In this work, we derive an a priori error estimate of order for the finite element approximation of a sparse optimal control problem governed by an elliptic equation, which is controlled in a finite dimensional space. Furthermore, box‐constrains on the control are considered and finitely many pointwise state‐constrains are imposed on specific points in the domain. With this choice for the control space

This paper addresses a pole‐assignment control problem for discrete‐time linear parameter varying (LPV) systems. Based on LPV modeling approach, time‐varying systems can be mathematically described via combining several linear systems and a specific weighting function. For the LPV systems, gain‐scheduled (GS) control scheme is applied to deal with stabilization problem subject to pole‐assignment constraint

Electric Vehicles (EVs) are gradually replacing conventional vehicles as they are environmentally friendly and cause less pollution problems. Unregulated charging has severe impacts on the distribution grid and may incur EV owners higher charging costs. Therefore, controlled charging infrastructures to supply the charging needs of large numbers of EVs are of vital importance. In this article, an optimal

The present article is a study of an optimal control problem having a non‐differentiable, but Lipschitz, cost function. It is inspired by the minimisation of the energy consumption of a car‐like vehicle or robot along a road which profile is known. This problem is stated by means of a simple model of the longitudinal dynamics and a running cost that comprises both an absolute value function and a function

We study the optimal control of district heating networks using a reduced order model based on a system theoretic description close to the underlying Euler equations. In the presented scenarios, the central task is to limit the maximal feed‐in power occurring as a product of control and state variables. The underlying dynamics of heating networks acting as optimization constraints pose the central

This paper aims to address the tracking control problem for the multi‐joint manipulator on a space robot subject to model uncertainties and external disturbances. A Gauss‐Newton interactive optimization algorithm is used to obtain the desired joint angle for each joint. In order to formulate the optimization problem, the Denaait‐Hartenberg (D‐H) method is employed to describe the model of the multi‐joint

This article proposes a new numerical approach for solving fractional optimal control problems including state and control inequality constraints using new biorthogonal multiwavelets. The properties of biorthogonal multiwavelets are first given. The Riemann‐Liouville fractional integral operator for biorthogonal multiwavelets is utilized to reduce the solution of optimal control problems to a nonlinear

This article deals with an optimal control problem governed by a system that models the dynamics of predator‐prey interactions. We study the minimization of the infective prey density. Furthermore, our purpose is here to establish the existence of weak solutions and derive some optimality conditions. Finally, the impact of the control terms are studied to get an insight of the predator‐prey model adopting

This article bestows the linear quadratic Gaussian (LQG)/Loop Transfer Recovery (LTR) optimal controller design for a perturbed linear system having insufficient information about systems states through a multiobjective optimization approach. A Kalman filter observer is required to estimate the unknown states at the output from the noisy data. However, the main downside of the LQG controller's is that

In this article, we discuss an infinite horizon optimal control of the stochastic system with partial information, where the state is governed by a mean‐field stochastic differential delay equation driven by Teugels martingales associated with Lévy processes and an independent Brownian motion. First, we show the existence and uniqueness theorem for an infinite horizon mean‐field anticipated backward

This article explores the impact of regular perturbations (ie, small terms) in input constrained optimal control problems for nonlinear systems. In detail, it is shown that perturbation terms of magnitude ε appearing in the dynamics or the cost function lead to a variation of magnitude Kε2 in the optimal cost. The scale factor K can be estimated from the nominal (ε=0) solution and the analytic expressions

Dealing with the interpatient and the intrapatient variability in type 1 diabetes mellitus (T1DM) patient are the prominent control challenges in the development of the artificial pancreas system (APS). An APS consider a nonlinear patient model that has many state variables, but the reality is that out of the many states only glucose concentration is measurable till date without any complication and

This article considers robust fusion algorithms for linear system with multichannel stochastic multiplicative disturbance by using projection theorem and projection formula. Based on the centralized and distributed (feedback and no feedback) fusion strategies, we present optimal filtering fusion algorithms, optimal fixed‐interval smoothing fusion algorithms, and fixed‐interval deconvolution fusion

We introduce a mathematical model for the composting process in biocells. The model includes several phenomena, like the aerobic biodegradation of the soluble substrate by means of a bacterial population, the hydrolysis of insoluble substrate, and the biomass decay. We investigate the best strategies to reduce substrate components in minimal time by controlling the effects of cell oxygen concentration

This paper presents the use of passive dynamics to generate the sagittal plane references for a biped walker. In order to achieve an adjustable gait width, a neural network reference generator, trained with passive walking data on different slopes, was applied. The control algorithm was implemented with an Nonlinear Model Predictive Control (NMPC) strategy, in order to perform multiple‐input multiple‐output

In this article, a novel neural network (NN) optimal control approach using adaptive critic designs is developed for nonlinear discrete‐time (DT) systems with time delays. First, to eliminate the delay term of control input, a time‐delay matrix function is developed by designing a M network. Furthermore, the cost function is approximated by the critic NN, and the control signal can be obtained directly

This paper studies the optimal reinsurance‐investment problems for an insurance company where the claim process follows a Brownian motion with drift. It turns out that there is a region where the probability of drawdown, namely, the probability that the value of the insurer's surplus process reaches some fixed fractional value of its maximum value to date is positive. Then in the complementary region

This paper is concerned with the stochastic near‐optimal control problem for a regime‐switching diffusion model, where the control domains are convex. The controlled system is described by the Itô‐type stochastic differential equation (SDE) with a continuous‐time Markov chain, which possesses a finite state structure. Some new estimates for state and adjoint processes are obtained in the presence of

In this article, we propose a higher order neural network, namely the functional link neural network (FLNN), for the model of linear and nonlinear delay fractional optimal control problems (DFOCPs) with mixed control‐state constraints. We consider DFOCPs using a new fractional derivative with nonlocal and nonsingular kernel that was recently proposed by Atangana and Baleanu. The derivative possesses

We propose a framework tailored to robust optimal control (OC) problems subject to parametric model uncertainty of system dynamics. First, we identify a generic class of robust objective kernels that are based on the class of deterministic quadratic objectives. It is demonstrated how such kernels can be expressed as a function of the stochastic moments of the state and how the objective terms relate

This paper introduces a new methodology for the design of fixed‐order multi‐objective output feedback controllers. The problem comprises a set of linear matrix inequalities and an additional rank constraint. The primary idea is to classify convex subsets of the set of rank constrained matrices in such formulations, based on which two noniterative and relatively fast methods are developed. The proposed

In the fast developing electric power system network, ancillary services like automatic generation control (AGC) plays a vital and significant role to ensure good quality of power supply in the system. To distribute good quality of power, a hybrid AGC system along with an efficient and intelligent controller is compelled. So, in this article, a cascaded proportional‐integral (PI)‐proportional‐derivative

This article focuses on the problem of linear quadratic Gaussian (LQG) control for discrete time‐varying system with input delay and state/control‐dependent noises. When the state variables can be exactly observed, first, we obtain the maximum principle by applying the method of variation. Second, a nonhomogeneous relationship between the state and the costate is developed in virtue of the obtained

The second part of our study is devoted to an analysis of the exactness of penalty functions for optimal control problems with terminal and pointwise state constraints. We demonstrate that with the use of the exact penalty function method one can reduce fixed‐endpoint problems for linear time‐varying systems and linear evolution equations with convex constraints on the control inputs to completely

This note is concerned with the problem of stabilizing a class of linear continuous‐time systems with completely unknown system dynamics subject to input energy constraint. To deal with this problem, a model‐based low gain feedback law is designed firstly by establishing a special algebraic Riccati equation. Such a low gain feedback law can semiglobally stabilize the linear systems subject to input

In this article, a real‐time nonlinear model predictive idle speed controller based on multiparametric programming is designed for an SI engine. Idle speed is a crucial recurring condition in urban vehicles demanding proper control to avoid stall. As will be seen, the nonlinear model predictive control (NMPC) system designed, besides complying with the predefined constraints, demonstrates a far better

This article discusses the design of a hybrid fuzzy variable structure control algorithm combined with genetic algorithm (GA) optimization technique to improve the adaptive proportional‐integral‐derivative (PID) continuous second‐order sliding mode control approach (APID2SMC), recently published in our previous article in the literature. In this article, first, as an improved extension to APID2SMC

In this article, a model‐free off‐policy reinforcement learning algorithm is applied to address the optimal tracking problem based on multiplayer non‐zero‐sum games for discrete‐time linear systems. In contrast to the traditional method and the policy iteration method for solving the optimal tracking problems, the proposed algorithm operates with the system data rather than the knowledge of the system

In this article, we study the optimal coordination of automated vehicles at intersections. The problem can be stated as an optimal control problem (OCP), which can be decomposed as a bi‐level scheme composed by one nonlinear program (NLP) which schedules the access to the intersection and one OCP per vehicle which computes the appropriate vehicle commands. We discuss a practical implementation of the

Collaborative robots have to adapt its motion plan to a dynamic environment and variation of task constraints. Currently, they detect collisions and interrupt or postpone their motion plan to prevent harm to humans or objects. The more advanced strategy proposed in this article uses online trajectory optimization to anticipate potential collisions, task variations, and to adapt the motion plan accordingly

In this article, a new numerical method based on Bernoulli wavelet basis has been applied to give the approximate solution of the fractional optimal control problems. The new operational matrices of multiplication and fractional integration are constructed. The proposed method is applied to reduce the problem to the solution of a system of algebraic equations. The fractional derivative is considered

Damping of low‐frequency oscillations due to the unpredictable perturbations of a power network has always been a challenging task. In an interconnected power network, power system stabilizers (PSSs) are in practice to damp out these low‐frequency oscillations by providing a necessary control signal to the automatic voltage regulator unit based on the deviation in generator speed/power output. This

In this article, based on a multidimensional control problem, in short (MCP), we introduce a modified multidimensional variational control problem involving first‐order partial differential equations and inequality‐type constraints. As well, we formulate and prove optimality conditions for this new variational control problem. Furthermore, we establish (under some generalized convexity assumptions)

In order to achieve the precise and agile homing control of the powered parafoil system, an optimal‐multiphase homing methodology is explored in this article. The proposed methodology is composed by a trajectory optimization method based on quantum genetic algorithm and a trajectory tracking method based on an improved active disturbance rejection control (ADRC). First, an improved optimization method

With the advent of intelligent transport, quadrotors are becoming an attractive solution while lifting or dropping of payloads during emergency evacuations, construction works, etc. During such operations, dynamic variations in (possibly unknown) payload cause considerable changes in the system dynamics. However, a systematic control solution to tackle such interchanging dynamical behavior is still

We study the blowup problem for nonautonomous systems of ordinary differential equations. Sufficient optimality conditions for the controlled blowup time are derived, in terms of a dual dynamic programming methodology. We define an ε‐optimal value function and we construct sufficient ε‐optimality conditions for that function again in terms of a dual dynamic programming inequality.

This paper extends a control system framework for the maintenance planning investment decision for building energy retrofitting. The interacting energy and reliability effects that are ignored by previous models are incorporated in the current study. A set of energy efficiency and population decay models with interacting parameters and decision variables are established, and a state‐space model with

In this article, we investigate the cluster synchronization in finite time for nonlinear complex dynamical networks (CDNs) with hybrid couplings via aperiodically intermittent control. First, a new lemma with respect to the convergence in finite time is developed for the nonnegative continuous functions. Second, the classification controller, which is dependent of the coupling of the dynamic nodes

This study proposes an effective adaptive dynamic surface control (DSC) method based on the radial basis function neural networks and the auxiliary system for hypersonic flight vehicle (HFV) systems in the presence of system uncertainties, external disturbances, and state variable and control input constraints. Firstly, to enhance the robustness of the system, the neural network is combined with the

Motivated by new aerospace applications, the condition of minimum‐energy achieving high accuracy of both terminal orbital injection and attitude angle is required for better navigation and observation. The stability of guidance command also needs to be improved considering the control system. In this article, an optimal guidance algorithm with an advanced numerical method of spacecrafts is proposed

This paper is concerned with an asymmetric information linear‐quadratic (AILQ) stochastic Stackelberg differential game with one leader and two followers, where the game system is governed by mean‐field type stochastic differential equation (MF‐SDE). With the help of two systems of Riccati equations, the followers solve a MF‐type stochastic LQ game problem with partial information first, and then,

This article investigates the robust estimation and observer‐based finite time sliding mode control problems for a class of switched systems with time‐delays and uncertainties. For the studied system model, a common sliding surface related to the estimated states is initially constructed. Then, a suitable sliding mode control law is designed to ensure the accessibility of sliding surface. By selecting

This article develops a predictive robust H∞ static output feedback control approach for networked control systems where random network‐induced delays in both forward and feedback communication channels are modeled as two mutually uncorrelated Markov chains. By making use of the system augmentation method, the closed‐loop system is formulated as a singular Markovian jump system with two modes, wherein

In this article, the problem of delay‐dependent dissipative filter design is studied for discrete‐time interval type‐2 (IT‐2) fuzzy singular systems with both external disturbance and mixed delays. Two kinds of delays are considered, namely time‐varying discrete delays and infinite distributed delays. First, considering the uncertainties in the membership functions, the nonlinear singular system and

This article studies singular systems with uncertain parameters by using a direct method which is called the first restricted equivalent transformation (FRET). The stochastic uncertain parameters we studied in the article, which are more general and challenging, are different from the two existing types: time‐invariant parameters and time‐varying parameters. We propose an optimal filtering algorithm

A control problem motivated by tissue engineering is formulated and solved in which control of the uptake of growth factors (signaling molecules) is necessary to spatially and temporally regulate cellular processes for the desired growth or regeneration of a tissue. Four approaches are compared for determining 1D optimal boundary control trajectories for a distributed parameter model with reaction

In this computational study we consider a generalized minimal model structure for the intravenously infused insulin-blood glucose dynamics, which can represent a wide variety of diabetic patients, and augment this model structure with a glucose rate disturbance signal that captures the aggregate effects of various internal and external factors on blood glucose. Then we develop a model-based, switching