In this article, searching the general Nash equilibrium in the noncooperation game is discussed under the general constraints of containing bounded constraint, coupled equality constraint, and private inequality constraint. Meanwhile, the continuous‐time event‐triggered distributed subgradient projective algorithm (C‐ETDSP algorithm), to greatly cut down the number of communication flows, is designed

This article presents novel schemes using which a robustly stable and feasible optimal controller can be obtained for uncertain vibrational systems. Furthermore, the aforementioned objectives are satisfied solely employing a rigid approximation of continuum mechanics systems. Simultaneously, significant reductions in control complexity and computation burden are attained. On this basis, a new model

Design of feedback control by an optimal control approach relies on the solutions of the Hamilton‐Jacobi‐Bellman (HJB) equation, while this equation rarely admits analytical solutions for arbitrary choices of the performance measure. An inverse optimal feedback design approach is proposed here in which analytical solutions are explored for the HJB equation that optimize some meaningful, but not necessarily

The aim of this article is to investigate an efficient computational method for solving distributed‐order fractional optimal control problems. In the proposed method, a new Riemann‐Liouville fractional integral operator for the Bernstein wavelet is given. This approach is based on a combination of the Bernstein wavelets basis, fractional integral operator, Gauss‐Legendre numerical integration, and

Hybrid systems have been attracting considerable attention in recent years because of their ability to model complex physical systems with both continuous and discrete dynamic behavior. When controlling such complex systems, a ubiquitous problem is the presence of large parametric uncertainties. Adaptive control has been used in recent years for hybrid systems to cope with parametric uncertainties

This article deals with the problems of stability and stabilization for a class of discrete‐time switched systems with time‐varying delay under arbitrary switching signal. First, sufficient conditions guaranteeing the asymptotic stability of the unforced system are developed, by using the switched Lyapunov‐Krasovskii functional method. Then, based on the obtained results, a state feedback controller

A method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation transforms the chance constrained optimal control problem into a deterministic optimal control problem that can be solved numerically. The new method developed in

In this article, we study a type of fully coupled mean‐field forward‐backward stochastic differential equations with jumps under the monotonicity condition, including the existence and the uniqueness of the solution of our equations as well as the continuity property of the solutions with respect to the parameters. Then we establish the stochastic maximum principle for the corresponding optimal control

This article investigates the optimal output feedback control problem for discrete‐time Markov jump linear system (MJLS) with input delay and packet losses in finite horizon. There are three main contributions. First, we assume that the state variable and the jump variable are available to the controller, and then we propose a new version of stochastic maximum principle. Based on the new proposed tool

In this article, a suboptimal nonlinear discrete control sequence for nonlinear discrete affine control systems is proposed. Using the dynamic programming approach in discrete time domain, the suboptimal control sequence is obtained in every step considering a quadratic performance index of finite horizon. The proposed control strategy is applied to improve the dynamic and energetic performances of

Minimum time solar sailing trajectories are introduced using a combination of indirect and direct optimal control techniques. Here, large‐scale, multiphase optimal control problems are solved using a pseudospectral collocation technique applied to an orbital debris mitigation concept. These solutions are obtained for realistic sail dimensions, producing multirevolution, Earth‐centered trajectories

This article presents an efficient numerical method for solving fractional optimal control problems (FOCPs) by utilizing the Hermite scaling function operational matrix of fractional‐order integration. The proposed technique is applied to transform the state and control variables into nonlinear programming (NLP) parameters at collocation points. The NLP solver is then used to solve FOCP. Furthermore

This article presents an alternating direction method of multipliers (ADMM) algorithm for solving large‐scale model predictive control (MPC) problems that are invariant under the symmetric‐group. Symmetry was used to find transformations of the inputs, states, and constraints of the MPC problem that decompose the dynamics and cost. We prove an important property of the symmetric decomposition for the

This article is concerned with the stochastic recursive optimal control problem with mixed delay. The connection between Pontryagin's maximum principle and Bellman's dynamic programming principle is discussed. Without containing any derivatives of the value function, relations among the adjoint processes and the value function are investigated by employing the notions of super‐ and sub‐jets introduced

This article is concerned with the tracking of nonequilibrium motions with model predictive control (MPC). It proposes to parametrize input and state trajectories of a dynamic system with basis functions to alleviate the computational burden in MPC. As a result of the parametrization, an optimization problem with fewer variables is obtained, and the memory requirements for storing the reference trajectories

Parametric uncertainties and the problems associated with the design of robust state feedback control tends to be a major concern for achieving stable operation of nonlinear systems. To overcome these drawbacks, this article provides a perspective on a randomized algorithm based probabilistic control for nonlinear systems. The control approach aims at development of randomized algorithms for control

In this work, a minimum variance estimator is designed for a networked system with inherent network imperfections in both sensor to estimator (S‐E) and controller to actuator (C‐A) channels simultaneously. The channels are affected by packet delays, dropouts, and uncertain observations. These effects are modeled using five Bernoulli distributed random variables. Correlation of noise at neighboring

This article investigates the optimal control problem of nonzero sum game mean‐field delayed Markov regime‐switching forward‐backward stochastic system with Lévy processes associated with Teugels martingales over the infinite time horizon. Based on the transversality conditions, assumption of convex control domain, infinite‐horizon version of stochastic maximum principle (Nash equilibrium), and necessary

In this article, considering one type of fuzzy discrete‐time networked control systems (NCSs) under stochastic communication protocol (SCP), a fuzzy‐based nonfragile H∞ filter is developed to detect the subsistent fault signal. The Takagi‐Sugeno (T‐S) mathematical model is employed to approximate the nonlinearities in the concerned fuzzy NCSs. The SCP is adopted to decide which sensor gets the access

In this article, an algorithm is presented for solving the optimal control problem for the general form of a hybrid switching system. The cost function comprises terminal, running and switching costs. The controlled system is an autonomous hybrid switching system with jumps either at some switching times or some time varying switching manifolds. The proposed algorithm is an extension of the first‐order

This study, under zero initial condition, aims to characterize the reachable set bound for a class of neutral Markovian jump systems (NMJSs) with interval time‐varying delays and bounded disturbances. To begin with, the time‐delays are considered to be mode‐dependent while delay mode and system mode are different. By utilizing free‐weighting matrix method and reciprocally convex combination technique

A derivative‐free estimator was introduced to alleviate the drawbacks of the conventional Kalman filter when performing nonlinear analyses under different circumstances. In this work, the scaled Unscented Kalman Filter, Divided Difference Kalman filter, and Cubature Kalman filter (CKF) were selected to investigate the effectiveness of these filters in predicting the states of a complex semi‐batch reaction

This paper researches the static output‐feedback stabilization of single‐input single‐output (SISO) positive coupled differential‐difference equations (CDDEs) with unbounded time‐varying delays. First, a necessary and sufficient condition is provided for the positivity and asymptotical stability of CDDEs with unbounded time‐varying delays. For this type of system, based on the constructed estimates

This work presents a multivariable predictive controller applied on a redundant robotic manipulator with three degrees of freedom. The article focuses on the design of a discrete model‐based predictive controller (DMPC) using the Laguerre function as a control effort weighting method to enhance the solution of Hildreth's quadratic programming and to minimize the trade‐off problem in constrained case

In this paper, guaranteed cost control for a class of switched linear systems subject to time delays is investigated, where a nonweighted quadratic performance index is considered. In particular, a novel quasi‐time‐dependent Lyapunov‐Krasovskii function based on a time‐varying positive definite matrix is proposed that is decreasing during the switching intervals and at the switching instants. By exploiting

This article addresses the problem of distributed controller design for linear discrete‐time systems. The problem is posed using the classical framework of state feedback gain optimization over an infinite‐horizon quadratic cost, with an additional sparsity constraint on the gain matrix to model the distributed nature of the controller. An equivalent formulation is derived that consists in the optimization

This article presents an optimal control strategy (OCS) for semiactive vehicle suspensions with road profile sensors. The suspension is modeled as a quarter‐car model with a magnetorheological (MR) damper. The OCS main objective is to minimize the fourth‐power acceleration of the sprung mass. In addition, three pointwise constraints of the model are taken into account when the optimal control problem

A new type of fast distributed Kalman consensus filtering algorithm based on local information feedback is presented to tackle filtering problems in wireless sensor networks. First, this fast filtering issues are transformed into a stochastic stability problem of the dynamic estimation errors, which can be solved by Lyapunov's second method and matrix theory. Then, two sufficient conditions about the

In this paper, we study fractional‐order optimal control problems (FOCPs) involving the Atangana‐Baleanu fractional derivative. A computational method based on B‐spline polynomials and their operational matrix of Atangana‐Baleanu fractional integration is proposed for the numerical solution of this class of problems. With this numerical technique, the FOCPs are reduced to a system of equations which

In this present contribution, an attempt has been taken to design and analyze the performance of elephant herding optimization (EHO) based controller for load frequency control (LFC) applications of interconnected power system. The studied system is a two‐area nonreheat thermal interconnected system which is widely used in literature. A proportional‐integral‐differential controller is utilized for

This research provides a new framework based on a hybrid of block‐pulse functions and Legendre polynomials for the numerical examination of a special class of scalar nonlinear fractional optimal control problems involving delay. The concepts of the fractional derivative and the fractional integral are employed in the Caputo sense and the Riemann‐Liouville sense, respectively. In accordance with the

The main purpose is the study of optimal control problem in a domain with rough boundary for the mixed Dirichlet‐Neumann boundary value problem for the strongly nonlinear elliptic equation with exponential nonlinearity. A density of surface traction u acting on a part of rough boundary is taken as a control. The optimal control problem is to minimize the discrepancy between a given distribution and

Time‐space network (TSN) models have been widely used for collision‐free path planning of automated guided vehicles. However, existing TSN models are planned globally. The global method suffers from computational complexity and uncertainties cannot be dealt with in the dynamic environment. To address these limitations, this article proposes a new methodology to decompose the global planning problem

In this article, we study the open‐loop and closed‐loop solvability for indefinite mean‐field stochastic linear quadratic (MF‐SLQ) optimal control problem and its application in finance, where the controlled stochastic system is driven by a Brownian motion and a Poisson random martingale measure and also disturbed by some stochastic processes. The intrinsic property of stochastic systems results in

A new mathematical model of tuberculosis (TB) featuring exogenous re‐infection and incomplete treatment is presented and analyzed. The model divides total population into susceptible, latently infected, actively infected (uninformed and enlightened), and treatment classes. The model with or without incomplete treatment exhibits backward bifurcation phenomenon, which is caused by the presence of exogenous

This article is concerned with the design and performance optimization of feedback controllers for state‐based switching bilinear systems (SBLSs), where subsystems take the form of bilinear systems in different state space polyhedra. First, by further dividing the subregions into smaller regions and designing region‐dependent feedback controllers in the resulting regions, the SBLSs can be transformed

Model predictive control (MPC) for linear dynamical systems requires solving an optimal control structured quadratic program (QP) at each sampling instant. This article proposes a primal active‐set strategy, called PRESAS, for the efficient solution of such block‐sparse QPs, based on a preconditioned iterative solver to compute the search direction in each iteration. Rank‐one factorization updates

Up to now, several numerical methods have been presented to solve finite horizon fractional optimal control problems by researchers, while solving fractional optimal control problems on infinite domain is a challenging work. Hence, in this article, a numerical method is proposed to solve fractional infinite horizon optimal control problems. At the first stage, a domain transformation technique is used

A batch to batch optimal control strategy based on multiinput multioutput adaptive hinging hyperplanes (MIMO AHH) prediction and Kalman filter correction is proposed for the products quality control of the batch process. The model of AHH is one kind of piecewise linear models and is extended to the MIMO case in this article. The MIMO AHH is then used to develop the predictive model of the batch process

For partially interdependent networks composed of two subnetworks, the finite‐time optimal pinning control problem is investigated. Among them, only a part of the nodes between the two subnetworks are interdependent on each other. In the network, the coupling relationship between any two nodes of the network is a continuous nonlinear function. Based on the pinning control, the optimal control theory

In this article, we study second‐order necessary optimality conditions for a discrete optimal control problem with a nonconvex cost function, nonlinear state equations and mixed constraints. In order to achieve these conditions, we first establish an abstract result on the second‐order necessary optimality conditions for a mathematical programming problem and then we derive the second‐order necessary

This article addresses a robust control problem of time‐varying stochastic systems with time‐delays. Through Linear Parameter Varying (LPV) modeling approach, the time‐varying parameters can be described via the convex combination. Therefore, the LPV stochastic system is interpreted by a weighting function and multiplicative noised linear systems. Furthermore, stabilization problem for the systems

When the observation equation of system has not been verified or corrected under certain environmental conditions, applying it will yield to unknown system error and filtering error. The unknown system error can be effectively eliminated by introducing the incremental equation. In this article, the local Kalman estimator for the incremental system with correlated noises is first presented. It solves

To promote artificial rain in India and other such developing countries, in this article, we have proposed and analyzed a nonlinear mathematical model for cloud seeding by considering that aerosols are introduced proportional to the density of water vapors present in the atmosphere. The model is analyzed using Lyapunov's stability theory of differential equations. To reduce the cost of cloud seeding

In this paper, the problem of social distancing in the spread of infectious diseases in the human network is extended by optimal control and differential game approaches. Hear, SEAIR model on simulation network is used. Total costs for both approaches are formulated as objective functions. SEAIR dynamics for group k that contacts with k individuals including susceptible, exposed, asymptomatically infected

This work is concerned with the H∞ state‐feedback control for the discrete‐time Markovian jump systems with incomplete knowledge of transition probabilities. A less conservative criterion is proposed via linear matrix inequalities (LMIs) such that the considered systems are stochastically stable and have a prescribed H∞ disturbance attention level. Furthermore, based on the obtained results, a state‐feedback

This article is devoted to the study of a controlled population of cells. The modeling of the problem leads to a mathematical formulation of stability and reachability properties of some controlled systems under uncertainties. We use the Hamilton‐Jacobi approach to address these problems and to design a numerical method that we analyze on several numerical simulations.

In this paper, we introduce a necessary and sufficient condition of optimality for a new class of multidimensional optimal control problems governed by path‐independent curvilinear integral functionals and mixed constraints involving first‐order partial differential equations (PDEs) of m ‐flow type. Furthermore, as a consequence, we establish the equivalence between the class of (strongly) b ‐invex

Here, we propose a novel nonfragile predictive control method for an omnidirectional rehabilitative training walker. The aim of the study was to design a tracking controller that includes simultaneous constraints on the tracking errors in the position and velocity in order to guarantee safe system states for the omnidirectional walker. The nonfragile controller uses incremental control to solve the

In this article, we study the robust solution set of a multitime first‐order PDE constrained control optimization problem with data uncertainty (MCOPU) and an unconstrained multitime control optimization problem (MCOPU)ρ. We establish the equivalence between a robust optimal solution of (MCOPU) and a robust minimizer of (MCOPU)ρ under the appropriate assumptions. Furthermore, we define the uncertain

The micro machine tool that can produce nanostructures by force modulation approach plays a significant role in nanotechnology. In this paper, to guarantee fast and high‐precision cutting subject to external disturbances and input saturation, a robust model predictive control (MPC) using a tube‐based method is exploited to develop a controller for the machining system consisting of a piezoelectric

In this work, the problem of regulating blood glucose (glycemia) in type I diabetic patients is studied by means of an impulsive zone model predictive control (iZMPC), which bases its predictions on a novel long‐term glucose‐insulin model. Taking advantage of the impulsive version of the model—which features real‐life properties of diabetes patients that some other popular models do not—the given control

In this article, the H∞ tracking control problem is first considered for two‐dimensional fuzzy networked control systems. The system is described by fuzzy blending of the so‐called second Fornasini‐Marchesini local linear state‐space model. Based on the fuzzy model, an observer‐based state feedback controller is employed to guarantee the H∞ tracking performance. The separation property is established

In this article, a starting control problem with two intermediate moments of observation in the mixed linear problem for the second‐order hyperbolic equation with quadratic functional is studied. The necessary and sufficient optimality conditions are obtained in the form of variational inequality.

In this article, a novel intermittent projected subgradient algorithm is presented to solve the randomized optimal consensus problem for heterogeneous multiagent systems with time‐varying communication topologies. The multiagent systems achieve the consensus meanwhile minimizing the global objective function via the proposed algorithm, where fi(x) is the convex objective function of agent i itself

By going to millimeter wave (mmWave) we can use large scale MIMO due to short mmWave wavelength to overcome path loss by using beamforming to focus power of signal to the receiver. System structure of mmWave band is different with conventional MIMO because of large scale MIMO which is leading to use many RF‐chains. For this reason Hybrid structure have been proposed for large Scale MIMO. By going to

This article addresses the adaptive fuzzy finite‐time control problem for a class of switched nonlinear systems whose powers are positive odd rational numbers and vary with the switching signal. The fuzzy logic systems (FLSs) are used to approximate the unknown nonlinearities of the controlled systems, and then by combining backstepping control algorithm with adding a power integrator technique, an

This article investigates the distributed adaptive consensus tracking control problem for a class of high‐order nonlinear multiagent systems with unmodeled system dynamics, uncertain external disturbances, and event‐triggered communication. Under an undirected graph condition, a robust distributed adaptive consensus control scheme is proposed. To deal with the lumped system uncertainties involved in

This article proposes a Fuzzy Second Order Integral Terminal Sliding Mode (FSOITSM) control approach for DFIG‐based wind turbines subject to grid faults and parameter variations. Since traditional terminal sliding mode control (SMC) suffers from singularity, a novel integral terminal sliding manifold is proposed to eliminate chattering and improve the wind turbine's performance in the presence of faults

A recent river environmental restoration problem is approached from a standpoint of stochastic control of hybrid regime‐switching diffusion processes with discrete and costly observations. This setting harmonizes with real problems because continuously obtaining environmental and ecological information is difficult, and is often costly. The main problem is to decide when and how much of the sediment