Dynamics modeling and optimal control for multi-information diffusion in Social Internet of Things

As an ingenious convergence between the Internet of Things and social networks,the Social Internet of Things(SIoT)can provide effective and intelligent information services and has become one of the main platforms for people to spread and share information.Nevertheless,SIoT is characterized by high openness and autonomy,multiple kinds of information can spread rapidly,freely and cooperatively in SIoT,which makes it challenging to accurately reveal the characteristics of the information diffusion process and effectively control its diffusion.To this end,with the aim of exploring multi-information cooperative diffusion processes in SIoT,we first develop a dynamics model for multi-information cooperative diffusion based on the system dynamics theory in this paper.Subsequently,the characteristics and laws of the dynamical evolution process of multi-information cooperative diffusion are theoretically investigated,and the diffusion trend is predicted.On this basis,to further control the multi-information cooperative diffusion process efficiently,we propose two control strategies for information diffusion with control objectives,develop an optimal control system for the multi-information cooperative diffusion process,and propose the corresponding optimal control method.The optimal solution distribution of the control strategy satisfying the control system constraints and the control budget constraints is solved using the optimal control theory.Finally,extensive simulation experiments based on real dataset from Twitter validate the correctness and effectiveness of the proposed model,strategy and method.

Matrix Riccati Equations in Optimal Control

In this paper, the matrix Riccati equation is considered. There is no general way for solving the matrix Riccati equation despite the many fields to which it applies. While scalar Riccati equation has been studied thoroughly, matrix Riccati equation of which scalar Riccati equations is a particular case, is much less investigated. This article proposes a change of variable that allows to find explicit solution of the Matrix Riccati equation. We then apply this solution to Optimal Control.

APPLICATION OF HYBRID AERO-ENGINE MODEL FOR INTEGRATED FLIGHT/PROPULSION OPTIMAL CONTROL

The real-time capability of integrated flight/propulsion optimal control （IFPOC） is studied. An appli- cation is proposed for IFPOC by combining the onboard hybrid aero-engine model with sequential quadratic pro- gramming （SQP）. Firstly, a steady-state hybrid aero-engine model is designed in the whole flight envelope with a dramatic enhancement of real-time capability. Secondly, the aero-engine performance seeking control including the maximum thrust mode and the minimum fuel-consumption mode is performed by SQP. Finally, digital simu- lations for cruise and accelerating flight are carried out. Results show that the proposed method improves real- time capability considerably with satisfactory effectiveness of optimization.

Least Squares Solution for Discrete Time Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences

In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical system with the quadratic criterion cost function, is employed. In our approach, the model-based optimal control problem is reformulated into the input-output equations. In this way, the Hankel matrix and the observability matrix are constructed. Further, the sum squares of output error is defined. In these point of views, the least squares optimization problem is introduced, so as the differences between the real output and the model output could be calculated. Applying the first-order derivative to the sum squares of output error, the necessary condition is then derived. After some algebraic manipulations, the optimal control law is produced. By substituting this control policy into the input-output equations, the model output is updated iteratively. For illustration, an example of the direct current and alternating current converter problem is studied. As a result, the model output trajectory of the least squares solution is close to the real output with the smallest sum squares of output error. In conclusion, the efficiency and the accuracy of the approach proposed are highly presented.

Application of Conjugate Gradient Approach for Nonlinear Optimal Control Problem with Model-Reality Differences

In this paper, an efficient computational algorithm is proposed to solve the nonlinear optimal control problem. In our approach, the linear quadratic optimal control model, which is adding the adjusted parameters into the model used, is employed. The aim of applying this model is to take into account the differences between the real plant and the model used during the calculation procedure. In doing so, an expanded optimal control problem is introduced such that system optimization and parameter estimation are mutually interactive. Accordingly, the optimality conditions are derived after the Hamiltonian function is defined. Specifically, the modified model-based optimal control problem is resulted. Here, the conjugate gradient approach is used to solve the modified model-based optimal control problem, where the optimal solution of the model used is calculated repeatedly, in turn, to update the adjusted parameters on each iteration step. When the convergence is achieved, the iterative solution approaches to the correct solution of the original optimal control problem, in spite of model-reality differences. For illustration, an economic growth problem is solved by using the algorithm proposed. The results obtained demonstrate the efficiency of the algorithm proposed. In conclusion, the applicability of the algorithm proposed is highly recommended.

Synthesis of an Optimal Control for Linear Stationary Discrete Dynamical Systems

In this paper, an algorithm designed by the author is used to construct the general solution to difference equations with constant coefficients. It is worth noting that the algorithm does not require any information on the multiple roots of the characteristic equation. This means one does not need to reconfigure the algorithm when changing the multiplicity groups. It is for this reason that the algorithm is called “universal”. In the present study, we solve the task of finding a linear optimal control for linear stationary discrete one- and higher-dimensional systems with scalar control. Moreover, we give analytical expressions for the control that minimize the quadratic criterion and ensure the asymptotic stability of the closed system. The obtained optimal control depends only on the parameters of the initial system and the roots of the characteristic equation.

A Gauss-Newton Approach for Nonlinear Optimal Control Problem with Model-Reality Differences

Output measurement for nonlinear optimal control problems is an interesting issue. Because the structure of the real plant is complex, the output channel could give a significant response corresponding to the real plant. In this paper, a least squares scheme, which is based on the Gauss-Newton algorithm, is proposed. The aim is to approximate the output that is measured from the real plant. In doing so, an appropriate output measurement from the model used is suggested. During the computation procedure, the control trajectory is updated iteratively by using the Gauss-Newton recursion scheme. Consequently, the output residual between the original output and the suggested output is minimized. Here, the linear model-based optimal control model is considered, so as the optimal control law is constructed. By feed backing the updated control trajectory into the dynamic system, the iterative solution of the model used could approximate to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, current converted and isothermal reaction rector problems are studied and the results are demonstrated. In conclusion, the efficiency of the approach proposed is highly presented.

A Priori and A Posteriori Error Estimates of Streamline Diffusion Finite Element Method for Optimal Control Problem Governed by Convection Dominated Diffusion Equation

In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.

An approximation for the boundary optimal control problem of a heat equation defined in a variable domain

In this paper, we consider a numerical approximation for the boundary optimal control problem with the control constraint governed by a heat equation defined in a variable domain. For this variable domain problem, the boundary of the domain is moving and the shape of theboundary is defined by a known time-dependent function. By making use of the Galerkin finite element method, we first project the original optimal control problem into a semi-discrete optimal control problem governed by a system of ordinary differential equations. Then, based on the aforementioned semi-discrete problem, we apply the control parameterization method to obtain an optimal parameter selection problem governed by a lumped parameter system, which can be solved as a nonlinear optimization problem by a Sequential Quadratic Programming （SQP） algorithm. The numerical simulation is given to illustrate the effectiveness of our numerical approximation for the variable domain problem with the finite element method and the control parameterization method.

Active suspension with optimal control based on a full vehicle model

The 7-DOF model of a full vehicle with an active suspension is developed in this paper.The model is written into the state equation style.Actuator forces are treated as inputs in the state equations.Based on the basic optimal control theory,the optimal gains for the control system are figured out.So an optimal controller is developed and implemented using Matlab/Simulink,where the Riccati equation with coupling terms is deduced using the Hamilton equation.The all state feedback is chosen for the controller.The gains for all vehicle variables are traded off so that majority of indexes were up to optimal.The active suspension with optimal control is simulated in frequency domain and time domain separately,and compared with a passive suspension.Throughout all the simulation results,the optimal controller developed in this paper works well in the majority of instances.In all,the comfort and ride performance of the vehicle are improved under the active suspension with optimal control.

Lax-Oleinik-Type Formulas and Efficient Algorithms for Certain High-Dimensional Optimal Control Problems

Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimensions.In this paper,we provide analytical solutions to certain optimal control problems whose running cost depends on the state variable and with constraints on the control.We also provide Lax-Oleinik-type representation formulas for the corresponding Hamilton-Jacobi partial differential equations with state-dependent Hamiltonians.Additionally,we present an efficient,grid-free numerical solver based on our representation formulas,which is shown to scale linearly with the state dimension,and thus,to overcome the curse of dimensionality.Using existing optimization methods and the min-plus technique,we extend our numerical solvers to address more general classes of convex and nonconvex initial costs.We demonstrate the capabilities of our numerical solvers using implementations on a central processing unit(CPU)and a field-programmable gate array(FPGA).In several cases,our FPGA implementation obtains over a 10 times speedup compared to the CPU,which demonstrates the promising performance boosts FPGAs can achieve.Our numerical results show that our solvers have the potential to serve as a building block for solving broader classes of high-dimensional optimal control problems in real-time.

SECOND-ORDER OPTIMALITY CONDITIONS FOR OPTIMAL CONTROL PROBLEMS GOVERNED BY 3-DIMENSIONAL NEVIER-STOKES EQUATIONS

This article is concerned with second-order necessary and sufficient optimality conditions for optimal control problems governed by 3-dimensional Navier-Stokes equations. The periodic state constraint is considered.

Modeling of optimal control for urban freeway corridor under incident conditions

Traffic control and management are effective measures to solve the problem of traffic congestion. The optimal control model for freeway corridor is developed under incident conditions, which is in the form of minimization of the sum of the square of the difference between traffic demand and capacity at each intersection and on the freeway bottleneck section. The model optimizes control parameters of phase splits at arterial intersections, off-ramp diversion rates at upstream off-ramps and on-ramp diversion rates at downstream on ramps. Finally, the objective function is discussed and it is showed that the optimal control model is simple and practical.

DYNAMIC ANALYSIS AND OPTIMAL CONTROL OF A FRACTIONAL ORDER SINGULAR LESLIE-GOWER PREY-PREDATOR MODEL

In this article,we investigate a fractional-order singular Leslie-Gower prey-predator bioeconomic model,which describes the interaction bet ween populations of prey and predator,and takes into account the economic interest.We firstly obtain the solvability condition and the st ability of the model sys tem,and discuss the singularity induced bifurcation phenomenon.Next,we introduce a st ate feedback controller to elimina te the singularity induced bifurcation phenomenon,and discuss the optimal control problems.Finally,numerical solutions and their simulations are considered in order to illustrate the theoretical results and reveal the more complex dynamical behavior.

Forward-backward Stochastic Differential Equations and Backward Linear Quadratic Stochastic Optimal Control Problem

In this paper, we use the solutions of forward-backward stochastic differential equations to get the optimal control for backward stochastic linear quadratic optimal control problem. And we also give the linear feedback regulator for the optimal control problem by using the solutions of a group of Riccati equations.

Modeling Anthrax with Optimal Control and Cost Effectiveness Analysis

Anthrax is an infection caused by bacteria and it affects both human and animal populations. The disease can be categorized under zoonotic diseases and humans can contract infections through contact with infected animals, ingest contaminated dairy and animal products. In this paper, we developed a mathematical model for anthrax transmission dynamics in both human and animal populations with optimal control. The qualitative solution of the model behaviour was analyzed by determining Rhv, equilibrium points and sensitivity analysis. A vaccination class was incorporated into the model with waning immunity. Local and global stability of the model’s equilibria was found to be locally asymptotically stable whenever Rhv Rhv. It was revealed that reducing animal and human interaction rate, would decrease Rhv. We extended the model to optimal control in order to find the best control strategy in reducing anthrax infections. It showed that the effective strategy in combating the anthrax epidemics is vaccination of animals and prevention of humans.

Batch Process Modelling and Optimal Control Based on Neural Network Model

This paper presents several neural network based modelling, reliable optimal control, and iterative learning control methods for batch processes. In order to overcome the lack of robustness of a single neural network, bootstrap aggregated neural networks are used to build reliable data based empirical models. Apart from improving the model generalisation capability, a bootstrap aggregated neural network can also provide model prediction confidence bounds. A reliable optimal control method by incorporating model prediction confidence bounds into the optimisation objective function is presented. A neural network based iterative learning control strategy is presented to overcome the problem due to unknown disturbances and model-plant mismatches. The proposed methods are demonstrated on a simulated batch polymerisation process.

SINGULARLY PERTURBED METHODS IN THE THEORY OF OPTIMAL CONTROL OF SYSTEMS GOVERNED BY PARTIAL DIFFERENTIAL EQUATIONS

In this paper, the various problems associaled with the optimal control of systemsgoverned by partial differential equations are introduced by using singularly perturbedmethods for analysis based on stale equations, or the cost funtction and also stateequations defined in perturbed domains.

Riccati difference equation in optimal control formagnetic bearings

A model predictive optimal control method for magnetically suspended flywheel is presented.In order to suppress the conical whirl of the rotor caused by gyroscopic effect,the synchronization error is added to the traditional quadratic performance index.The target performance index is composed of the translatory error,the synchronization error,and the control output predicted by the discrete-time state model.The optimal controller is obtained by means of iterating a Riccati difference equation(RDE).Stability of the control scheme is investigated through fake algebraic Riccati technique(FART).The robust performance of the controller with respect to control parameters is studied by simulation.Results of the simulation and experiment on a compact magnetically suspended flywheel demonstrate that the proposed controller with consideration of the synchronization error is very effective to suppress the conical whirl caused by gyroscopic effect.

Domain Decomposition of an Optimal Control Problem for Semi-Linear Elliptic Equations on Metric Graphs with Application to Gas Networks

We consider optimal control problems for the flow of gas in a pipe network. The equations of motions are taken to be represented by a semi-linear model derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a given network and introduce a time discretization thereof. We then study the well-posedness of the corresponding time-discrete optimal control problem. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a non-overlapping domain decomposition of the semi-linear elliptic optimal control problem on the graph into local problems on a small part of the network, ultimately on a single edge.