Pub Date : 2024-06-17DOI: 10.1016/j.ejcon.2024.101063
Hannah Häring, Dennis Gramlich, Christian Ebenbauer, Carsten W. Scherer
We develop a convex relaxation for the minimum energy control problem of the well-known unicycle model in the form of a semidefinite program. Through polynomialization techniques, the infinite-dimensional optimal control problem is first reformulated as a non-convex, infinite-dimensional quadratic program which can be viewed as a trajectory generation problem. This problem is then discretized to arrive at a finite-dimensional, albeit, non-convex quadratically constrained quadratic program. By applying the moment relaxation method to this quadratic program, we obtain a hierarchy of semidefinite relaxations. We construct an approximate solution for the infinite-dimensional trajectory generation problem by solving the first- or second-order moment relaxation. A comprehensive simulation study provided in this paper suggests that the second-order moment relaxation is lossless.
{"title":"Trajectory generation for the unicycle model using semidefinite relaxations","authors":"Hannah Häring, Dennis Gramlich, Christian Ebenbauer, Carsten W. Scherer","doi":"10.1016/j.ejcon.2024.101063","DOIUrl":"https://doi.org/10.1016/j.ejcon.2024.101063","url":null,"abstract":"We develop a convex relaxation for the minimum energy control problem of the well-known unicycle model in the form of a semidefinite program. Through polynomialization techniques, the infinite-dimensional optimal control problem is first reformulated as a non-convex, infinite-dimensional quadratic program which can be viewed as a trajectory generation problem. This problem is then discretized to arrive at a finite-dimensional, albeit, non-convex quadratically constrained quadratic program. By applying the moment relaxation method to this quadratic program, we obtain a hierarchy of semidefinite relaxations. We construct an approximate solution for the infinite-dimensional trajectory generation problem by solving the first- or second-order moment relaxation. A comprehensive simulation study provided in this paper suggests that the second-order moment relaxation is lossless.","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141577019","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 : 2024-06-15DOI: 10.1016/j.ejcon.2024.101054
Igor G. Vladimirov, Ian R. Petersen
This paper is concerned with open quantum systems whose dynamic variables have an algebraic structure, similar to that of the Pauli matrices for finite-level systems. The Hamiltonian and the operators of coupling of the system to the external bosonic fields depend linearly on the system variables. The fields are represented by quantum Wiener processes which drive the system dynamics according to a quasilinear Hudson–Parthasarathy quantum stochastic differential equation whose drift vector and dispersion matrix are affine and linear functions of the system variables. This setting includes the zero-Hamiltonian isolated system dynamics as a particular case, where the system variables are constant in time, which makes them potentially applicable as a quantum memory. In a more realistic case of nonvanishing system-field coupling, we define a memory decoherence time when a mean-square deviation of the system variables from their initial values becomes relatively significant as specified by a weighting matrix and a fidelity parameter. We consider the decoherence time maximization over the energy parameters of the system and obtain a condition under which the zero Hamiltonian provides a suboptimal solution. This optimization problem is also discussed for a direct energy coupling interconnection of such systems.
{"title":"Decoherence time control by interconnection for finite-level quantum memory systems","authors":"Igor G. Vladimirov, Ian R. Petersen","doi":"10.1016/j.ejcon.2024.101054","DOIUrl":"https://doi.org/10.1016/j.ejcon.2024.101054","url":null,"abstract":"This paper is concerned with open quantum systems whose dynamic variables have an algebraic structure, similar to that of the Pauli matrices for finite-level systems. The Hamiltonian and the operators of coupling of the system to the external bosonic fields depend linearly on the system variables. The fields are represented by quantum Wiener processes which drive the system dynamics according to a quasilinear Hudson–Parthasarathy quantum stochastic differential equation whose drift vector and dispersion matrix are affine and linear functions of the system variables. This setting includes the zero-Hamiltonian isolated system dynamics as a particular case, where the system variables are constant in time, which makes them potentially applicable as a quantum memory. In a more realistic case of nonvanishing system-field coupling, we define a memory decoherence time when a mean-square deviation of the system variables from their initial values becomes relatively significant as specified by a weighting matrix and a fidelity parameter. We consider the decoherence time maximization over the energy parameters of the system and obtain a condition under which the zero Hamiltonian provides a suboptimal solution. This optimization problem is also discussed for a direct energy coupling interconnection of such systems.","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141510838","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 : 2024-06-15DOI: 10.1016/j.ejcon.2024.101042
Kunpeng Zhang, Xinlei Yi, Yuzhe Li, Ming Cao, Tianyou Chai, Tao Yang
This paper focuses on the distributed online convex optimization problem with time-varying inequality constraints over a network of agents, where each agent collaborates with its neighboring agents to minimize the cumulative network-wide loss over time. To reduce communication overhead between the agents, we propose a distributed event-triggered online primal–dual algorithm over a time-varying directed graph. With several classes of appropriately chose decreasing parameter sequences and non-increasing event-triggered threshold sequences, we establish dynamic network regret and network cumulative constraint violation bounds. Finally, a numerical simulation example is provided to verify the theoretical results.
{"title":"Distributed online constrained convex optimization with event-triggered communication","authors":"Kunpeng Zhang, Xinlei Yi, Yuzhe Li, Ming Cao, Tianyou Chai, Tao Yang","doi":"10.1016/j.ejcon.2024.101042","DOIUrl":"https://doi.org/10.1016/j.ejcon.2024.101042","url":null,"abstract":"This paper focuses on the distributed online convex optimization problem with time-varying inequality constraints over a network of agents, where each agent collaborates with its neighboring agents to minimize the cumulative network-wide loss over time. To reduce communication overhead between the agents, we propose a distributed event-triggered online primal–dual algorithm over a time-varying directed graph. With several classes of appropriately chose decreasing parameter sequences and non-increasing event-triggered threshold sequences, we establish dynamic network regret and network cumulative constraint violation bounds. Finally, a numerical simulation example is provided to verify the theoretical results.","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141510837","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 : 2024-06-15DOI: 10.1016/j.ejcon.2024.101053
Xiao Tan, Antonis Papachristodoulou, Dimos V. Dimarogonas
This paper proposes a (control) barrier function synthesis and safety verification scheme for interconnected nonlinear systems based on assume-guarantee contracts (AGC) and sum-of-squares (SOS) techniques. It is well-known that the SOS approach does not scale well for barrier function synthesis for high-dimensional systems. In this paper, we show that compositional methods like AGC can mitigate this problem. We formulate the synthesis problem into a set of small-size problems, which constructs local contracts for subsystems, and propose a negotiation scheme among the subsystems at the contract level. The proposed scheme is then implemented numerically on two examples: vehicle platooning and room temperature regulation.
{"title":"A contract negotiation scheme for safety verification of interconnected systems","authors":"Xiao Tan, Antonis Papachristodoulou, Dimos V. Dimarogonas","doi":"10.1016/j.ejcon.2024.101053","DOIUrl":"https://doi.org/10.1016/j.ejcon.2024.101053","url":null,"abstract":"This paper proposes a (control) barrier function synthesis and safety verification scheme for interconnected nonlinear systems based on assume-guarantee contracts (AGC) and sum-of-squares (SOS) techniques. It is well-known that the SOS approach does not scale well for barrier function synthesis for high-dimensional systems. In this paper, we show that compositional methods like AGC can mitigate this problem. We formulate the synthesis problem into a set of small-size problems, which constructs local contracts for subsystems, and propose a negotiation scheme among the subsystems at the contract level. The proposed scheme is then implemented numerically on two examples: vehicle platooning and room temperature regulation.","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532484","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 : 2024-06-15DOI: 10.1016/j.ejcon.2024.101055
Riya Mathew, Juan G. Rueda-Escobedo, Johannes Schiffer
Phase-locked loop (PLL) algorithms are key elements for the successful integration of converter-interfaced renewable energy sources to the grid. Their main task is to estimate the phase angle of the terminal grid voltage with the aim to keep the converter output current synchronized to it. Yet, due to the increasing penetration of power-electronics-interfaced devices in power systems, the grid voltage signal becomes increasingly disturbed, making the reliable phase estimation a highly demanding task. To address this challenge, we present a robust design method based on matrix inequalities to tune the PLL gains, such that the estimation errors remain bounded in the presence of additive disturbances. Our design approach is formulated as a set of bilinear matrix inequalities (BMIs), which we then propose to solve using the P-K iteration method. This results in a convex problem to be solved at each step. Finally, the benefits of the proposed robust design are illustrated via a numerical example.
{"title":"Robust design of phase-locked loops in grid-connected power converters","authors":"Riya Mathew, Juan G. Rueda-Escobedo, Johannes Schiffer","doi":"10.1016/j.ejcon.2024.101055","DOIUrl":"https://doi.org/10.1016/j.ejcon.2024.101055","url":null,"abstract":"Phase-locked loop (PLL) algorithms are key elements for the successful integration of converter-interfaced renewable energy sources to the grid. Their main task is to estimate the phase angle of the terminal grid voltage with the aim to keep the converter output current synchronized to it. Yet, due to the increasing penetration of power-electronics-interfaced devices in power systems, the grid voltage signal becomes increasingly disturbed, making the reliable phase estimation a highly demanding task. To address this challenge, we present a robust design method based on matrix inequalities to tune the PLL gains, such that the estimation errors remain bounded in the presence of additive disturbances. Our design approach is formulated as a set of bilinear matrix inequalities (BMIs), which we then propose to solve using the P-K iteration method. This results in a convex problem to be solved at each step. Finally, the benefits of the proposed robust design are illustrated via a numerical example.","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141510836","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 : 2024-06-15DOI: 10.1016/j.ejcon.2024.101035
Christoforos N. Hadjicostis, Alejandro D. Domínguez-García
We consider the problem of average consensus in a distributed system comprising a set of nodes that can exchange information among themselves. We focus on a class of algorithms for solving such a problem whereby each node maintains a state and updates it iteratively as a linear combination of the states maintained by its in-neighbors, i.e., nodes from which it receives information directly. Averaging algorithms within this class can be thought of as discrete-time linear time-varying systems without external driving inputs and whose state matrix is column stochastic. As a result, the algorithms exhibit a global invariance property in that the sum of the state variables remains constant at all times. In this paper, we report on another invariance property for the aforementioned class of averaging algorithms. This property is local to each node and reflects the conservation of certain quantities capturing an aggregate of all the values received by a node from its in-neighbors and all the values sent by said node to its out-neighbors (i.e., nodes to which it sends information directly) throughout the execution of the averaging algorithm. We show how this newly-discovered invariant can be leveraged for detecting errors while executing the averaging algorithm.
{"title":"Invariant properties of linear-iterative distributed averaging algorithms and application to error detection","authors":"Christoforos N. Hadjicostis, Alejandro D. Domínguez-García","doi":"10.1016/j.ejcon.2024.101035","DOIUrl":"https://doi.org/10.1016/j.ejcon.2024.101035","url":null,"abstract":"We consider the problem of average consensus in a distributed system comprising a set of nodes that can exchange information among themselves. We focus on a class of algorithms for solving such a problem whereby each node maintains a state and updates it iteratively as a linear combination of the states maintained by its in-neighbors, i.e., nodes from which it receives information directly. Averaging algorithms within this class can be thought of as discrete-time linear time-varying systems without external driving inputs and whose state matrix is column stochastic. As a result, the algorithms exhibit a global invariance property in that the sum of the state variables remains constant at all times. In this paper, we report on another invariance property for the aforementioned class of averaging algorithms. This property is local to each node and reflects the conservation of certain quantities capturing an aggregate of all the values received by a node from its in-neighbors and all the values sent by said node to its out-neighbors (i.e., nodes to which it sends information directly) throughout the execution of the averaging algorithm. We show how this newly-discovered invariant can be leveraged for detecting errors while executing the averaging algorithm.","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141577078","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 : 2024-06-15DOI: 10.1016/j.ejcon.2024.101043
Andreas A. Malikopoulos
{"title":"Combining learning and control in linear systems","authors":"Andreas A. Malikopoulos","doi":"10.1016/j.ejcon.2024.101043","DOIUrl":"https://doi.org/10.1016/j.ejcon.2024.101043","url":null,"abstract":"","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141530139","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 : 2024-06-13DOI: 10.1016/j.ejcon.2024.101065
Sofia Trombini, Edoardo Pasta, Lorenzo Fagiano
This study investigates deep offshore, pumping Airborne Wind Energy systems, focusing on the kite-platform interaction. The considered system includes a 360 m soft-wing kite, connected by a tether to a winch installed on a 10-meter-deep spar with four mooring lines. Wind power is converted into electricity with a feedback controlled periodic trajectory of the kite and corresponding reeling motion of the tether. An analysis of the mutual influence between the platform and the kite dynamics, with different wave regimes, reveals a rather small sensitivity of the flight pattern to the platform oscillations; on the other hand, the frequency of tether force oscillations can be close to the platform resonance peaks, resulting in possible increased fatigue loads and damage of the floating and submerged components. A control design procedure is then proposed to avoid this problem, acting on the kite path planner. Simulation results confirm the effectiveness of the approach.
{"title":"On the kite-platform interactions in offshore Airborne Wind Energy Systems: Frequency analysis and control approach","authors":"Sofia Trombini, Edoardo Pasta, Lorenzo Fagiano","doi":"10.1016/j.ejcon.2024.101065","DOIUrl":"https://doi.org/10.1016/j.ejcon.2024.101065","url":null,"abstract":"This study investigates deep offshore, pumping Airborne Wind Energy systems, focusing on the kite-platform interaction. The considered system includes a 360 m soft-wing kite, connected by a tether to a winch installed on a 10-meter-deep spar with four mooring lines. Wind power is converted into electricity with a feedback controlled periodic trajectory of the kite and corresponding reeling motion of the tether. An analysis of the mutual influence between the platform and the kite dynamics, with different wave regimes, reveals a rather small sensitivity of the flight pattern to the platform oscillations; on the other hand, the frequency of tether force oscillations can be close to the platform resonance peaks, resulting in possible increased fatigue loads and damage of the floating and submerged components. A control design procedure is then proposed to avoid this problem, acting on the kite path planner. Simulation results confirm the effectiveness of the approach.","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141510839","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 : 2024-06-12DOI: 10.1016/j.ejcon.2024.101044
Nishanth Venkatesh, Aditya Dave, Ioannis Faros, Andreas A. Malikopoulos
In this paper, we investigate the control of a cyber–physical system (CPS) while accounting for its vulnerability to external attacks. We formulate a constrained stochastic problem with a robust constraint to ensure robust operation against potential attacks. We seek to minimize the expected cost subject to a constraint limiting the worst-case expected damage an attacker can impose on the CPS. We present a dynamic programming decomposition to compute the optimal control strategy in this robust-constrained formulation and prove its recursive feasibility. We also illustrate the utility of our results by applying them to a numerical simulation.
{"title":"Stochastic control with distributionally robust constraints for cyber–physical systems vulnerable to attacks","authors":"Nishanth Venkatesh, Aditya Dave, Ioannis Faros, Andreas A. Malikopoulos","doi":"10.1016/j.ejcon.2024.101044","DOIUrl":"https://doi.org/10.1016/j.ejcon.2024.101044","url":null,"abstract":"In this paper, we investigate the control of a cyber–physical system (CPS) while accounting for its vulnerability to external attacks. We formulate a constrained stochastic problem with a robust constraint to ensure robust operation against potential attacks. We seek to minimize the expected cost subject to a constraint limiting the worst-case expected damage an attacker can impose on the CPS. We present a dynamic programming decomposition to compute the optimal control strategy in this robust-constrained formulation and prove its recursive feasibility. We also illustrate the utility of our results by applying them to a numerical simulation.","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141530176","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 : 2024-06-12DOI: 10.1016/j.ejcon.2024.101038
Jonathan Frey, Katrin Baumgärtner, Moritz Diehl
This work proposes an efficient treatment of continuous-time optimal control problems with long horizons and nonlinear least-squares costs. In particular, we present the Gauss–Newton Runge–Kutta (GNRK) integrator which provides a high-order cost integration. Crucially, the Hessian of the cost terms required within an SQP-type algorithm is approximated with a Gauss–Newton Hessian. Moreover, penalty formulations for constraints are shown to be particularly effective for optimization with GNRK. An efficient implementation of GNRK is provided in the open-source software framework . We demonstrate the effectiveness of the proposed approach and its implementation on an illustrative example showing a reduction of relative suboptimality by a factor greater than 10 while increasing the runtime by only 10%.
{"title":"Gauss–Newton Runge–Kutta integration for efficient discretization of optimal control problems with long horizons and least-squares costs","authors":"Jonathan Frey, Katrin Baumgärtner, Moritz Diehl","doi":"10.1016/j.ejcon.2024.101038","DOIUrl":"https://doi.org/10.1016/j.ejcon.2024.101038","url":null,"abstract":"This work proposes an efficient treatment of continuous-time optimal control problems with long horizons and nonlinear least-squares costs. In particular, we present the Gauss–Newton Runge–Kutta (GNRK) integrator which provides a high-order cost integration. Crucially, the Hessian of the cost terms required within an SQP-type algorithm is approximated with a Gauss–Newton Hessian. Moreover, penalty formulations for constraints are shown to be particularly effective for optimization with GNRK. An efficient implementation of GNRK is provided in the open-source software framework . We demonstrate the effectiveness of the proposed approach and its implementation on an illustrative example showing a reduction of relative suboptimality by a factor greater than 10 while increasing the runtime by only 10%.","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141510841","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}
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