive power control. EAOA reports a significant reduction in a power loss of 23.2 MW, which is 18.596% smaller than the system's base case power loss of 28.5 MW as compared to Artificial Bee Colony (ABC), Firefly Algorithm (FA), Bat‐inspired Algorithm (BAT), Cuckoo Search Algorithm (CSA), and Modified Ant Lion Algorithm (MALO) which reports a reduction in a power loss of 14.73%, 15.43%, 15.43%, 16.14%, and 16.14% respectively. EAOA reduces the TVD to 0.76 pu, compared to ABC, FA, BAT, CSA, and MALO, which minimizes the TVD to 0.84, 0.82, 0.88, 0.82, and 0.79, respectively. This proves that EAOA performs better in resolving ORCP problems regarding the quality of solutions and convergence. A detailed comparative statistical analysis of EAOA with CSA, BAT, and WOA (Whale Optimization Algorithm) is conducted in terms of Probability Distribution Functions (PDF) and Cumulative Distribution Functions (CDF), along with the Wilcoxson sign rank test, which proves that EAOA gives the solution with a higher degree of precision.","PeriodicalId":105945,"journal":{"name":"Optimal Control Applications and Methods","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135744880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Differential privacy optimal control with asymmetric information structure","authors":"Di Zhang, Yuan‐Hua Ni","doi":"10.1002/oca.3062","DOIUrl":"https://doi.org/10.1002/oca.3062","url":null,"abstract":"Abstract A linear‐quadratic optimal control is investigated in this article under the differential privacy (DP) philosophy to trade off the performance and privacy of sensitive information, where the two controllers have asymmetric information structure and some prescribed signal needs to be tracked. Note that the system output and tracking signal are always sensitive and easy to be filched by adversaries; thus the DP methodology is explored to protect them. Under DP Gaussian mechanism, the optimal linear controllers are first studied for finite‐horizon and infinite‐horizon problems. Then, the bounds of mean‐square error of steady‐state Kalman filter estimator is provided, and the DP parameter design will be guided that characterizes the privacy of sensitive information. As the DP Gaussian noise will degrade the controlled performance, the degraded performance is quantitatively calculated. Finally, a numerical example is given that shows the efficiency of obtained results.","PeriodicalId":105945,"journal":{"name":"Optimal Control Applications and Methods","volume":"128 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135744879","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal control problem governed by a highly nonlinear singular Volterra equation: Existence of solutions and maximum principle","authors":"Dariusz Idczak","doi":"10.1002/oca.3057","DOIUrl":"https://doi.org/10.1002/oca.3057","url":null,"abstract":"Abstract We consider a Lagrange optimal control problem for a Volterra integral equation of fractional potential type. We prove a theorem on the existence of an optimal solution and derive a maximum principle. The proof of the existence theorem is based on the lower closure theorem for orientor fields due to Cesari and Filippov‐type selection theorem due to Rockafellar. The proof of the maximum principle is based on an extremum principle for smooth problems proved in Idczak and Walczak ( Games . 2020;11:56).","PeriodicalId":105945,"journal":{"name":"Optimal Control Applications and Methods","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135243161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite‐horizon optimal trajectory control of near space hypersonic vehicle with multi‐constraints","authors":"Rongsheng Xia, Chunlei Bu, Xiaohui Yan, Tongle Zhou","doi":"10.1002/oca.3058","DOIUrl":"https://doi.org/10.1002/oca.3058","url":null,"abstract":"Abstract In this article, a finite‐horizon optimal trajectory control strategy is developed for near space hypersonic vehicle (NSHV) longitudinal model with multi‐constraints including external disturbance, system modeling error, and input saturation. The whole control process has two parts: inner‐loop attitude control and outer‐loop trajectory control. First, the feedback linearization method is applied to design a tracking controller for outer‐loop system, and reference signals for inner‐loop attitude control can be obtained using Newton iteration method. Second, for the inner‐loop attitude system with multi‐constraints, a finite‐horizon optimal tracking control scheme consists of feedforward control input and adaptive dynamic programming based optimal feedback controller is designed. In this way, not only the adverse effects of above multi‐constraints are eliminated, but also the optimally tracking performances are guaranteed. Finally, the Lyapunov analysis method is utilized to ensure the stability of the entire closed‐loop control system, and simulation tests with respect to NSHV longitudinal trajectory tracking are supplied to verify the availability of the proposed strategy.","PeriodicalId":105945,"journal":{"name":"Optimal Control Applications and Methods","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135344593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Implementation of suitable optimal control strategy through introspection of different delay induced mathematical models for leprosy: A comparative study","authors":"Salil Ghosh, Amit Kumar Roy, Priti Kumar Roy","doi":"10.1002/oca.3060","DOIUrl":"https://doi.org/10.1002/oca.3060","url":null,"abstract":"Abstract Involving intracellular delay into a mathematical model and investigating the delayed systems by incorporating optimal control is of great importance to study the cell‐to‐cell interactions of the disease leprosy. Keeping this in mind, we have proposed two different variants of delay‐induced mathematical models with time delay in the process of proliferation of Mycobacterium leprae bacteria from the infected cells and a similar delay to indicate the time‐lag both in the proliferation of M. leprae bacteria and the infection of healthy cells after getting attached with the bacterium. In this research article, we have performed a comparative study between these two delayed systems equipped with optimal control therapeutic approach to determine which one acts better to unravel the complexities of the transmission and dissemination of leprosy into a human body as far as scheduling a perfect drug dose regime depending on this analysis remains our main priority. Our investigations suggest that adopting optimal control strategy consisting of combined drug therapy eliminates the oscillatory behavior of the delayed systems completely. Existence of optimal control solutions are demonstrated in detail. To achieve the optimal control profiles of the drug therapies and to obtain the optimality systems, Pontryagin's Minimum principle with delay in state are employed for our controlled systems. Furthermore, the analytical as well as the numerical outcomes obtained in this research article indicate that the delayed bacterial proliferation and M. leprae ‐induced infection model equipped with optimal control policy performs more realistically and accurately in the form of a safe and cost‐effective double‐drug therapeutic regimen. All the mathematical results are verified numerically and the numerical results are compared with some recent clinical data in our article as well.","PeriodicalId":105945,"journal":{"name":"Optimal Control Applications and Methods","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135719669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite‐time observer‐based fault detection with nonfragile control design for switched nonlinear networked systems with time‐delays","authors":"Dhanya Velmurugan, Arunkumar Arumugam, Karthick Arumugam","doi":"10.1002/oca.3056","DOIUrl":"https://doi.org/10.1002/oca.3056","url":null,"abstract":"Abstract The strategy of observer‐based nonfragile control and fault‐detection over finite‐time horizon has been examined for a class of uncertain switched nonlinear networked control systems (NNCSs) contingent with time varying delays inferred by the networks from sensor to controller and controller to actuator. Also, in this study, an observer‐based fault detection control has been designed for the NNCSs. By making use of fault detection control as residual generator, the conveyed fault detection problem is then transformed into attenuation problem. By employing multiple Lyapunov function and average dwell time (ADT) approach, sufficient conditions in terms of linear matrix inequalities (LMIs) ensures the finite‐time boundedness (FTB) criterion of the resulting switched NNCSs with a prescribed disturbance attenuation. Subsequently, the preferred LMIs constraints realizes the controller and observer gains. Finally, two numerical examples are proffered to showcase the efficacity of the proposed technique.","PeriodicalId":105945,"journal":{"name":"Optimal Control Applications and Methods","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135926308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}