Pub Date : 2024-11-26DOI: 10.1016/j.ejcon.2024.101149
Hue Luu Thi , Van Chung Nguyen , Tung Lam Nguyen
This paper introduces a new method to control a 5-DOF tower crane (3DTC). By considering the 3DTC as a flat system, a time-optimal trajectory is proposed for the payload. System states and control signal references can be calculated based on the flatness theory. In addition, the 3DTC works in an environment containing many factors impacting control performance and the system states are hard to measure. An adaptive finite-time extended state observer (AFT-ESO) is introduced to solve these problems. With AFT-ESO, system states and lumped disturbances can be estimated accurately, facilitating the prediction for Lyapunov-based model predictive control (LMPC) when an accurate model is required. The LMPC takes advance of the second-order sliding mode control stability conditions as a strict constraint to guarantee the global stabilization of the closed-loop system. Finally, simulations based on the quasi-physical model are proposed to show the effectiveness and robustness of the proposed strategy.
{"title":"Adaptive finite-time extended state observer-based model predictive control with Flatness motivated trajectory planning for 5-DOF tower cranes","authors":"Hue Luu Thi , Van Chung Nguyen , Tung Lam Nguyen","doi":"10.1016/j.ejcon.2024.101149","DOIUrl":"10.1016/j.ejcon.2024.101149","url":null,"abstract":"<div><div>This paper introduces a new method to control a 5-DOF tower crane (3DTC). By considering the 3DTC as a flat system, a time-optimal trajectory is proposed for the payload. System states and control signal references can be calculated based on the flatness theory. In addition, the 3DTC works in an environment containing many factors impacting control performance and the system states are hard to measure. An adaptive finite-time extended state observer (AFT-ESO) is introduced to solve these problems. With AFT-ESO, system states and lumped disturbances can be estimated accurately, facilitating the prediction for Lyapunov-based model predictive control (LMPC) when an accurate model is required. The LMPC takes advance of the second-order sliding mode control stability conditions as a strict constraint to guarantee the global stabilization of the closed-loop system. Finally, simulations based on the quasi-physical model are proposed to show the effectiveness and robustness of the proposed strategy.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"81 ","pages":"Article 101149"},"PeriodicalIF":2.5,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142746072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-24DOI: 10.1016/j.ejcon.2024.101147
Owais Khan , Ghulam Mustafa , Nouman Ashraf , Muntazir Hussain , Abdul Qayyum Khan , Muhammad Asim Shoaib
Controlling flexible joint robots has drawn the attention of many industry professionals during the past two decades. It is a difficult task because various structural features that make the control of rigid robots easier, such as passivity of the motor torque to link velocity, full actuation, and separate control of each joint, are lost when we consider joint flexibility in the control design of these robots. However, we must consider joint flexibility while designing the controller; otherwise, the system may become unstable. In this article, we devise a robust model predictive controller scheme for flexible joint robots modeled as sampled-data Lipschitz nonlinear systems with unknown bounded disturbances. It is assumed that the state of the system is accessible for feedback. Therefore, a state-feedback control law is designed using a robust stability criterion and can be computed by solving an online optimization problem. The control law optimizes the performance index by reducing its worst-case value. The proposed control design scheme is applied to the one-link flexible joint robot. Simulation results validate the effectiveness of the controller in handling nonlinearities while minimizing the effect of unknown bounded disturbances.
{"title":"Robust model predictive control of sampled-data Lipschitz nonlinear systems: Application to flexible joint robots","authors":"Owais Khan , Ghulam Mustafa , Nouman Ashraf , Muntazir Hussain , Abdul Qayyum Khan , Muhammad Asim Shoaib","doi":"10.1016/j.ejcon.2024.101147","DOIUrl":"10.1016/j.ejcon.2024.101147","url":null,"abstract":"<div><div>Controlling flexible joint robots has drawn the attention of many industry professionals during the past two decades. It is a difficult task because various structural features that make the control of rigid robots easier, such as passivity of the motor torque to link velocity, full actuation, and separate control of each joint, are lost when we consider joint flexibility in the control design of these robots. However, we must consider joint flexibility while designing the controller; otherwise, the system may become unstable. In this article, we devise a robust model predictive controller scheme for flexible joint robots modeled as sampled-data Lipschitz nonlinear systems with unknown bounded disturbances. It is assumed that the state of the system is accessible for feedback. Therefore, a state-feedback control law is designed using a robust stability criterion and can be computed by solving an online optimization problem. The control law optimizes the performance index by reducing its worst-case value. The proposed control design scheme is applied to the one-link flexible joint robot. Simulation results validate the effectiveness of the controller in handling nonlinearities while minimizing the effect of unknown bounded disturbances.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"81 ","pages":"Article 101147"},"PeriodicalIF":2.5,"publicationDate":"2024-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142719689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The increasing prominence of wind energy underscores the need to prioritize cybersecurity measures, with a focus on recognizing vulnerabilities and formulating defensive strategies. Specifically, False Data Injection (FDI) attacks targeted at the communication between rotor speed sensors and wind turbine (WT) controllers can disrupt operations, potentially causing drive-train overload and reduced power generation efficiency. To mitigate these threats, this study introduces an adaptive prescribed performance optimal secure control strategy that employs a reinforcement learning (RL) to compensate the detrimental effects of FDI attack as well as actuator fault. To derive the optimal control policy, the complex Hamilton–Jacobi–Bellman (HJB) equation is solved, facilitated by an actor–critic-based RL approach, where actor and critic neural network (NN) manage control actions and performance assessment. To detect FDI attack, an anomaly detection is developed using a fixed-time disturbance observer. Stability analysis is performed using Lyapunov theory which guarantees semi-global uniformly ultimately bounded (SGUUB) of the error signal. To rigorously validate our approach, we implemented the controller using FAST code for the NREL WindPACT 1.5 MW reference turbine. Simulation results convincingly demonstrate the effectiveness of our proposed control strategy, confirming its potential to enhance both performance and security in real-world WT operations.
{"title":"Self-learning-based secure control of wind power generation systems under cyber threat: Ensuring prescribed performance","authors":"Mahmood Mazare , Hossein Ramezani , Mostafa Taghizadeh","doi":"10.1016/j.ejcon.2024.101152","DOIUrl":"10.1016/j.ejcon.2024.101152","url":null,"abstract":"<div><div>The increasing prominence of wind energy underscores the need to prioritize cybersecurity measures, with a focus on recognizing vulnerabilities and formulating defensive strategies. Specifically, False Data Injection (FDI) attacks targeted at the communication between rotor speed sensors and wind turbine (WT) controllers can disrupt operations, potentially causing drive-train overload and reduced power generation efficiency. To mitigate these threats, this study introduces an adaptive prescribed performance optimal secure control strategy that employs a reinforcement learning (RL) to compensate the detrimental effects of FDI attack as well as actuator fault. To derive the optimal control policy, the complex Hamilton–Jacobi–Bellman (HJB) equation is solved, facilitated by an actor–critic-based RL approach, where actor and critic neural network (NN) manage control actions and performance assessment. To detect FDI attack, an anomaly detection is developed using a fixed-time disturbance observer. Stability analysis is performed using Lyapunov theory which guarantees semi-global uniformly ultimately bounded (SGUUB) of the error signal. To rigorously validate our approach, we implemented the controller using FAST code for the NREL WindPACT 1.5 MW reference turbine. Simulation results convincingly demonstrate the effectiveness of our proposed control strategy, confirming its potential to enhance both performance and security in real-world WT operations.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"81 ","pages":"Article 101152"},"PeriodicalIF":2.5,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142719688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.ejcon.2024.101150
Gabriele Maroni, Loris Cannelli, Dario Piga
Common regularization algorithms for linear regression, such as LASSO and Ridge regression, rely on a regularization hyperparameter that balances the trade-off between minimizing the fitting error and the norm of the learned model coefficients. As this hyperparameter is scalar, it can be easily selected via random or grid search optimizing a cross-validation criterion. However, using a scalar hyperparameter limits the algorithm’s flexibility and potential for better generalization. In this paper, we address the problem of linear regression with -regularization, where a different regularization hyperparameter is associated with each input variable. We optimize these hyperparameters using a gradient-based approach, wherein the gradient of a cross-validation criterion with respect to the regularization hyperparameters is computed analytically through matrix differential calculus. Additionally, we introduce two strategies tailored for sparse model learning problems aiming at reducing the risk of overfitting to the validation data. Numerical examples demonstrate that the proposed multi-hyperparameter regularization approach outperforms LASSO, Ridge, and Elastic Net regression in terms of score both in a static regression and in a system identification problem. Moreover, the analytical computation of the gradient proves to be more efficient in terms of computational time compared to automatic differentiation, especially when handling a large number of input variables, with an improvement of more than an order of magnitude. Application to the identification of over-parameterized Linear Parameter-Varying models is also presented.
{"title":"Gradient-based bilevel optimization for multi-penalty Ridge regression through matrix differential calculus","authors":"Gabriele Maroni, Loris Cannelli, Dario Piga","doi":"10.1016/j.ejcon.2024.101150","DOIUrl":"10.1016/j.ejcon.2024.101150","url":null,"abstract":"<div><div>Common regularization algorithms for linear regression, such as LASSO and Ridge regression, rely on a regularization hyperparameter that balances the trade-off between minimizing the fitting error and the norm of the learned model coefficients. As this hyperparameter is scalar, it can be easily selected via random or grid search optimizing a cross-validation criterion. However, using a scalar hyperparameter limits the algorithm’s flexibility and potential for better generalization. In this paper, we address the problem of linear regression with <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-regularization, where a different regularization hyperparameter is associated with each input variable. We optimize these hyperparameters using a gradient-based approach, wherein the gradient of a cross-validation criterion with respect to the regularization hyperparameters is computed analytically through matrix differential calculus. Additionally, we introduce two strategies tailored for sparse model learning problems aiming at reducing the risk of overfitting to the validation data. Numerical examples demonstrate that the proposed multi-hyperparameter regularization approach outperforms LASSO, Ridge, and Elastic Net regression in terms of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> score both in a static regression and in a system identification problem. Moreover, the analytical computation of the gradient proves to be more efficient in terms of computational time compared to automatic differentiation, especially when handling a large number of input variables, with an improvement of more than an order of magnitude. Application to the identification of over-parameterized Linear Parameter-Varying models is also presented.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"81 ","pages":"Article 101150"},"PeriodicalIF":2.5,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142719687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-19DOI: 10.1016/j.ejcon.2024.101146
Dhafer Almakhles , Mahmoud Abdelrahim
This paper presents a novel framework for periodic event-triggered control (PETC) coupled with dynamic quantization for linear systems. Unlike traditional time-driven control methods, our approach leverages event-based mechanisms to judiciously update control actions, thus minimizing computational load and network traffic. We introduce a two-level dynamic quantizer for encoding feedback information with a single bit, thereby enhancing resource efficiency. The proposed PETC mechanism decides the transmission instants based on the quantized output samples. The resulting system is modeled as a hybrid dynamical system to capture both continuous and discrete dynamics. Sufficient conditions for ensuring the stability of the closed-loop system are presented in the form of a linear matrix inequality. Through numerical simulations, we demonstrate that our approach captures the initial output within a finite time and significantly reduces data transmissions compared to traditional methods. This paper makes key contributions in the integration of dynamic quantization with PETC, leading to resource-efficient and stable control systems.
{"title":"Output feedback control of LTI systems using quantized periodic event-triggering and 1-bit data transmission","authors":"Dhafer Almakhles , Mahmoud Abdelrahim","doi":"10.1016/j.ejcon.2024.101146","DOIUrl":"10.1016/j.ejcon.2024.101146","url":null,"abstract":"<div><div>This paper presents a novel framework for periodic event-triggered control (PETC) coupled with dynamic quantization for linear systems. Unlike traditional time-driven control methods, our approach leverages event-based mechanisms to judiciously update control actions, thus minimizing computational load and network traffic. We introduce a two-level dynamic quantizer for encoding feedback information with a single bit, thereby enhancing resource efficiency. The proposed PETC mechanism decides the transmission instants based on the quantized output samples. The resulting system is modeled as a hybrid dynamical system to capture both continuous and discrete dynamics. Sufficient conditions for ensuring the stability of the closed-loop system are presented in the form of a linear matrix inequality. Through numerical simulations, we demonstrate that our approach captures the initial output within a finite time and significantly reduces data transmissions compared to traditional methods. This paper makes key contributions in the integration of dynamic quantization with PETC, leading to resource-efficient and stable control systems.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"81 ","pages":"Article 101146"},"PeriodicalIF":2.5,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142719686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-17DOI: 10.1016/j.ejcon.2024.101141
Habib Ayadi , Mariem Jlassi
This paper deals with the well-posedness and exponential stabilization problems of a cascaded control system consisting of a linear ordinary differential equation (ODE) and the one-dimensional linear Korteweg–de Vries (KdV) partial differential equation posed on a bounded interval , where the states are subject to an arbitrary constant delay. The control input for the whole system acts at the left boundary of the KdV domain by Dirichlet condition, whereas the right boundary injects a Dirichlet term in the ODE subsystem. Based on the infinite dimensional backstepping method for the delay-free case, an explicit feedback control law is constructed. Under this feedback, we prove the well-posedness of the considered system in Hilbert space by using semigroup theory and its exponential stability in the topology of -norm by combining Lyapunov method with Halanay’s inequality and linear matrix inequalities (LMIs). A numerical example is provided to illustrate the result.
{"title":"Boundary exponential stabilization of a time-delay ODE-KdV cascaded system","authors":"Habib Ayadi , Mariem Jlassi","doi":"10.1016/j.ejcon.2024.101141","DOIUrl":"10.1016/j.ejcon.2024.101141","url":null,"abstract":"<div><div>This paper deals with the well-posedness and exponential stabilization problems of a cascaded control system consisting of a linear ordinary differential equation (ODE) and the one-dimensional linear Korteweg–de Vries (KdV) partial differential equation posed on a bounded interval <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>l</mi><mo>]</mo></mrow></math></span>, where the states are subject to an arbitrary constant delay. The control input for the whole system acts at the left boundary of the KdV domain by Dirichlet condition, whereas the right boundary injects a Dirichlet term in the ODE subsystem. Based on the infinite dimensional backstepping method for the delay-free case, an explicit feedback control law is constructed. Under this feedback, we prove the well-posedness of the considered system in Hilbert space <span><math><mrow><mi>H</mi><mo>=</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>l</mi><mo>)</mo></mrow></mrow></math></span> by using semigroup theory and its exponential stability in the topology of <span><math><msub><mrow><mo>‖</mo><mi>⋅</mi><mo>‖</mo></mrow><mrow><mi>H</mi></mrow></msub></math></span>-norm by combining Lyapunov method with Halanay’s inequality and linear matrix inequalities (LMIs). A numerical example is provided to illustrate the result.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"81 ","pages":"Article 101141"},"PeriodicalIF":2.5,"publicationDate":"2024-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142719690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-15DOI: 10.1016/j.ejcon.2024.101142
Haleh Hayati , Carlos Murguia , Nathan van de Wouw
We present a framework for designing distorting mechanisms that allow the remote operation of anomaly detectors while preserving privacy. We consider a problem setting in which a remote station seeks to identify anomalies in dynamical systems using system input–output signals transmitted over communication networks. However, disclosing the true input–output signals of the system is not desired, as it can be used to infer private information. To maintain privacy, we propose a privacy-preserving mechanism that distorts input and measurement data before transmission using additive dependent Gaussian random processes and sends the distorted data to the remote station (which inevitably leads to degraded detection performance). We formulate constructive design conditions for the probability distributions of these additive processes while taking into account the trade-off between privacy, quantified using information-theoretic metrics (mutual information and differential entropy), and anomaly detection performance, characterized by the detector false alarm rate. The design of the privacy mechanisms is formulated as the solution of a convex optimization problem where we maximize privacy over a finite window of realizations while guaranteeing a bound on performance degradation of the anomaly detector.
{"title":"Privacy-preserving anomaly detection in stochastic dynamical systems: Synthesis of optimal Gaussian mechanisms","authors":"Haleh Hayati , Carlos Murguia , Nathan van de Wouw","doi":"10.1016/j.ejcon.2024.101142","DOIUrl":"10.1016/j.ejcon.2024.101142","url":null,"abstract":"<div><div>We present a framework for designing distorting mechanisms that allow the remote operation of anomaly detectors while preserving privacy. We consider a problem setting in which a remote station seeks to identify anomalies in dynamical systems using system input–output signals transmitted over communication networks. However, disclosing the true input–output signals of the system is not desired, as it can be used to infer private information. To maintain privacy, we propose a privacy-preserving mechanism that distorts input and measurement data before transmission using additive dependent Gaussian random processes and sends the distorted data to the remote station (which inevitably leads to degraded detection performance). We formulate constructive design conditions for the probability distributions of these additive processes while taking into account the trade-off between privacy, quantified using information-theoretic metrics (mutual information and differential entropy), and anomaly detection performance, characterized by the detector false alarm rate. The design of the privacy mechanisms is formulated as the solution of a convex optimization problem where we maximize privacy over a finite window of realizations while guaranteeing a bound on performance degradation of the anomaly detector.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"81 ","pages":"Article 101142"},"PeriodicalIF":2.5,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142746007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-15DOI: 10.1016/j.ejcon.2024.101143
Adil Shiyas , Sachit Rao
In the literature, a distributed consensus protocol by which a connected swarm of agents can generate artistic patterns in 2-dimensional space is proposed. Motivated by this protocol, in this paper, we design the parameters of this protocol for a 3-agent swarm of non-holonomic robots of finite size that results in the generation of periodic trochoidal trajectories that satisfy a set of geometric and speed constraints; this design also includes selecting the initial positions of the robots. This problem finds applications in persistent surveillance and coverage, guarding a region of interest, and target detection. While the trajectories may be self-intersecting, imposing geometric constraints i. eliminates collisions between robots; ii. ensures minimum and maximum separation distance between any robot and a fixed point, thus ensuring the robots are in communication range. Imposing speed constraints ensure that tracking these trajectories becomes feasible. It is also shown that robots can be injected to these paths at specific locations, in order to increase the refresh rate, without violating any of the geometric constraints. Conditions for the existence of the protocol parameters that satisfy all constraints are identified. The designs are implemented in an indoor mobile robot platform.
文献中提出了一种分布式共识协议，通过该协议，连接的代理群可以在二维空间中生成艺术图案。受这一协议的启发，我们在本文中为一个由有限大小的非自主机器人组成的 3 个代理群设计了这一协议的参数，从而生成满足一系列几何和速度限制的周期性三弦轨迹；这一设计还包括选择机器人的初始位置。这一问题可应用于持久监视和覆盖、保护感兴趣区域以及目标检测。虽然轨迹可能是自交的，但施加几何约束 i. 可消除机器人之间的碰撞； ii. 确保任何机器人与固定点之间的最小和最大分离距离，从而确保机器人处于通信范围内。施加速度限制可确保跟踪这些轨迹变得可行。实验还表明，在不违反任何几何约束的情况下，可以在特定位置向这些路径注入机器人，以提高刷新率。还确定了满足所有约束条件的协议参数的存在条件。这些设计在室内移动机器人平台上得以实现。
{"title":"Design of planar collision-free trochoidal paths for a multi-robot swarm","authors":"Adil Shiyas , Sachit Rao","doi":"10.1016/j.ejcon.2024.101143","DOIUrl":"10.1016/j.ejcon.2024.101143","url":null,"abstract":"<div><div>In the literature, a distributed consensus protocol by which a connected swarm of agents can generate artistic patterns in 2-dimensional space is proposed. Motivated by this protocol, in this paper, we design the parameters of this protocol for a 3-agent swarm of non-holonomic robots of finite size that results in the generation of periodic trochoidal trajectories that satisfy a set of geometric and speed constraints; this design also includes selecting the initial positions of the robots. This problem finds applications in persistent surveillance and coverage, guarding a region of interest, and target detection. While the trajectories may be self-intersecting, imposing geometric constraints <em>i</em>. eliminates collisions between robots; <em>ii</em>. ensures minimum and maximum separation distance between any robot and a fixed point, thus ensuring the robots are in communication range. Imposing speed constraints ensure that tracking these trajectories becomes feasible. It is also shown that robots can be injected to these paths at specific locations, in order to increase the <em>refresh rate</em>, without violating any of the geometric constraints. Conditions for the existence of the protocol parameters that satisfy all constraints are identified. The designs are implemented in an indoor mobile robot platform.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"81 ","pages":"Article 101143"},"PeriodicalIF":2.5,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142719691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-01DOI: 10.1016/j.ejcon.2024.101064
Anders Hilmar Damm Christensen, John Bagterp Jørgensen
This paper compares the impact of iterated and direct approaches to sensitivity computation in fixed step-size explicit singly diagonally implicit Runge–Kutta (ESDIRK) methods when applied to optimal control problems (OCPs). We strictly use the principle of internal numerical differentiation (IND) for the iterated approach, i.e., reusing iteration matrix factorizations, the number of Newton-type iterations, and Newton iterates, to compute the sensitivities. The direct method computes the sensitivities without using the Newton schemes. We compare the impact of these sensitivity computations in OCPs for the quadruple tank system (QTS). We discretize the OCPs using multiple shooting and solve these with a sequential quadratic programming (SQP) solver. We benchmark the iterated and direct approaches against a base case. This base case applies the ESDIRK methods with exact Newton schemes and a direct approach for sensitivity computations. In these OCPs, we vary the number of integration steps between control intervals and evaluate the performance based on the number of SQP and QPs iterations, KKT violations, function evaluations, Jacobian updates, and iteration matrix factorizations. We also provide examples using the continuous-stirred tank reactor (CSTR), and the IPOPT algorithm instead of the SQP. For OCPs solved using SQP, the QTS results show the direct method converges only once, while the iterated approach and base case converges in all situations. Similar results are seen with the CSTR. Using IPOPT, both the iterated approach and base case converge in all cases. In contrast, the direct method only converges in all cases regarding the CSTR.
{"title":"A comparative study of sensitivity computations in ESDIRK-based optimal control problems","authors":"Anders Hilmar Damm Christensen, John Bagterp Jørgensen","doi":"10.1016/j.ejcon.2024.101064","DOIUrl":"10.1016/j.ejcon.2024.101064","url":null,"abstract":"<div><div>This paper compares the impact of iterated and direct approaches to sensitivity computation in fixed step-size explicit singly diagonally implicit Runge–Kutta (ESDIRK) methods when applied to optimal control problems (OCPs). We strictly use the principle of internal numerical differentiation (IND) for the iterated approach, i.e., reusing iteration matrix factorizations, the number of Newton-type iterations, and Newton iterates, to compute the sensitivities. The direct method computes the sensitivities without using the Newton schemes. We compare the impact of these sensitivity computations in OCPs for the quadruple tank system (QTS). We discretize the OCPs using multiple shooting and solve these with a sequential quadratic programming (SQP) solver. We benchmark the iterated and direct approaches against a base case. This base case applies the ESDIRK methods with exact Newton schemes and a direct approach for sensitivity computations. In these OCPs, we vary the number of integration steps between control intervals and evaluate the performance based on the number of SQP and QPs iterations, KKT violations, function evaluations, Jacobian updates, and iteration matrix factorizations. We also provide examples using the continuous-stirred tank reactor (CSTR), and the IPOPT algorithm instead of the SQP. For OCPs solved using SQP, the QTS results show the direct method converges only once, while the iterated approach and base case converges in all situations. Similar results are seen with the CSTR. Using IPOPT, both the iterated approach and base case converge in all cases. In contrast, the direct method only converges in all cases regarding the CSTR.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"80 ","pages":"Article 101064"},"PeriodicalIF":2.5,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141510833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-01DOI: 10.1016/j.ejcon.2024.101040
Zhixin Zhao, Antoine Girard, Sorin Olaru
One of the fundamental issues in Nonlinear Model Predictive Control (NMPC) is to be able to guarantee the recursive feasibility of the underlying receding horizon optimization. In other terms, the primary condition for a safe NMPC design is to ensure that the closed-loop solution remains indefinitely within the feasible set of the optimization problem. This issue can be addressed by introducing a terminal constraint described in terms of a control invariant set. However, the control invariant sets of nonlinear systems are often impractical to use or even to construct due to their complexity. The -step control invariant sets are representing generalizations of the classical one-step control invariant sets and prove to retain the useful properties for MPC design, but often with simpler representations, and thus greater applicability. In this paper, a novel NMPC scheme based on -step control invariant sets is proposed. We employ symbolic control techniques to compute a -step control invariant set and build the NMPC framework by integrating this set as a terminal constraint, thereby ensuring recursive feasibility.
非线性模型预测控制（NMPC）的基本问题之一是能够保证基础后退视界优化的递归可行性。换句话说，安全 NMPC 设计的首要条件是确保闭环解决方案无限期地保持在优化问题的可行集内。这个问题可以通过引入以控制不变集描述的终端约束来解决。然而，非线性系统的控制不变集往往由于其复杂性而难以使用，甚至难以构建。K 步控制不变集是对经典的一步控制不变集的概括，并被证明保留了 MPC 设计的有用特性，但通常具有更简单的表示方法，因此具有更大的适用性。本文提出了一种基于 K 步控制不变集的新型 NMPC 方案。我们采用符号控制技术计算 K 步控制不变集，并通过将该不变集整合为终端约束来构建 NMPC 框架，从而确保递归可行性。
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