| 1. |
- Cao, Yuexin, et al.
(author)
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Network Controllability of Turing Reaction and Diffusion Model
- 2022
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In: 2022 41St Chinese Control Conference (Ccc). - : IEEE. ; , s. 259-264
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Conference paper (peer-reviewed)abstract
- In this paper, the controllability problem of the reaction-diffusion (RD) model, or Turing model is studied. Turing model provides a valuable framework for self-organized system and has been widely used to explain to pattern formation in the real life. With the rapidly development of the biology technology, biologists are trying to control the pattern formation artificially and has achieved some progress. However, the influence that exerted on the pattern formation by the external factors, such as light and temperature, remains to be solved. In this work, The RD model is obtained following the assumptions in Turing's original paper and spatially discretized into square grids. The nodes in the outermost layer are considered as candidates for control. Controllability of the RD system with all such nodes as control is first shown. Then controllability of the RD system with minimal number of control nodes is studied. Our results show that nearly 87.5% control nodes can be saved while the system is still controllable. Numerical simulations are provided to demonstrate the effects of controlling the reaction and diffusion of the morphogens.
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| 2. |
- Li, Yibei, 1993-, et al.
(author)
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A Convex Optimization Approach to Inverse Optimal Control
- 2018
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In: 2018 37Th Chinese Control Conference, CCC (CCC). - : IEEE. - 9789881563958 ; , s. 257-262
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Conference paper (peer-reviewed)abstract
- In this paper, the problem of inverse optimal control (IOC) is investigated, where the quadratic cost function of a dynamic process is required to be recovered based on the observation of optimal control sequences. In order to guarantee the feasibility of the problem, the IOC is reformulated as an infinite-dimensional convex optimization problem, which is then solved in the primal-dual framework. In addition, the feasibility of the original IOC could be determined from the optimal value of reformulated problem, which also gives out an approximate solution when the original problem is not feasible. In addition, several simplification methods are proposed to facilitate the computation, by which the problem is reduced to a boundary value problem of ordinary differential equations. Finally, numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed methods.
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| 3. |
- Li, Yibei, 1993-, et al.
(author)
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A Differential Game Approach to Intrinsic Formation Control
- 2022
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In: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 136
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Journal article (peer-reviewed)abstract
- This paper addresses the formation control problem of a multi-agent system in a non-cooperative differential game framework. Both finite horizon and infinite horizon games are considered and their Nash equilibria are studied. The desired formation patterns are achieved by Nash equilibrium strategies in an intrinsic way in the sense that they are only attributed to the inter-agent interaction and geometric properties of the network, where the desired formations are not designated directly in the controller. The whole formation manifold of the desired relative pattern is studied by allowing all orientations of the formation and all permutations of the agents. For finite horizon games the terminal formation of Nash equilibrium trajectories is shown to converge to desired pattern as the length of the time interval tends to infinity. Furthermore the asymptotic stability of the desired formation manifold is also guaranteed in infinite horizon games. Relative patterns of regular polyhedra and antipodal formations are achieved by designing the interaction graph while inter-agent collisions are avoided. Finally, numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed methods.
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| 4. |
- Li, Yibei, 1993-, et al.
(author)
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A Differential Game Approach to Optimal Intrinsic Formation Control
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Other publication (other academic/artistic)abstract
- In this paper, the optimal formation control problem of a multi-agent system is investigated. The foraging behavior of N agents is modeled as a finite-horizon non-cooperative differential game under local information, and its Nash equilibrium is studied. The formations are achieved in an intrinsic way in the sense that they are only attributed to the inter-agent interaction and geometric properties of the network, where the desired formations are not designated beforehand. Through the design of individual costs and network topology, regular polygons, antipodal formations and Platonic solids can be achieved as Nash equilibria while inter-agent collisions are avoided. Finally, numerical simulations are provided in both two-dimensional and three-dimensional Euclidean space to demonstrate the effectiveness and feasibility of the proposed methods.
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| 5. |
- Li, Yibei, 1993-, et al.
(author)
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Continuous-Time Inverse Quadratic Optimal Control Problem
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Other publication (other academic/artistic)abstract
- In this paper, the problem of finite horizon inverse optimal control (IOC) is investigated, where the quadratic cost function of a dynamic process is required to be recovered based on the observation of optimal control sequences.We propose the first complete result of the necessary and sufficient condition for the existence of corresponding LQ cost functions. Under feasible cases, the analytic expression of the whole solution space is derived and the equivalence of weighting matrices in LQ problems is discussed. For infeasible problems, an infinite dimensional convex problem is formulated to obtain a best-fit approximate solution with minimal control residual. And the optimality condition is solved under a static quadratic programming framework to facilitate the computation. Finally, numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed methods.
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| 6. |
- Li, Yibei, 1993-, et al.
(author)
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Continuous-time inverse quadratic optimal control problem
- 2020
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In: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 117
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Journal article (peer-reviewed)abstract
- In this paper, the problem of finite horizon inverse optimal control (IOC) is investigated, where the quadratic cost function of a dynamic process is required to be recovered based on the observation of optimal control sequences. We propose the first complete result of the necessary and sufficient condition for the existence of corresponding standard linear quadratic (LQ) cost functions. Under feasible cases, the analytic expression of the whole solution space is derived and the equivalence of weighting matrices in LQ problems is discussed. For infeasible problems, an infinite dimensional convex problem is formulated to obtain a best-fit approximate solution with minimal control residual. And the optimality condition is solved under a static quadratic programming framework to facilitate the computation. Finally, numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed methods.
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| 7. |
- Li, Yibei, 1993-, et al.
(author)
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Credit Scoring by Incorporating Dynamic Network Information
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Other publication (other academic/artistic)abstract
- In this paper, the credit scoring problem is studied by incorporating network information, where the advantages of such incorporation are investigated in two scenarios. Firstly, a Bayesian optimal filter is proposed to provide a prediction for lenders assuming that published credit scores are estimated merely from structured individual data. Such prediction is used as a monitoring indicator for the risk warning in lenders' future financial decisions. Secondly, we further propose a recursive Bayes estimator to improve the accuracy of credit scoring estimation by incorporating the dynamic interaction topology of clients as well. It is shown that under the proposed evolution framework, the designed estimator has a higher precision than any efficient estimator, and the mean square errors are strictly smaller than the Cram\'er--Rao lower bound for clients within a certain range of scores. Finally, simulation results for a specific case illustrate the effectiveness and feasibility of the proposed methods.
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| 8. |
- Li, Yibei, 1993-, et al.
(author)
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Credit scoring by incorporating dynamic networked information
- 2020
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In: European Journal of Operational Research. - : Elsevier B.V.. - 0377-2217 .- 1872-6860. ; 286:3, s. 1103-1112
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Journal article (peer-reviewed)abstract
- In this paper, the credit scoring problem is studied by incorporating networked information, where the advantages of such incorporation are investigated theoretically in two scenarios. Firstly, a Bayesian optimal filter is proposed to provide risk prediction for lenders assuming that published credit scores are estimated merely from structured financial data. Such prediction can then be used as a monitoring indicator for the risk management in lenders’ future decisions. Secondly, a recursive Bayes estimator is further proposed to improve the precision of credit scoring by incorporating the dynamic interaction topology of clients. It is shown theoretically that under the proposed evolution framework, the designed estimator has a higher precision than any efficient estimator, and the mean square errors are strictly smaller than the Cramér–Rao lower bound for clients within a certain range of scores. Finally, simulation results for a special case illustrate the feasibility and effectiveness of the proposed algorithms.
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| 9. |
- Li, Yibei, 1993-
(author)
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Dynamic Optimization for Agent-Based Systems and Inverse Optimal Control
- 2019
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Licentiate thesis (other academic/artistic)abstract
- This dissertation is concerned with three problems within the field of optimization for agent--based systems. Firstly, the inverse optimal control problem is investigated for the single-agent system. Given a dynamic process, the goal is to recover the quadratic cost function from the observation of optimal control sequences. Such estimation could then help us develop a better understanding of the physical system and reproduce a similar optimal controller in other applications. Next, problems of optimization over networked systems are considered. A novel differential game approach is proposed for the optimal intrinsic formation control of multi-agent systems. As for the credit scoring problem, an optimal filtering framework is utilized to recursively improve the scoring accuracy based on dynamic network information.In paper A, the problem of finite horizon inverse optimal control problem is investigated, where the linear quadratic (LQ) cost function is required to be estimated from the optimal feedback controller. Although the infinite-horizon inverse LQ problem is well-studied with numerous results, the finite-horizon case is still an open problem. To the best of our knowledge, we propose the first complete result of the necessary and sufficient condition for the existence of corresponding LQ cost functions. Under feasible cases, the analytic expression of the whole solution space is derived and the equivalence of weighting matrices is discussed. For infeasible problems, an infinite dimensional convex problem is formulated to obtain a best-fit approximate solution with minimal control residual, where the optimality condition is solved under a static quadratic programming framework to facilitate the computation.In paper B, the optimal formation control problem of a multi-agent system is studied. The foraging behavior of N agents is modeled as a finite-horizon non-cooperative differential game under local information, and its Nash equilibrium is studied. The collaborative swarming behaviour derived from non-cooperative individual actions also sheds new light on understanding such phenomenon in the nature. The proposed framework has a tutorial meaning since a systematic approach for formation control is proposed, where the desired formation can be obtained by only intrinsically adjusting individual costs and network topology. In contrast to most of the existing methodologies based on regulating formation errors to the pre-defined pattern, the proposed method does not need to involve any information of the desired pattern beforehand. We refer to this type of formation control as intrinsic formation control. Patterns of regular polygons, antipodal formations and Platonic solids can be achieved as Nash equilibria of the game while inter-agent collisions are naturally avoided.Paper C considers the credit scoring problem by incorporating dynamic network information, where the advantages of such incorporation are investigated in two scenarios. Firstly, when the scoring publishment is merely individual--dependent, an optimal Bayesian filter is designed for risk prediction, where network observations are utilized to provide a reference for the bank on future financial decisions. Furthermore, a recursive Bayes estimator is proposed to improve the accuracy of score publishment by incorporating the dynamic network topology as well. It is shown that under the proposed evolution framework, the designed estimator has a higher precision than all the efficient estimators, and the mean square errors are strictly smaller than the Cramér-Rao lower bound for clients within a certain range of scores.
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| 10. |
- Li, Yibei, 1993-, et al.
(author)
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Identifiability and Solvability in Inverse Linear Quadratic Optimal Control Problems
- 2021
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In: Journal of Systems Science and Complexity. - : Springer Nature. - 1009-6124 .- 1559-7067. ; 34:5, s. 1840-1857
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Journal article (peer-reviewed)abstract
- In this paper, the inverse linear quadratic (LQ) problem over finite time-horizon is studied. Given the output observations of a dynamic process, the goal is to recover the corresponding LQ cost function. Firstly, by considering the inverse problem as an identification problem, its model structure is shown to be strictly globally identifiable under the assumption of system invertibility. Next, in the noiseless case a necessary and sufficient condition is proposed for the solvability of a positive semidefinite weighting matrix and its unique solution is obtained with two proposed algorithms under the condition of persistent excitation. Furthermore, a residual optimization problem is also formulated to solve a best-fit approximate cost function from sub-optimal observations. Finally, numerical simulations are used to demonstrate the effectiveness of the proposed methods.
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