Search

In this paper, we consider the adaptive stabilization problem for a basic class of linearquadratic noncooperative stochastic differential games when the systems matrices are unknown to the regulator and the players. This is a typical problem of game-based control systems (GBCS) introduced and studied recently, which have a hierarchical decision-making structure: there is a controller at the upper level acting as a global regulator which makes its decision first, and the players at the lower level are assumed to play a typical zero-sum differential games. The main purpose of the paper is to study how the adaptive regulator can be designed to make the GBCS globally stable and at the same time to ensure a Nash equilibrium reached by the players, where the adaptive strategies of the players are assumed to be constructed based on the standard least squares estimators. The design of the global regulator is an integration of the weighted least squares parameter estimator, random regularization and diminishing excitation methods. Under the assumption that the system matrix pair (A, B) is controllable and there exists a stabilizing solution for the corresponding algebraic Riccati equation, it is shown that the closed-loop adaptive GBCS will be globally stable, and at the same time reach a Nash equilibrium by the players. [ABSTRACT FROM AUTHOR]

In this paper, we study optimal stochastic control problems for stochastic systems driven by non-Markov subdiffusion BLt, which have mixed features of deterministic and stochastic controls. Here Bt is the standard Brownian motion on R, and Lt := inf { r > 0 : Sr > t}, t ≥ 0, is the inverse of a subordinator St with drift κ > 0 that is independent of Bt. We obtain stochastic maximum principles (SMPs) for these systems using both convex and spiking variational methods, depending on whether or not the domain is convex. To derive SMPs, we first establish a martingale representation theorem for subdiffusions BLt , and then use it to derive the existence and uniqueness result for the solutions of backward stochastic differential equations (BSDEs) driven by subdiffusions, which may be of independent interest. We also derive sufficient SMPs. Application to a linear quadratic system is given to illustrate the main results of this paper. [ABSTRACT FROM AUTHOR]

Though there are hundreds of papers on rational spectral factorization, most of them are concerned with full-rank spectral densities. In this paper we propose a novel approach for spectral factorization of a rank-deficient spectral density, leading to a minimum-phase full-rank spectral factor, in both the discrete-time and continuous-time cases. Compared with several approaches to low-rank spectral factorization, our approach exploits a deterministic relation inside the factor, leading to high computational efficiency. In addition, we show that this method is easily used in identification of low-rank processes and in Wiener filtering. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the tracking performance and antidisturbance ability of the widely used proportional-integral-derivative (PID) controllers in practice. Towards this end, we consider a basic class of second-order nonlinear stochastic control systems subject to model uncertainties and external disturbances, and focus on the ability of the classical PID controller to track time-varying reference signals. First, under some suitable conditions on the system nonlinear functions, reference signals, and external disturbances, we show that such control systems can be stabilized in the mean square sense, provided that the three PID gains are selected from a stability region constructed in the paper. Besides, it is shown that the steady-state tracking error has an upper bound proportional to the sum of the varying rates of reference signals, the varying rates of external disturbances, and the intensity of random noises. Meanwhile, its proportional coefficient depends on the selection of PID gains, which can be made arbitrarily small by choosing suitably large PID gains. Finally, by introducing a desired transient process which is shaped from the reference signal, a new PID tuning rule is presented, which can guarantee both the expected steady state and transient tracking performance. [ABSTRACT FROM AUTHOR]

In this paper, we focus on a general linear time-invariant multiagent system with heterogeneous actuator saturation to answer the main question: how to achieve global consensus under the premise of asymptotically null controllable with bounded controls of each agent so as to make breakthroughs from the perspectives of global consensus, heterogeneous actuator saturation, communication noises, and distributed characteristic preservation. We introduce a distributed control algorithm that incorporates a redesigned saturation function featuring a decentralized dynamic saturation level to achieve these objectives. Each component of the dynamic saturation level self-updates according to an adaptive strategy. The proposed method effectively eliminates heterogeneous actuator saturation by carefully selecting both the constant and time-varying saturation parameters in the adaptive strategy of the dynamic saturation level. Our approach achieves both state feedback--based and output feedback--based global consensus, with the latter utilizing a special coordinate decomposition. Numerical simulations demonstrate the efficacy of our method. [ABSTRACT FROM AUTHOR]

We consider dynamic games defined over an infinite horizon, characterized by linear, discrete-time dynamics and quadratic cost functionals. Considering such linear-quadratic dynamic games, we focus on their solutions in terms of Nash equilibrium strategies. Both feedback (F-NE) and open-loop (OL-NE) Nash equilibrium solutions are considered. The contributions of the paper are threefold. First, our detailed study reveals some interesting structural insights in relation to F-NE solutions. Second, as a stepping stone toward our consideration of OL-NE strategies, we consider a specific infinite-horizon discrete-time (single-player) optimal control problem, wherein the dynamics are influenced by a known exogenous input and draw connections between its solution obtained via dynamic programming and Pontryagin's minimum principle. Finally, we exploit the latter result to provide a characterization of OL-NE strategies of the class of infinite-horizon dynamic games. The results and key observations made throughout the paper are illustrated via a numerical example. [ABSTRACT FROM AUTHOR]

Unlike regular linear quadratic regulator (LQR) problems, singular LQR problems, in general, cannot be solved using a static state-feedback controller. This work is primarily focused on the design of feedback controllers which solve the singular LQR problem. We show that such problems can be solved using proportional-derivative (PD) state-feedback controllers. It is well known in the literature that the maximal rank-minimizing solution of the singular LQR linear matrix inequality (LMI) is pivotal in solving the singular LQR problem. In this paper, we first make use of this maximal rank-minimizing solution to compute the optimal trajectories. Then we provide a PD feedback controller that restricts the trajectories of the closed-loop system to these optimal ones and thus solves the singular LQR problem. While numerous solutions to this problem have been proposed over the course of the extensive research efforts in this field, a controller in the form of a PD state feedback has been long sought after. Our approach is based on the notion of weakly unobservable (slow) and strongly reachable (fast) subspaces developed in [M. Hautus and L. Silverman, Linear Algebra Appl., 50 (1983), pp. 369--402]. But, unlike in that reference, we employ these notions to the corresponding Hamiltonian system and not to the plant. This crucial extension of these well-known subspaces to the corresponding Hamiltonian system is key to the optimal PD feedback design that we propose in this paper. It is well known that an optimal state feedback for the singular LQR problem does not exist; the limiting state-feedback controller of the suboptimal ones (high gain controllers) has unbounded coefficients as optimality is approached. We show in this paper that the limiting high gain controller is in fact a PD controller. [ABSTRACT FROM AUTHOR]

This paper studies several problems related to quadratic matrix inequalities (QMIs), i.e., inequalities in the Loewner order involving quadratic functions of matrix variables. In particular, we provide conditions under which the solution set of a QMI is nonempty, convex, or bounded or has a nonempty interior. We also provide a parameterization of the solution set of a given QMI. In addition, we state results regarding the image of such sets under linear maps, which characterize a subset of "structured"" solutions to a QMI. Thereafter, we derive matrix versions of the classical S-lemma and Finsler's lemma that provide conditions under which all solutions to one QMI also satisfy another QMI. The results will be compared to related work in the robust control literature, such as the full block S-procedure and Petersen's lemma, and it is demonstrated how existing results can be obtained from the results of this paper as special cases. Finally, we show how the various results for QMIs can be applied to the problem of data-driven stabilization. This problem involves finding a stabilizing feedback controller for an unknown dynamical system influenced by noise on the basis of a finite set of data. We provide general necessary and sufficient conditions for data-based quadratic stabilization. In addition, we demonstrate how to reduce the computational complexity of data-based stabilization by leveraging the aforementioned results. This involves separating the computation of the Lyapunov function and the controller and also leads to explicit formulas for data-guided feedback gains. [ABSTRACT FROM AUTHOR]

This paper investigates the sampled-data stabilization of continuous-time probabilistic logical control networks (CT-PLCNs). CT-PLCNs can provide quantitative and accurate descriptions for the transient kinetics in comparing discrete-time probabilistic logical control networks (DT-PLCNs). First, CT-PLCNs are transformed into switched continuous-time probabilistic logical networks by regarding the control input as a switching signal. In this setup, CT-PLCNs can be classified into two types: one with stable modes and the other with only unstable modes. Then the concept of average l-sample dwell time is proposed to describe the scenario, where the dwell time of each mode is an integral multiple of the sampling period l. Based on this, the stabilization conditions for CT-PLCNs are established by restricting the sampling dwell time of controller modes. Furthermore, a copositive Lyapunov function is constructed for the case with stable modes and is discretized for the case without stable modes, providing a new framework for studying the stabilization of CT-PLCNs. Finally, a chemical model generated by GINsim is provided to demonstrate the feasibility of the obtained theoretical results. Overall, this paper provides new insights into the stabilization of CT-PLCNs and presents practical applications for chemical models. [ABSTRACT FROM AUTHOR]

This paper studies the linearization of the viscous tank--liquid system. The linearization of the tank--liquid system gives a high-order partial differential equation, which is a combination of a wave equation with Kelvin--Voigt damping and a Euler--Bernoulli beam equation. The single input appears in two of the boundary conditions (boundary input). The paper provides results both for the open-loop system (existence/uniqueness of solutions and stability properties of the open-loop system) as well as results for the construction of feedback stabilizers. More specifically, the feedback design methodology is based on control Lyapunov functionals (CLFs). The proposed CLFs are modifications and augmentations of the total energy functionals for the tank--liquid system so that the dissipative effects of viscosity, friction, and surface tension are captured. By focusing on the linearized water--tank system, we are able to provide results that are not provided in the nonlinear case: (1) existence and uniqueness of solutions, (2) simultaneous presence of friction and surface tension, and (3) stabilization in a stronger norm, using a different CLF. [ABSTRACT FROM AUTHOR]

This paper investigates a reversible investment problem with finite horizon, in which a social planner aims to determine the project's capacity level to minimize the expected total costs. These costs depend on the demand for the good, the supply in terms of production capacity, and the proportional costs. The issue of irreversible investment has been examined by Han and Yi [Commun. Nonlinear Sci. Numer. Simul., 109 (2022), 106302]. Mathematically, the reversible investment problem can be formulated as a singular stochastic control problem. The value function satisfies a two-dimensional parabolic variational inequality subject to gradient constraint, which leads to two time-dependent free boundaries representing optimal investment and disinvestment strategies. We employ a partial differential equation approach to characterize the continuity, monotonicity, and horizontal asymptotes of free boundaries, as well as establish the C2,1 regularity of the value function. To the best of our knowledge, the approach to analyze the behavior of free boundaries is novel in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the exact controllability for a refined stochastic wave equation with three controls by establishing a novel Carleman estimate for a backward hyperbolic-like operator. Compared with the known result [Q. L\"u and X Zhang, Mathematical Control Theory for Stochastic Partial Differential Equations, Springer, Cham, Switzerland, 2021], the novelty of this paper is twofold: (1) Our model contains the effects in the drift terms when we put controls directly in the diffusion terms, which is more sensible for practical applications; (2) We provide an explicit description of the waiting time which is sharp in the case of dimension one and is independent of the coefficents of lower terms. [ABSTRACT FROM AUTHOR]

The use of coordinate processes for the modeling of impulse control for general Markov processes typically involves the construction of a probability measure on a countable product of copies of the path space. In addition, admissibility of an impulse control policy requires that the random times of the interventions be stopping times with respect to different filtrations arising from the different component coordinate processes. When the underlying Markov process has continuous paths, however, a simpler model can be developed which takes the single path space as its probability space and uses the natural filtration with respect to which the intervention times must be stopping times. Moreover, this model construction allows for impulse control with random effects whereby the decision maker selects a distribution of the new state. This paper gives the construction of the probability measure on the path space for an admissible intervention policy subject to a randomized impulse mechanism. In addition, a class of polices is defined for which the paths between interventions are independent and a further subclass for which the cycles following the initial cycle are identically distributed. A benefit of this smaller subclass of policies is that one is allowed to use classical renewal arguments to analyze long-term average control problems. Further, the paper defines a class of stationary impulse policies for which the family of models gives a Markov family. The decision to use an (s,S) ordering policy in inventory management provides an example of an impulse policy for which the process has independent and identically distributed cycles and the family of models forms a Markov family. [ABSTRACT FROM AUTHOR]

We investigate the control-coding (CC) capacity of general dynamical decision models (DMs) that involve nonlinear filtering, which is absent in the specific DMs investigated in [C. K. Kourtellaris and C. D. Charalambous, IEEE Trans. Inform. Theory, 64 (2018), pp. 4962--4992]. We derive characterizations of CC capacity and we show their equivalence to extremum problems of maximizing the information theoretic measure of directed information from the input process to the output process of the DM over randomized strategies. Due to the generality of the DMs, the CC capacity is shown to be equivalent to partially observable Markov decision problems, contrary to the DMs in the above mentioned paper, which give rise to fully observable Markov decision problems. Subsequently, the CC capacity is transformed, using nonlinear filtering theory, to fully observable Markov decision problems. For the application example of a Gaussian DM with past dependence on inputs and outputs, we prove a decentralized separation principle that states optimal inputs are Gaussian and consist of (i) a control, (ii) an estimation, and (iii) an information transmission part, which interact in a specific order. The optimal control and estimation parts are related to linear-quadratic Gaussian stochastic optimal control problems with partial information. Various degenerated cases are discussed, including examples from the above mentioned paper, which do not involve estimation. [ABSTRACT FROM AUTHOR]

The title of the present work is a nod to the paper "The hybrid maximum principle is a consequence of Pontryagin maximum principle" by Dmitruk and Kaganovich [Systems Control Lett., 57 (2008), pp. 964--970]. We investigate a similar framework of hybrid optimal control problems that is also different from Dmitruk and Kaganovich's. Precisely, we consider a general control system that is described by a differential equation involving a spatially heterogeneous dynamics. In that context, the sequence of dynamics followed by the trajectory and the corresponding switching times are fully constrained by the state position. We prove with an explicit counterexample that the augmentation technique used by Dmitruk and Kaganovich cannot be fully applied to our setting, but we show that it can be adapted by introducing a new notion of local solution to classical optimal control problems and by establishing a corresponding Pontryagin maximum principle. Thanks to this method, we derive a hybrid maximum principle adapted to our setting, with a simple proof that does not require any technical tools (such as implicit function arguments) to handle the dynamical discontinuities. [ABSTRACT FROM AUTHOR]

This paper investigates new sufficient conditions for the stability, asymptotic stability, and global asymptotic stability of nonlinear autonomous systems, specifically in cases where the first derivative of the Lyapunov function candidate may have both positive and negative values on its domain. The main contribution of this approach is the introduction of a new auxiliary function that relaxes the stability conditions, allowing the first derivative of the Lyapunov function candidate to be less than or equal to a nonnegative function. The suggested auxiliary function should be integrable within our first theorem. Meanwhile, our first corollary presents a technique that simplifies the task by establishing specific conditions related to differential inequalities. This weaker condition in the proposed results enables the establishment of stability properties in cases where the Lyapunov function candidate is not well chosen or finding a Lyapunov function is not straightforward. Additionally, it is proven that the original Lyapunov method for autonomous systems is a special case of our first theorem. Furthermore, it is demonstrated that assumptions in previous studies, such as Matrosov's theorem or results on higher-order derivatives of the Lyapunov function, guarantee the existence of our auxiliary function. Finally, lemmas are provided to construct these auxiliary functions, and examples are presented to demonstrate the effectiveness of this approach. This work will contribute to the development of stability analysis techniques for nonlinear autonomous systems. [ABSTRACT FROM AUTHOR]

We consider the Hegselmann--Krause opinion formation model with leadership and time delay, which is a generalization of the model studied byWongkaew, Caponigro, and Borzi [Math. Models Methods Appl. Sci., 25 (2015), pp. 565--585], dealing with the control strategies without time delay effect. Numerical simulations suggest that the consensus can still emerge asymptotically in the opinion evolution flow under the leader's control even when the time delay is large. However, rigorous theoretical analysis for such consensus dynamics still lacks a complete understanding. In this paper, we present an iterated framework for the consensus control behavior for the delayed Hegselmann--Krause model with leadership, without any restriction on the length of the time delay. After that, we design a simple control strategy which can steer all agents to any target opinion and give a theoretical proof of its validity. Numerical simulations are performed to confirm theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the prescribed-time output feedback stabilization problem for a class of nonlinear time-delay systems. First, a novel dual-gain function is put forward by exploiting the dynamic gain and the time-varying gain function to design the reduced-order observer for reconstructing unavailable states. Then, by utilizing the Lyapunov--Krasovskii functional and state variables of the reduced-order observer, a new prescribed-time controller is presented based on the nonscaling design framework. Since no state scaling is required in controller design process under this framework, our control strategy is simpler and can greatly reduce the computational burden. Further, compared with the previous prescribed-time stabilization results, our designed controller acts on the entire time domain, not just a limited time interval. Based on our proposed stability criterion, it is proved that the controller can render that all system state variables converge to the origin within the prescribed time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

We consider a class of zero-sum stopper versus singular-controller games in which the controller can only act on a subset d0 < d of the d coordinates of a controlled diffusion. Due to the constraint on the control directions these games fall outside the framework of recently studied variational methods. In this paper we develop an approximation procedure, based on L1-stability estimates for the controlled diffusion process and almost sure convergence of suitable stopping times. That allows us to prove existence of the game's value and to obtain an optimal strategy for the stopper under continuity and growth conditions on the payoff functions. This class of games is a natural extension of (single-agent) singular control problems, studied in the literature, with similar constraints on the admissible controls. [ABSTRACT FROM AUTHOR]

In this paper, we study discounted stochastic games with an additive rewards and transitions (ARAT) structure. We assume that the transition probabilities are dominated by some probability measures on a countably generated measurable state space and are norm continuous in actions of the players. We prove the existence of Markov perfect equilibria in which the players can use randomization on two pure actions in each state. When the state space is countable, then we show that there exists a pure Markov perfect equilibrium. Assuming additionally that the transition probabilities have no conditional atoms, we establish some existence results on pure Markov perfect equilibria for ARAT games with uncountable state space using a version of Lyapunov's theorem for conditional expectation of correspondences due to Dynkin and Evstigneev. We also include a wide-ranging discussion on equilibria for discounted stochastic games with a general state space. [ABSTRACT FROM AUTHOR]

In this paper we study discrete-time Markov decision processes with Borel state and action spaces under the risk-sensitive average cost criterion. The cost function can be unbounded. We introduce a new kernel and prove the quasi-compactness of the kernel from which the multiplicative Poisson equation is derived. Moreover, we develop a new approach to show the existence of a solution to the risk-sensitive average cost optimality equation and obtain the existence of an optimal deterministic stationary policy. Furthermore, we give two examples to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of optimal pairs for optimal control problems with their states constrained pointwise to Riemannian manifolds. For this purpose, by means of the Riemannian geometric tool, we introduce a crucial Cesari-type property, which is an extension of the classical Cesari property (see Definition 3.3, p. 51 in [L. D. Berkovitz, Optimal Control Theory, Appl. Math. Sci. 12, Springer-Verlag, New York, Heidelberg, 1974]) from the setting of Euclidean spaces to that of Riemannian manifolds. Moreover, we show the efficiency of our result by a concrete example. [ABSTRACT FROM AUTHOR]

This paper studies stochastic control problems with the action space taken to be probability measures, with the objective penalized by the relative entropy. We identify a suitable metric space on which we construct a gradient flow for the measure-valued control process, in the set of admissible controls, along which the cost functional is guaranteed to decrease. It is shown that any invariant measure of this gradient flow satisfies the Pontryagin optimality principle. If the problem we work with is sufficiently convex, the gradient flow converges exponentially fast. Furthermore, the optimal measure-valued control process admits a Bayesian interpretation, which means that one can incorporate prior knowledge when solving such stochastic control problems. This work is motivated by a desire to extend the theoretical underpinning for the convergence of stochastic gradient type algorithms widely employed in the reinforcement learning community to solve control problems. [ABSTRACT FROM AUTHOR]

The Vlasov--Poisson system describes the time evolution of a plasma in the so-called collisionless regime. The investigation of a high-temperature plasma that is influenced by an exterior magnetic field is one of the most significant aspects of thermonuclear fusion research. In this paper, we formulate and analyze a kinetic optimal control problem for the Vlasov--Poisson system where the control is represented by an external magnetic field. The main goal of such optimal control problems is to confine the plasma to a certain region in phase space. We first investigate the optimal control problem in terms of mathematical analysis, i.e., we show the existence of at least one global minimizer and rigorously derive a first-order necessary optimality condition for local minimizers by the adjoint approach. Then we build a Monte Carlo framework to solve the state equations as well as the adjoint equations by means of a particle-in-cell method, and we apply a nonlinear conjugate gradient method to solve the optimization problem. Eventually, we present numerical experiments that successfully validate our optimization framework. [ABSTRACT FROM AUTHOR]

Though extensively studied, the longstanding pinning synchronization problem of dynamical networks with coupling delay has not been well solved until now. In this paper, we further investigate this problem. By proposing a system of functional differential inequalities, we derive synchronization criteria for dynamical networks with coupling delay under linear pinning control, where the threshold of the admissible delay and the control gain threshold are estimated. Since the estimated control gain threshold could be very large when the delay draws close to the delay threshold, we also use the adaptive pinning control scheme to avoid control gain estimation. Pinning synchronization criteria of networks under adaptive control are derived and the delay threshold is given. This is the first time that general coupling delay has been addressed in the field of pinning control. Finally, two numerical examples are presented to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study stabilization of discrete-time systems in which control inputs are transmitted over a random delay and packet drop channel. A predictor-like linear feedback controller is proposed by a reduction technique in which the reduced system has the same dimension as that of the original system. A necessary and sufficient condition to stabilize the original system in the mean-square sense is obtained based on an algebraic Riccati equation. Some necessary and sufficient stabilizability conditions based on the Lyapunov criterion are also presented. Interestingly, it is shown that the stabilization problem considered in this paper is equivalent to the stabilization problem of a particular delay-free system with control-dependent correlated noises. Simulation examples are provided to illustrate the effectiveness and advantages of the proposed stabilizing controller. [ABSTRACT FROM AUTHOR]

This paper studies the stabilizability problem with respect to an arbitrary stability domain for strict closed convex processes. The main result states necessary and sufficient conditions in terms of the eigenstructure of the dual processes under different assumptions depending on whether the convex process of interest is additive or not. The results presented in this paper are stronger than those existing in the literature in two respects: (i) they are valid for arbitrary stability domains and (ii) they guarantee existence of Bohl-type stable trajectories. We also illustrate the main result by means of examples for both nonadditive and additive processes. [ABSTRACT FROM AUTHOR]

This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on the agent's current state and an estimate of the macroscopic population state, given by a weighted average of the neighboring states. When the number of agents is large and the network is a complete graph (has all-to-all information access), the macroscopic behavior of the population can be well-approximated by a set of deterministic differential equations called a mean-field approximation. For incomplete networks such characterizations remained previously unclear, i.e., in general whether a suitable mean-field approximation exists for the macroscopic behavior of the population. The paper addresses this gap by establishing a generic theory describing when various mean-field approximations are accurate for arbitrary interaction structures. Our results are threefold. Letting W be the matrix describing agent interactions, we first show that a simple mean-field approximation that incorrectly assumes a homogeneous interaction structure is accurate provided W has a large spectral gap. Second, we show that a more complex mean-field approximation which takes into account agent interactions is accurate as long as the Frobenius norm of W is small. Finally, we compare the predictions of the two mean-field approximations through simulations, highlighting cases where using mean-field approximations that assume a homogeneous interaction structure can lead to inaccurate qualitative and quantitative predictions. [ABSTRACT FROM AUTHOR]

This paper presents an interior point method for pure state and mixed-constraint optimal control problems for dynamics, mixed constraints, and cost function all affine in the control variable. This method relies on resolving a sequence of two-point boundary value problems of differential and algebraic equations. This paper establishes a convergence result for primal and dual variables of the optimal control problem. A primal and a primal-dual solving algorithm are presented, and a challenging numerical example is treated for illustration. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of stochastic stabilization for the neutral stochastic delay systems (NSDSs) based on discrete observations. Specifically, we design sampled-data based controllers (SDBCs) to stabilize NSDSs. To conquer the difficulties caused by the neutral term and stochastic stabilization, we introduce a new nominal system. By using the Lyapunov function method, we discuss the stability of the nominal system and provide a stability criterion. For the part of SDBC design, there are two methods: the lifting technique method (LTM) and the input delay method (IDM). The LTM is more effective for linear delay-free systems, but there is little research on the LTM for nonlinear stochastic delay systems. In this research, we combine the LTM with the equivalence technique for NSDSs, resulting in improved results. Additionally, to overcome the difficulty caused by LTM, we propose a series of mathematical tools, such as Gronwall's inequality of the discrete version. We compared our method with the IDM presented in X. Mao, IEEE Trans. Automat. Control, 61 (2016), pp. 1619--1624., and our method performs better. Finally, to showcase the efficiency and correctness of our proposed approach, we provide an application. [ABSTRACT FROM AUTHOR]

In this paper we get error bounds for fully discrete approximations of infinite horizon problems via the dynamic programming approach. It is well known that, considering a time discretization with a positive step size h, an error bound of size h can be proved for the difference between the value function (viscosity solution of the Hamilton-Jacobi-Bellman equation corresponding to the infinite horizon) and the value function of the discrete time problem. However, including also a spatial discretization based on elements of size k, an error bound of size O(k/h) can be found in the literature for the error between the value functions of the continuous problem and the fully discrete problem. In this paper we revise the error bound of the fully discrete method and prove, under assumptions similar to those of the time discrete case, that the error of the fully discrete case is in fact O(h + k), which gives first order in time and space for the method. This error bound matches the numerical experiments of many papers in the literature in which the behavior 1/h from the bound O(k/h) has not been observed. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of placing a minimal number of controls to achieve controllability for a class of networked control systems that are based on the original Turing reaction-diffusion model, which is governed by a set of ordinary differential equations with interactions defined by a ring graph. Turing model considers two morphogens reacting and diffusing over the spatial domain and has been widely accepted as one of the most fundamental models to explain pattern formation in a developing embryo. It is of great importance to understand the mechanism behind the various reaction kinetics that generate such a wide range of patterns. As a first step towards this goal, in this paper we study controllability of Turing model for the case of cells connected as a square grid in which controls can be applied to the boundary cells. We first investigate the minimal control placement problem for the diffusion only system. The eigenvalues of the diffusion matrix are classified by their geometric multiplicity, and the properties of the corresponding eigenspaces are studied. The symmetric control sets are designed to categorize control candidates by symmetry of the network topology. Then the necessary and sufficient condition is provided for placing the minimal control to guarantee controllability for the diffusion system. Furthermore, we show that the necessary condition can be extended to Turing model by a natural expansion of the symmetric control sets. Under certain circumstances, we prove that it is also sufficient to ensure controllability of Turing model. [ABSTRACT FROM AUTHOR]

In this paper we consider pathwise state constraint optimal control problems in which unknown parameters intervene in the dynamics, the cost, the endpoint constraint, and the state constraint. The cost criteria to minimize take an integral form of a given endpoint cost function with respect to a reference probability measure that is defined on the set of the unknown parameters. For this class of problems we derive necessary optimality conditions. [ABSTRACT FROM AUTHOR]

Consider the motion of a Brownian particle in n dimensions, whose coordinate processes are standard Brownian motions with zero drift initially, and then at some random/unobservable time, exactly k of the coordinate processes get a (known) nonzero drift permanently. Given that the position of the Brownian particle is being observed in real time, the problem is to detect the time at which the k coordinate processes get the drift as accurately as possible. We solve this problem in the most uncertain scenario when the random/unobservable time is (i) exponentially distributed and (ii) independent from the initial motion without drift. The solution is expressed in terms of a stopping time that minimizes the probability of a false early detection and the expected delay of a missed late detection. The elliptic case k = 1 has been settled in [4] where the hypoelliptic case 1< k

This paper investigates adaptive sampled-data control for strict-feedback nonlinear plants with unmatched uncertainties by means of radial basis function neural networks (RBFNNs). First, the continuous-time plant is locally discretized as a disturbed strict-feedback model by using the approximate Euler model approach. Then, as a basis of rigorous stability analysis, the concept of validity is proposed, which, considering the locality of the universal approximation capacity in RBFNNs, requires that the argument of each RBFNN be inside the corresponding compact set all the time. Meanwhile, to address the noncausality issue, delayed signals are utilized in the backstepping method for discrete-time plants. Subsequently, the validity and stability are proved rigorously; meanwhile, a practical output tracking problem is solved under a time-varying reference signal, the order of whose continuous derivatives is the same as the plants. This is the first time the interdependence on the design of sampling periods and RBFNNs in different design steps has been shown. Finally, simulation results are provided to illustrate the efficiency and feasibility of the obtained results. [ABSTRACT FROM AUTHOR]

This paper proposes criteria for establishing the asymptotic moment stability of semi-Markovian impulsive switched systems. Under some mild assumptions, we formulate an auxiliary linear time-delayed system based on the Lyapunov characterizations of the subsystems and impulses, as well as the properties of the underlying semi-Markovian impulsive switching signal. Our main result provides an upper bound on the moment, which is directly related to a solution of the aforementioned linear time-delayed system. Specifically, the semi-Markovian impulsive switched system is asymptotically moment stable if the auxiliary linear time-delayed system is asymptotically stable. In situations where the mode-dependent sojourn time distributions of the underlying impulsive switching signals are all exponential, uniform, or trigonometric, we deduce explicit formulae for the auxiliary linear time-delayed systems. To prove the main result, we compute the expected gain function, which requires formulating a generalized renewal equation. Finally, we test our stability criteria on a numerical example in different scenarios and show that our stability results are nonconservative compared to the statistically obtained average of state-norms and state-norm-squares. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of global uniform finite-time output feedback stabilization for a class of generalized disturbed high-order nonlinear uncertain systems. The presence of nonlinear uncertainties and unknown disturbances makes it challenging to design a state observer and an output feedback controller. To address this problem, a new technique of output feedback design is proposed. Firstly, based on a backstepping-like method, a finite-time extended state observer (FT-ESO) is constructed to estimate the unmeasured states and unknown disturbances of the system. Then, utilizing the nonseparation principle and disturbance-estimation--compensation method, a continuous output--based finite-time active anti-disturbance control (FT-AADC) method is developed by integrating the finite-time state feedback controller with the proposed FT-ESO. The global uniform finite-time stability of the entire observer-control system is proven using Lyapunov theory. Simulation results are provided to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper is devoted to the development and convergence analysis of greedy reconstruction algorithms based on the strategy presented in [Y. Maday and J. Salomon, Joint Proceedings of the 48th IEEE Conference on Decision and Control and the 28th Chinese Control Conference, 2009, pp. 375--379]. These procedures allow the design of a sequence of control functions that ease the identification of unknown operators in nonlinear dynamical systems. The original strategy of greedy reconstruction algorithms is based on an offline/online decomposition of the reconstruction process and an ansatz for the unknown operator obtained by an a priori chosen set of linearly independent matrices. In the previous work [S. Buchwald, G. Ciaramella, and J. Salomon, SIAM J. Control Optim., 59 (2021), pp. 4511--4537], convergence results were obtained in the case of linear identification problems. We tackle here the more general case of nonlinear systems. More precisely, we introduce a new greedy algorithm based on the linearized system. We show that the controls obtained with this new algorithm lead to the local convergence of the classical Gauss--Newton method applied to the online nonlinear identification problem. We then extend this result to the controls obtained on nonlinear systems where a local convergence result is also proved. The main convergence results are obtained for dynamical systems with linear and bilinear control structures. [ABSTRACT FROM AUTHOR]

In this paper, we study the optimal stopping problem in the so-called exploratory framework, in which the agent takes actions randomly conditioning on the current state and a regularization term is added to the reward functional. Such a transformation reduces the optimal stopping problem to a standard optimal control problem. For the American put option model, we derive the related HJB equation and prove its solvability. Furthermore, we give a convergence rate of policy iteration and compare our solution to the classical American put option problem. Our results indicate a trade-off between the convergence rate and bias in the choice of the temperature constant. Based on the theoretical analysis, a reinforcement learning algorithm is designed and numerical results are demonstrated for several models. [ABSTRACT FROM AUTHOR]

This paper studies two-player stochastic differential games with diffusion control on finite time horizons. The players' state processes are described in terms of controlled martingale problems, and we allow for correlation between the players' states, described by some correlation coefficient. We consider zero-sum ranking games in the sense that the criterion to optimize only depends on the difference of the two players' state processes at the finite time horizon. We explicitly compute saddle points of the game depending on the correlation coefficient. In particular, for correlation coefficients smaller than some explicit threshold, the game has a value and a saddle point (in strict controls). For correlation coefficients exceeding the threshold, we introduce the larger class of relaxed controls that can be interpreted as mixed strategies. We show that the game has a value and a saddle point in relaxed controls for all correlation coefficients. [ABSTRACT FROM AUTHOR]

In this paper, we tackle a topology optimization problem which consists in finding the optimal shape of a solid located inside a fluid that minimizes a given cost function. The motion of the fluid is modeled thanks to the Boussinesq system which involves the unsteady Navier-Stokes equation coupled with a heat equation. In order to cover several models presented in the literature, we choose a nonsmooth formulation for the outlet boundary conditions. This paper aims at proving the existence of solutions to the resulting equations, along with the study of a relaxation scheme of the nonsmooth conditions. A second part covers the topology optimization problem itself for which we proved the existence of optimal solutions and provides the definition of first order necessary optimality conditions. [ABSTRACT FROM AUTHOR]

This paper presents approaches to mean-field control, motivated by distributed control of multiagent systems. Control solutions are based on a convex optimization problem, whose domain is a convex set of probability mass functions (pmfs). The main contributions follow: (1) Kullback--Leibler-quadratic (KLQ) optimal control is a special case in which the objective function is composed of a control cost in the form of Kullback--Leibler divergence between a candidate pmf and the nominal, plus a quadratic cost on the sequence of marginals. Theory in this paper extends prior work on deterministic control systems, establishing that the optimal solution is an exponential tilting of the nominal pmf. Transform techniques are introduced to reduce complexity of the KLQ solution, motivated by the need to consider time horizons that are much longer than the intersampling times required for reliable control. (2) Infinite-horizon KLQ leads to a state feedback control solution with attractive properties. It can be expressed as state feedback, in which the state is the sequence of marginal pmfs, or an open loop solution is obtained that is more easily computed. (3) Numerical experiments are surveyed in an application of distributed control of residential loads to provide grid services, similar to utility-scale battery storage. The results show that KLQ optimal control enables the aggregate power consumption of a collection of flexible loads to track a time-varying reference signal, while simultaneously ensuring each individual load satisfies its own quality of service constraints. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes an optimal control approach for acoustic full waveform inversion (FWI) to reconstruct the speed wave parameter entering the hyperbolic acoustic PDE model in the coefficient of the second-order time derivative of the acoustic pressure. We develop a novel technique accounting for an auxiliary first-order system. In contrast to the original state equation, the underlying control parameter appears in the auxiliary system not only as the coefficient of the time derivative but also as the initial data under the image of the solution operator for a specific elliptic problem. On this basis, we construct an adjoint state explicitly using the corresponding dual semigroup, leading to necessary optimality conditions with a low adjoint regularity such that no Sobolev smoothing effect occurs in the optimal solution. The final part of the paper is devoted to the second-order analysis of the optimal control approach. We study the two- and three-dimensional case where the reconstruction is only considered in an open set strictly contained in the hold-all domain. For this case, under additional regularity and compatibility assumptions on the data, we are able to prove second-order optimality conditions yielding local optimality in an L2-neighborhood. A numerical test based on a synthetic configuration with nonsmooth data is provided, illustrating the performance of the control approach. [ABSTRACT FROM AUTHOR]

Part of the motivation of this paper comes from the recent paper [W. Guo and H.-Z. Zhou, SIAM J. Control Optim., 57 (2019), pp. 1890--1928], where an adaptive control approach was used to estimate in real time all amplitudes and phases of the external harmonic sinusoidal disturbance with known frequencies to achieve output regulation for a 1-d Euler--Bernoulli beam equation. In our paper, we change the landscape in a completely different way for the output regulation of the Euler--Bernoulli beam equation for which the disturbances are generated from a completely unknown finite-dimensional exosystem; i.e., the frequencies of the sinusoidal signals that appear in the reference signal and disturbances are completely unknown. In addition, the number of frequencies is also assumed to be unknown yet has a known upper bound. We apply the technique of the Sylvester equation to decouple the ODE of the exosystem and the PDE of the plant first, and then adopt the adaptive observer to estimate all possible unknown frequencies that have entered into the tracking error. By designing two different adaptive observers to estimate the unknown frequencies as well as the state of the plant and exosystem, we propose two tracking error based feedback controls for achieving output regulation for this PDE. [ABSTRACT FROM AUTHOR]

This paper examines the analysis and optimal control of an H(curl)-quasilinear first kind variational inequality with a bilateral vector curl-constraint, stemming from the ferromagnetic shielding phenomenon. We propose a tailored regularization approach based on the Helmholtz decomposition and a reduction of the first-order constraint to the zeroth-order one in combination with a smoothed Yosida penalization. In this way, a suitable family of approximating quasilinear variational equalities is obtained. The corresponding limiting analysis not only leads to a well-posedness result for the variational inequality but also reveals its dual formulation. Thereafter, as a second novelty, we prove a regularity result for the dual multiplier by means of the Lp-Helmholtz decomposition in a careful combination with elliptic regularity results for Dirichlet and Neumann problems. The last part of this paper is devoted to the analysis of the corresponding optimal control, which is mainly complicated by the involving H(curl)-quasilinearity, the bilateral vector curl-constraint, and the nonsmoothness. On the basis of the proposed regularization, as the final novelty, we derive necessary optimality conditions, including a characterization of the limiting dual multiplier through curl-projection and cut-off type arguments. [ABSTRACT FROM AUTHOR]

This paper studies the exponential stabilization problem for a class of discretetime linear switched systems arising from establishing the output-based distributed observer and the output-based adaptive distributed observer for discrete-time linear leader systems over jointly connected switching networks. The existing results on distributed observers and adaptive distributed observers are state-based in the sense that they need to make use of the full state of the leader system, which is quite restrictive since, in many applications, only the output of the leader system is available. As an application, the output-based distributed observer is used to solve a leader-following consensus problem for discrete-time linear multiagent systems by distributed output feedback control. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effects of applying generalized (nonexponential) discounting on a long-run impulse control problem for a Feller--Markov process. We show that the optimal value of the discounted problem is the same as the optimal value of its undiscounted version. Next, we prove that an optimal strategy for the undiscounted discrete-time functional is also optimal for the discrete-time discounted criterion and nearly optimal for the continuous-time discounted one. This shows that the discounted problem, being time-inconsistent in nature, admits a time-consistent solution. Also, instead of a complex time-dependent Bellman equation, one may consider its simpler time-independent version. [ABSTRACT FROM AUTHOR]

In this paper, we propose consensus-based optimization for saddle point problems (CBO-SP), a novel multi-particle metaheuristic derivative-free optimization method capable of provably finding global Nash equilibria. Following the idea of swarm intelligence, the method employs two groups of interacting particles, one which performs a minimization over one variable while the other performs a maximization over the other variable. The two groups constantly exchange information through a suitably weighted average. This paradigm permits a passage to the mean-field limit, which makes the method amenable to theoretical analysis, and it allows to obtain rigorous convergence guarantees under reasonable assumptions about the initialization and the objective function, which most notably include nonconvex-nonconcave objectives. We further provide numerical evidence for the success of the algorithm. [ABSTRACT FROM AUTHOR]

Currently, output-feedback control still necessitates severe constraints on systems, e.g., system nonlinearities cannot exceed certain degree and uncertainties should belong to specific types. In this paper, by exploiting dynamic-compensation mechanisms, we essentially extend system nonlinearities and uncertainties. Specifically, the nonlinearities heavily rely on unmeasured states and particularly have unknown arbitrary function-of-output growth rates. Unknown control coefficients whether with known or unknown bounds are admitted, which have been excluded before in the context of such inclusive nonlinearities. The key to our novel solution lies in realizing the potential of filter-based observers, dynamic high gains, design/analysis parameter designation, and composite Lyapunov functions. In detail, two dynamic-high-gain filters are worked out to provide available states for controller design. The filter states, after weighted by the unknown control coefficient, also make up the estimated states which lead to control-free and tractable error dynamics. Two dynamic high gains with new dynamics are put forward to counteract the nonlinearities and uncertainties and, meanwhile, to enable the adaptive controller to own a concise structure. During the controller design, crucial design parameters can no longer be expressed explicitly due to unknown control coefficients, but rather need to be pursued through a recursive algorithm. With a set of analysis parameters, important (dynamic-high-gain) input-to-state stable properties of some vital variables are uncovered, and exhaustive Lyapunov analysis is performed for the closed-loop boundedness and convergence. [ABSTRACT FROM AUTHOR]

This paper provides some sufficient conditions for the existence and uniqueness and the stochastic stability of the global solution for nonlinear neutral stochastic functional differential equations. When the drift term and the diffusion term satisfy a locally Lipschitz condition, and the Lyapunov monotonicity condition has a sign-changed time-varying coefficient, the existence and uniqueness of the global solution for such equations will be studied by using the Lyapunov--Krasovskii function approach and the theory of stochastic analysis. The stability in pth-moment, the asymptotical stability in pth-moment, and the exponential stability in pth-moment will be investigated. Different characterizations for these three kinds of stochastic stability in moment will be established, which are presented with respect to integration conditions. These results have seldom been reported in the existing literature. The almost surely exponential stability for the global solution of such equations is also discussed. Some discussions and comparisons are provided. Two examples are given to check the effectiveness of the theoretical results obtained. [ABSTRACT FROM AUTHOR]