This paper investigates the inverse optimal control problems for continuous-time linear quadratic regulators over finite-time horizons, aiming to reconstruct the control, state, and terminal cost matrices in the objective function from observed optimal inputs. Previous studies have mainly explored the recovery of state cost matrices under the assumptions that the system is controllable and the control cost matrix is given. Motivated by various applications in which the control cost matrix is unknown and needs to be identified, the authors present two reconstruction methods. The first exploits the full trajectory of the feedback matrix and establishes the necessary and sufficient condition for unique recovery. To further reduce the computational complexity, the second method utilizes the feedback matrix at some time points, where sufficient conditions for uniqueness are provided. Moreover, the authors study the recovery of the state and terminal cost matrices in a more general manner. Unlike prior works that assume system controllability, the authors analyse its impact on well-posedness, and derive expressions for unknown matrices for both controllable and uncontrollable cases. Finally, the authors characterize the structural connection between the inverse problems with the control cost matrix either to be reconstructed or given as a prior.

In this paper, the formation control problem for a multi-agent system is studied. Two new robust control algorithms for serial and parallel formations respectively are proposed, which take the constraints of limited field of view into consideration. Without the need for any global information, the only relative information required is distance and bearing angle, thus is easy to implement with onboard directional sensors. It is then demonstrated how complex formations can be realized by combining the proposed basic controllers. Finally, effectiveness of the proposed algorithms is illustrated by numerical examples.

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. 

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.

In this paper, the problem of inverse quadratic optimal control over finite time-horizon for discrete-time linear systems is considered. Our goal is to recover the corresponding quadratic objective function using noisy observations. First, the identifiability of the model structure for the inverse optimal control problem is analyzed under relative degree assumption and we show the model structure is strictly globally identifiable. Next, we study the inverse optimal control problem whose initial state distribution and the observation noise distribution are unknown, yet the exact observations on the initial states are available. We formulate the problem as a risk minimization problem and approximate the problem using empirical average. It is further shown that the solution to the approximated problem is statistically consistent under the assumption of relative degrees. We then study the case where the exact observations on the initial states are not available, yet the observation noises are known to be white Gaussian distributed and the distribution of the initial state is also Gaussian (with unknown mean and covariance). EM-algorihm is used to estimate the parameters in the objective function. The effectiveness of our results are demonstrated by numerical examples.

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.

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.

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.

In this paper, the formation control problem of a multi-agent system is studied. The foraging behavior is modeled as a finite-horizon non-cooperative differential game under local information, and the existence and properties of Nash equilibria are 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 are achieved as Nash equilibria while inter-agent collision is avoided. While the focus is on the finite horizon case, it is also studied how the formation patterns would change as the length of the time interval tends to infinity. Finally, numerical simulations are provided in both two-dimensional and three-dimensional Euclidean space to demonstrate the effectiveness and feasibility of the proposed methods.

This paper addresses the intrinsic formation control problem of a multi-agent system. The foraging behavior of N agents is modeled as an infinite-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, patterns of Platonic solids can be achieved as Nash equilibria while inter-agent collisions are avoided. Exponential convergence to the manifold of Platonic patterns is proved. Finally, numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed methods.