Pub Date : 2021-12-14DOI: 10.1109/CDC45484.2021.9683057
P. Tooranjipour, Bahare Kiumarsi-Khomartash
In this paper, a data-driven output feedback approach is developed for solving H∞ control problem of linear discrete-time systems based on off-policy reinforcement learning (RL) algorithm. Past input-output measurements are leveraged to implicitly reconstruct the system's states to alleviate the requirement to measure or estimate the system's states. Then, an off-policy input-output Bellman equation is derived based on this implicit reconstruction to evaluate control policies using only input-output measurements. An improved control policy is then learned utilizing the solution to the Bellman equation without knowing the system's dynamics. In the proposed approach, unlike the on-policy methods, the disturbance does not need to be updated in a predefined manner at each iteration, which makes it more practical. While the state-feedback off-policy RL method is shown to be a bias-free approach for deterministic systems, it is shown that once the system's states have been reconstructed from the input-output measurements, the input-output off-policy method cannot be considered as an immune approach against the probing noises. To cope with this, a discount factor is utilized in the performance function to decay the deleterious effect of probing noises. Finally, to illustrate the sensitivity of the problem to the probing noises and the efficacy of the proposed approach, the flight control system is tested in the simulation.
{"title":"Output Feedback H∞ Control of Unknown Discrete-time Linear Systems: Off-policy Reinforcement Learning","authors":"P. Tooranjipour, Bahare Kiumarsi-Khomartash","doi":"10.1109/CDC45484.2021.9683057","DOIUrl":"https://doi.org/10.1109/CDC45484.2021.9683057","url":null,"abstract":"In this paper, a data-driven output feedback approach is developed for solving H∞ control problem of linear discrete-time systems based on off-policy reinforcement learning (RL) algorithm. Past input-output measurements are leveraged to implicitly reconstruct the system's states to alleviate the requirement to measure or estimate the system's states. Then, an off-policy input-output Bellman equation is derived based on this implicit reconstruction to evaluate control policies using only input-output measurements. An improved control policy is then learned utilizing the solution to the Bellman equation without knowing the system's dynamics. In the proposed approach, unlike the on-policy methods, the disturbance does not need to be updated in a predefined manner at each iteration, which makes it more practical. While the state-feedback off-policy RL method is shown to be a bias-free approach for deterministic systems, it is shown that once the system's states have been reconstructed from the input-output measurements, the input-output off-policy method cannot be considered as an immune approach against the probing noises. To cope with this, a discount factor is utilized in the performance function to decay the deleterious effect of probing noises. Finally, to illustrate the sensitivity of the problem to the probing noises and the efficacy of the proposed approach, the flight control system is tested in the simulation.","PeriodicalId":229089,"journal":{"name":"2021 60th IEEE Conference on Decision and Control (CDC)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131435315","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}
Pub Date : 2021-12-14DOI: 10.1109/CDC45484.2021.9682965
I. Bhogaraju, M. Farasat, Michael A. Malisoff
We build delay-compensating feedback controls for a class of nonlinear systems that include bilinear systems with arbitrarily long known constant input delays. Unlike prior sequential predictor work, we cover bilinear systems whose state measurements have uncertainty, and we prove input-to-state stability with respect to the uncertainty. We do not require constructing or estimating distributed terms in the controls. We illustrate our result in a power systems example.
{"title":"Sequential Predictors for Stabilization of Bilinear Systems under Measurement Uncertainty","authors":"I. Bhogaraju, M. Farasat, Michael A. Malisoff","doi":"10.1109/CDC45484.2021.9682965","DOIUrl":"https://doi.org/10.1109/CDC45484.2021.9682965","url":null,"abstract":"We build delay-compensating feedback controls for a class of nonlinear systems that include bilinear systems with arbitrarily long known constant input delays. Unlike prior sequential predictor work, we cover bilinear systems whose state measurements have uncertainty, and we prove input-to-state stability with respect to the uncertainty. We do not require constructing or estimating distributed terms in the controls. We illustrate our result in a power systems example.","PeriodicalId":229089,"journal":{"name":"2021 60th IEEE Conference on Decision and Control (CDC)","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132251704","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}
Pub Date : 2021-12-14DOI: 10.1109/CDC45484.2021.9683419
Anna Stuhlmacher, Line A. Roald, J. Mathieu
Drinking water distribution networks can be treated as flexible, controllable assets for power distribution networks (e.g., to provide voltage support) by leveraging the power consumption of water pumps and storage capabilities of water tanks. We formulate an adjustable robust optimization problem to determine the scheduled water distribution network pumping and real-time pump adjustments that ensure that the power and water distribution network constraints are satisfied with respect to uncertain power demand. We extend the monotonicity properties of dissipative flow networks to water distribution networks which requires assumptions on water tank operation. Then, to make the problem tractable, we leverage these properties, along with constraint approximations and an affine pump control policy, to reformulate the problem as an affinely adjustable robust counterpart that solves for the pumping schedule and the parameters of an affine control policy that determines the real-time pump adjustments. Through a case study, we demonstrate that the approach produces robust solutions and is computationally tractable. We also evaluate the impact of restricting water tank operation to enforce monotonicity and find it leads to a significantly restricted feasible region and more conservative solutions.
{"title":"Tractable Robust Drinking Water Pumping to Provide Power Network Voltage Support","authors":"Anna Stuhlmacher, Line A. Roald, J. Mathieu","doi":"10.1109/CDC45484.2021.9683419","DOIUrl":"https://doi.org/10.1109/CDC45484.2021.9683419","url":null,"abstract":"Drinking water distribution networks can be treated as flexible, controllable assets for power distribution networks (e.g., to provide voltage support) by leveraging the power consumption of water pumps and storage capabilities of water tanks. We formulate an adjustable robust optimization problem to determine the scheduled water distribution network pumping and real-time pump adjustments that ensure that the power and water distribution network constraints are satisfied with respect to uncertain power demand. We extend the monotonicity properties of dissipative flow networks to water distribution networks which requires assumptions on water tank operation. Then, to make the problem tractable, we leverage these properties, along with constraint approximations and an affine pump control policy, to reformulate the problem as an affinely adjustable robust counterpart that solves for the pumping schedule and the parameters of an affine control policy that determines the real-time pump adjustments. Through a case study, we demonstrate that the approach produces robust solutions and is computationally tractable. We also evaluate the impact of restricting water tank operation to enforce monotonicity and find it leads to a significantly restricted feasible region and more conservative solutions.","PeriodicalId":229089,"journal":{"name":"2021 60th IEEE Conference on Decision and Control (CDC)","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132479609","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}
Pub Date : 2021-12-14DOI: 10.1109/CDC45484.2021.9683119
G. Männel, J. Grasshoff, P. Rostalski, H. S. Abbas
Model predictive control (MPC) is becoming one of the leading modern control approaches applied to physiological control systems. However, intra- and interpatient variability usually requires an adaptation of the model to each individual patient or otherwise deeming the controller too conservative. The incorporation of learning in model predictive control is subject to ongoing intensive research to provide tractable and safe implementation in practice. Gaussian processes (GPs) among other learning approaches have been proposed for learning uncertain or unknown system dynamics as well as time varying disturbances. However, the naïve incorporation of GPs into MPC, commonly results in complex and nonlinear optimization problems. In this paper, we propose a practical stochastic MPC implementation, that utilizes estimates of the parameter uncertainties and nonlinearities of the system as well as external additive disturbances. By using a linear nominal model augmented with two separate GPs, nonlinearities depending on the state and input as well as temporal disturbances can be considered efficiently in the MPC framework. An iterative optimization scheme is introduced using quadratic programming to circumvent solving a stochastic nonlinear program. The applicability of the proposed approach is demonstrated on a pressure controlled mechanical ventilation problem.
{"title":"Iterative Gaussian Process Model Predictive Control with Application to Physiological Control Systems*","authors":"G. Männel, J. Grasshoff, P. Rostalski, H. S. Abbas","doi":"10.1109/CDC45484.2021.9683119","DOIUrl":"https://doi.org/10.1109/CDC45484.2021.9683119","url":null,"abstract":"Model predictive control (MPC) is becoming one of the leading modern control approaches applied to physiological control systems. However, intra- and interpatient variability usually requires an adaptation of the model to each individual patient or otherwise deeming the controller too conservative. The incorporation of learning in model predictive control is subject to ongoing intensive research to provide tractable and safe implementation in practice. Gaussian processes (GPs) among other learning approaches have been proposed for learning uncertain or unknown system dynamics as well as time varying disturbances. However, the naïve incorporation of GPs into MPC, commonly results in complex and nonlinear optimization problems. In this paper, we propose a practical stochastic MPC implementation, that utilizes estimates of the parameter uncertainties and nonlinearities of the system as well as external additive disturbances. By using a linear nominal model augmented with two separate GPs, nonlinearities depending on the state and input as well as temporal disturbances can be considered efficiently in the MPC framework. An iterative optimization scheme is introduced using quadratic programming to circumvent solving a stochastic nonlinear program. The applicability of the proposed approach is demonstrated on a pressure controlled mechanical ventilation problem.","PeriodicalId":229089,"journal":{"name":"2021 60th IEEE Conference on Decision and Control (CDC)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130113163","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}
Pub Date : 2021-12-14DOI: 10.1109/CDC45484.2021.9683080
Ting Bai, Alexander Johansson, K. Johansson, J. Mårtensson
This paper considers the problem of hub-based platoon coordination for a large-scale transport system, where trucks have individual utility functions to optimize. An event-triggered distributed model predictive control method is pro-posed to solve the optimal scheduling of waiting times at hubs for individual trucks. In this distributed framework, trucks are allowed to decide their waiting times independently and only limited information is shared between trucks. Both the predicted reward gained from platooning and the predicted cost for waiting at hubs are included in each truck’s utility function. The performance of the coordination method is demonstrated in a simulation with one hundred trucks over the Swedish road network.
{"title":"Event-Triggered Distributed Model Predictive Control for Platoon Coordination at Hubs in a Transport System","authors":"Ting Bai, Alexander Johansson, K. Johansson, J. Mårtensson","doi":"10.1109/CDC45484.2021.9683080","DOIUrl":"https://doi.org/10.1109/CDC45484.2021.9683080","url":null,"abstract":"This paper considers the problem of hub-based platoon coordination for a large-scale transport system, where trucks have individual utility functions to optimize. An event-triggered distributed model predictive control method is pro-posed to solve the optimal scheduling of waiting times at hubs for individual trucks. In this distributed framework, trucks are allowed to decide their waiting times independently and only limited information is shared between trucks. Both the predicted reward gained from platooning and the predicted cost for waiting at hubs are included in each truck’s utility function. The performance of the coordination method is demonstrated in a simulation with one hundred trucks over the Swedish road network.","PeriodicalId":229089,"journal":{"name":"2021 60th IEEE Conference on Decision and Control (CDC)","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130248466","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}
Pub Date : 2021-12-14DOI: 10.1109/CDC45484.2021.9683079
T. Faulwasser, L. Grüne, Jukka-Pekka Humaloja, M. Schaller
This paper investigates an interval turnpike result for the adjoints/costates of finite- and infinite-dimensional nonlinear optimal control problems under the assumption of an interval turnpike on states and controls. We consider stabilizable dynamics governed by a generator of a semigroup with finite-dimensional unstable part satisfying a spectral decomposition condition and show the desired turnpike property under continuity assumptions on the first-order optimality conditions. We further provide a numerical example with a semilinear heat equation to illustrate the results.
{"title":"Inferring the adjoint turnpike property from the primal turnpike property","authors":"T. Faulwasser, L. Grüne, Jukka-Pekka Humaloja, M. Schaller","doi":"10.1109/CDC45484.2021.9683079","DOIUrl":"https://doi.org/10.1109/CDC45484.2021.9683079","url":null,"abstract":"This paper investigates an interval turnpike result for the adjoints/costates of finite- and infinite-dimensional nonlinear optimal control problems under the assumption of an interval turnpike on states and controls. We consider stabilizable dynamics governed by a generator of a semigroup with finite-dimensional unstable part satisfying a spectral decomposition condition and show the desired turnpike property under continuity assumptions on the first-order optimality conditions. We further provide a numerical example with a semilinear heat equation to illustrate the results.","PeriodicalId":229089,"journal":{"name":"2021 60th IEEE Conference on Decision and Control (CDC)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130443958","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}
Pub Date : 2021-12-14DOI: 10.1109/CDC45484.2021.9683664
Lucas Brivadis, Ludovic Sacchelli
We consider the problem of dynamic output feedback stabilization at an unobservable target point. The challenge lies in according the antagonistic nature of the objective and the properties of the system: the system tends to be less observable as it approaches the target. In the literature, switching techniques rapidly appeared as a suitable approach to deal with this issue. On a case of systems with linear conservative dynamics and nonlinear output, this approach is used in conjunction with an embedding into bilinear systems that admit observers with dissipative error. Combining these two elements, global stabilization by means of a dynamic periodic time-varying output feedback is proved, and numerical simulations are provided.
{"title":"A switching technique for output feedback stabilization at an unobservable target","authors":"Lucas Brivadis, Ludovic Sacchelli","doi":"10.1109/CDC45484.2021.9683664","DOIUrl":"https://doi.org/10.1109/CDC45484.2021.9683664","url":null,"abstract":"We consider the problem of dynamic output feedback stabilization at an unobservable target point. The challenge lies in according the antagonistic nature of the objective and the properties of the system: the system tends to be less observable as it approaches the target. In the literature, switching techniques rapidly appeared as a suitable approach to deal with this issue. On a case of systems with linear conservative dynamics and nonlinear output, this approach is used in conjunction with an embedding into bilinear systems that admit observers with dissipative error. Combining these two elements, global stabilization by means of a dynamic periodic time-varying output feedback is proved, and numerical simulations are provided.","PeriodicalId":229089,"journal":{"name":"2021 60th IEEE Conference on Decision and Control (CDC)","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134094542","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}
Pub Date : 2021-12-14DOI: 10.1109/CDC45484.2021.9683386
Khaled Laib, J. Watson, Y. Ojo, Ioannis Lestas
We consider the problem of ensuring stability in a DC microgrid by means of decentralized conditions. Such conditions are derived which are formulated as input-output properties of locally defined subsystems. These follow from various decompositions of the microgrid and corresponding properties of the resulting representations. It is shown that these stability conditions can be combined together by means of appropriate homotopy arguments, thus reducing the conservatism relative to more conventional decentralized approaches that often rely on a passivation of the bus dynamics. Examples are presented to demonstrate the applicability and the efficiency of the results derived.
{"title":"Decentralized Stability Conditions in DC Microgrids","authors":"Khaled Laib, J. Watson, Y. Ojo, Ioannis Lestas","doi":"10.1109/CDC45484.2021.9683386","DOIUrl":"https://doi.org/10.1109/CDC45484.2021.9683386","url":null,"abstract":"We consider the problem of ensuring stability in a DC microgrid by means of decentralized conditions. Such conditions are derived which are formulated as input-output properties of locally defined subsystems. These follow from various decompositions of the microgrid and corresponding properties of the resulting representations. It is shown that these stability conditions can be combined together by means of appropriate homotopy arguments, thus reducing the conservatism relative to more conventional decentralized approaches that often rely on a passivation of the bus dynamics. Examples are presented to demonstrate the applicability and the efficiency of the results derived.","PeriodicalId":229089,"journal":{"name":"2021 60th IEEE Conference on Decision and Control (CDC)","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134105214","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}
Pub Date : 2021-12-14DOI: 10.1109/CDC45484.2021.9682953
M. A. Hernández-Ortega, A. Chakrabortty, A. R. Messina, C. M. Rergis
Recently, the perturbed Koopman mode analysis (PKMA) was proposed for analyzing oscillations arising from power system models under stressed operating conditions, using both linear and nonlinear Koopman eigenfunctions. A question of current interest is how one can use the information provided by these PKMA models to complement and enhance estimations obtained through data-driven Koopman operator-based approaches. Motivated by this question, in this paper we derive nonlinear Koopman measures of observability for a third-order PKMA model to assess the most dominant global dynamics underlying a selected set of observables. These nonlinear measures are generic by formulation; however, the focus is on a subset of the state variables of a power system. With the selected observables, we illustrate the usefulness of our approach in identifying a relatively small subset of dominant Koopman modes that closely mimic the global dynamical behavior. We validate our results on a test system, followed by a comparison with the extended dynamic mode decomposition (EDMD). The simulations demonstrate how the proposed model-based approach is complementary to these data-driven approaches. Utility of this method for model-order reduction, wide-area monitoring, and optimal sensor placement are also highlighted.
{"title":"Nonlinear Koopman Observability Measures on Subsets of Power System State Variables","authors":"M. A. Hernández-Ortega, A. Chakrabortty, A. R. Messina, C. M. Rergis","doi":"10.1109/CDC45484.2021.9682953","DOIUrl":"https://doi.org/10.1109/CDC45484.2021.9682953","url":null,"abstract":"Recently, the perturbed Koopman mode analysis (PKMA) was proposed for analyzing oscillations arising from power system models under stressed operating conditions, using both linear and nonlinear Koopman eigenfunctions. A question of current interest is how one can use the information provided by these PKMA models to complement and enhance estimations obtained through data-driven Koopman operator-based approaches. Motivated by this question, in this paper we derive nonlinear Koopman measures of observability for a third-order PKMA model to assess the most dominant global dynamics underlying a selected set of observables. These nonlinear measures are generic by formulation; however, the focus is on a subset of the state variables of a power system. With the selected observables, we illustrate the usefulness of our approach in identifying a relatively small subset of dominant Koopman modes that closely mimic the global dynamical behavior. We validate our results on a test system, followed by a comparison with the extended dynamic mode decomposition (EDMD). The simulations demonstrate how the proposed model-based approach is complementary to these data-driven approaches. Utility of this method for model-order reduction, wide-area monitoring, and optimal sensor placement are also highlighted.","PeriodicalId":229089,"journal":{"name":"2021 60th IEEE Conference on Decision and Control (CDC)","volume":"18 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131653026","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}
Pub Date : 2021-12-14DOI: 10.1109/CDC45484.2021.9683248
J. Poveda, M. Krstić
Motivated by recent (semi-global practical) fixed-time convergence results in time-invariant model-free optimization problems, in this paper we introduce new tracking bounds and guidelines for the design of extremum seeking controllers in model-free optimization problems with dynamic cost functions. Using semi-global practical input-to-state stability characterizations, we show that the proposed non-smooth ES dynamics are able to significantly reduce the tracking error compared to the traditional smooth algorithms studied in the literature. Moreover, under a suitable tuning of the gains of the algorithm, the nominal average dynamics of the controller are able to achieve global fixed-time tracking for a general class of dynamic cost functions. For tuning parameters that do not completely eliminate the tracking error in the nominal average dynamics, but which preserve the continuity of the vector field, we show that "almost complete" error rejection is achieved whenever the gain of the algorithm exceeds a particular threshold. Numerical results are presented to illustrate the performance of the algorithms.
{"title":"Fixed-Time Seeking and Tracking of Time-Varying Extrema","authors":"J. Poveda, M. Krstić","doi":"10.1109/CDC45484.2021.9683248","DOIUrl":"https://doi.org/10.1109/CDC45484.2021.9683248","url":null,"abstract":"Motivated by recent (semi-global practical) fixed-time convergence results in time-invariant model-free optimization problems, in this paper we introduce new tracking bounds and guidelines for the design of extremum seeking controllers in model-free optimization problems with dynamic cost functions. Using semi-global practical input-to-state stability characterizations, we show that the proposed non-smooth ES dynamics are able to significantly reduce the tracking error compared to the traditional smooth algorithms studied in the literature. Moreover, under a suitable tuning of the gains of the algorithm, the nominal average dynamics of the controller are able to achieve global fixed-time tracking for a general class of dynamic cost functions. For tuning parameters that do not completely eliminate the tracking error in the nominal average dynamics, but which preserve the continuity of the vector field, we show that \"almost complete\" error rejection is achieved whenever the gain of the algorithm exceeds a particular threshold. Numerical results are presented to illustrate the performance of the algorithms.","PeriodicalId":229089,"journal":{"name":"2021 60th IEEE Conference on Decision and Control (CDC)","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129399110","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：