Automatica最新文献

To investigate objects driven by external input and players’ interests, the game-based control system (GBCS) was established. In this system, the high-level leader does not participate directly but regulates the low-level game to make followers’ Nash equilibrium(NE) “better”. This article focuses on a specific type of GBCSs with rational players, where the open-loop NE is unique under any given initial state and macro-regulation. We discuss two kinds of regulations on NEs: achieving reachability among NEs through macro-regulation and Pareto improvability on NEs that can benefit at least one follower without harming anyone else. These regulations help reduce the widespread inconsistency between individual and collective rationality. Moreover, conditions are provided to determine controllability and Pareto improvability on NEs. Finally, an example on opinion dynamics is presented to demonstrate the effectiveness of obtained theoretical results.

Optimal control strategies are studied through the application of the Pontryagin’s Maximum Principle for a class of non-linear differential systems that are commonly used to describe resource allocation during bacterial growth. The approach is inspired by the optimality of numerous regulatory mechanisms in bacterial cells. In this context, we aim to predict natural feedback loops as optimal control solutions so as to gain insight on the behavior of microorganisms from a control-theoretical perspective. The problem is posed in terms of a control function $u_0\left(t\right)$ representing the fraction of the cell dedicated to protein synthesis, and $n$ additional controls $u_i\left(t\right)$ modeling the fraction of the cell responsible for the consumption of the available nutrient sources in the medium. By studying the necessary conditions for optimality, it is possible to prove that the solutions follow a bang–singular–bang structure, and that they are characterized by a sequential uptake pattern known as diauxic growth, which prioritizes the consumption of richer substrates over poor nutrients. Numerical simulations obtained through an optimal control solver confirm the theoretical results. Finally, we provide an application to batch cultivation of E. coli growing on glucose and lactose. For that, we propose a state feedback law that is based on the optimal control, and we calibrate the obtained closed-loop model to experimental data.

Recent years have witnessed a booming interest in data-driven control of dynamical systems. However, the implicit data-driven output predictors are vulnerable to uncertainty such as process disturbance and measurement noise, causing unreliable predictions and unexpected control actions. In this brief, we put forward a new data-driven approach to output prediction of stochastic linear time-invariant (LTI) systems. By utilizing the innovation form, the uncertainty in stochastic LTI systems is recast as innovations that can be readily estimated from input–output data without knowing system matrices. In this way, by applying the fundamental lemma to the innovation form, we propose a new innovation-based data-driven output predictor (OP) of stochastic LTI systems, which bypasses the need for identifying state–space matrices explicitly and building a state estimator. The boundedness of the second moment of prediction errors in closed-loop is established under mild conditions. The proposed data-driven OP can be integrated into optimal control design for better performance. Numerical simulations demonstrate the outperformance of the proposed innovation-based methods in output prediction and control design over existing formulations.

The problem of online change point detection is to detect abrupt changes in properties of time series, ideally as soon as possible after those changes occur. Existing work on online change point detection either assumes i.i.d. data, focuses on asymptotic analysis, does not present theoretical guarantees on the trade-off between detection accuracy and detection delay, or is only suitable for detecting single change points. In this work, we study the online change point detection problem for linear dynamical systems with unknown dynamics, where the data exhibits temporal correlations and the system could have multiple change points. We develop a data-dependent threshold that can be used in our test that allows one to achieve a pre-specified upper bound on the probability of making a false alarm. We further provide a finite-sample-based bound for the probability of detecting a change point. Our bound demonstrates how parameters used in our algorithm affect the detection probability and delay, and provides guidance on the minimum required time between changes to guarantee detection.

In this paper, the distributed time-varying optimization problem is investigated for networked Lagrangian systems with parametric uncertainties. Usually, in the literature, to address some distributed control problems for nonlinear systems, a networked virtual system is constructed, and a tracking algorithm is designed such that the agents’ physical states track the virtual states. It is worth pointing out that such an idea requires the exchange of the virtual states and hence necessitates communication among the group. In addition, due to the complexities of the Lagrangian dynamics and the distributed time-varying optimization problem, there exist significant challenges. This paper proposes distributed time-varying optimization algorithms that achieve zero optimum-tracking errors for the networked Lagrangian agents without the communication requirement. The main idea behind the proposed algorithms is to construct a reference system for each agent to generate a reference velocity using absolute and relative physical state measurements with no exchange of virtual states needed, and to design adaptive controllers for Lagrangian systems such that the physical states are able to track the reference velocities and hence the optimal trajectory. The algorithms introduce mutual feedback between the reference systems and the local controllers via physical states/measurements and are amenable to implementation via local onboard sensing in a communication unfriendly environment. Specifically, first, a base algorithm is proposed to solve the distributed time-varying optimization problem for networked Lagrangian systems under switching graphs. Then, based on the base algorithm, a continuous function is introduced to approximate the signum function, forming a continuous distributed optimization algorithm and hence removing the chattering. Such a continuous algorithm is convergent with bounded ultimate optimum-tracking errors, which are proportion to approximation errors. Finally, numerical simulations are provided to illustrate the validity of the proposed algorithms.

For $n$-qubit stochastic open quantum systems, an online quantum state estimation (OQSE) algorithm and the associated online estimated-based-state feedback control (OQSE-FC) are proposed in this paper. The proposed OQSE algorithm integrates the online alternating direction multiplier method (OADM) to the continuous weak measurement (CWM). The quantum state feedback control laws are designed based on the Lyapunov stability theorem, and the states for feedback control are online estimated by OQSE algorithm. The convergence of OQSE algorithm and the asymptotic stability of the state feedback control laws are proved.

We propose a scalable, distributed algorithm for the optimal transport of large-scale multi-agent systems. We formulate the problem as one of steering the collective towards a target probability measure while minimizing the total cost of transport, with the additional constraint of distributed implementation. Using optimal transport theory, we realize the solution as an iterative transport based on a stochastic proximal descent scheme. At each stage of the transport, the agents implement an online, distributed primal–dual algorithm to obtain local estimates of the Kantorovich potential for optimal transport from the current distribution of the collective to the target distribution. Using these estimates as their local objective functions, the agents then implement the transport by stochastic proximal descent. This two-step process is carried out recursively by the agents to converge asymptotically to the target distribution. We rigorously establish the underlying theoretical framework and convergence of the algorithm and test its behavior in numerical experiments.

This paper presents a switching control strategy as a criterion for policy selection in stochastic Dynamic Programming problems over an infinite time horizon. In particular, the Bellman operator, applied iteratively to solve such problems, is generalized to the case of stochastic policies, and formulated as a discrete-time switched affine system. Then, a Lyapunov-based policy selection strategy is designed to ensure the practical convergence of the resulting closed-loop system trajectories towards an appropriately chosen reference value function. This way, it is possible to verify how the chosen reference value function can be approached by using a stabilizing switching signal, the latter defined on a given finite set of stationary stochastic policies. Finally, the presented method is applied to the Value Iteration algorithm, and an illustrative example of a recycling robot is provided to demonstrate its effectiveness in terms of convergence performance.

In this paper, we propose a new property of quantitative nonblockingness of an automaton with respect to a given cover on its set of marker states. This property quantifies the standard nonblocking property by capturing the practical requirement that every subset (i.e. cell) of marker states can be reached within a prescribed number of steps from any reachable state and following any trajectory of the system. Accordingly, we formulate a new problem of quantitatively nonblocking supervisory control, and characterize its solvability in terms of a new concept of quantitative language completability. It is proven that there exists the unique supremal quantitatively completable sublanguage of a given language, and we develop an effective algorithm to compute the supremal sublanguage. Finally, combining with the algorithm of computing the supremal controllable sublanguage, we design an algorithm to compute the maximally permissive solution to the formulated quantitatively nonblocking supervisory control problem.

This study focuses on the problem of optimal mismatched disturbance rejection control for uncontrollable linear discrete-time systems. In contrast to previous studies, by introducing a quadratic performance index such that the regulated state can track a reference trajectory and minimize the effects of disturbances, mismatched disturbance rejection control is transformed into a linear quadratic tracking problem. The necessary and sufficient conditions for the solvability of this problem over a finite horizon and a disturbance rejection controller are derived by solving a forward–backward difference equation. In the case of an infinite horizon, a sufficient condition for the stabilization of the system is obtained under the detectable condition. Additionally, in combination with the generalized extended state observer, a controller design method is proposed, and the stability analysis of the system under this controller is presented. This paper details our novel approach to disturbance rejection. Finally, four examples are provided to demonstrate the effectiveness of the proposed method.