A Singular Linear Quadratic Time-Inconsistent Optimal Control Problem

Yong J [Acta Math. Appl. Sin. Engl. Ser. 28(2012), 1–30] [Math. Control Relat. Fields1(2011), 83–118] studied a standard linear quadratic time-inconsistent optimal control problem via a cooperative and non-cooperative approach, respectively. The authors extend his results to a singular case. To handle the singularity, the authors prove the solvability of a generalized Riccati equation,and introduce a notion of MP-convergence of matrix. It is shown that the authors can obtain a family of parameter equilibrium controls in both cases. Another interesting outcome is that a new type of parameter forward-backward Volterra integral equations is derived.

AN OPTIMAL CONTROL PROBLEM FOR A LOTKA-VOLTERRA COMPETITION MODEL WITH CHEMO-REPULSION

In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of ℝ^(ℕ),N=2,3.This model describes the competition of two species in which one of them avoid encounters with rivals through a chemo-repulsion mechanism.We prove the existence and uniqueness of weak-strong solutions,and then we analyze the existence of a global optimal solution for a related bilinear optimal control problem,where the control is acting on the chemical signal.Posteriorly,we derive first-order optimality conditions for local optimal solutions using the Lagrange multipliers theory.Finally,we propose a discrete approximation scheme of the optimality system based on the gradient method,which is validated with some computational experiments.

Optimal and robust control of population transfer in asymmetric quantum-dot molecules

We present an optimal and robust quantum control method for efficient population transfer in asymmetric double quantum-dot molecules.We derive a long-duration control scheme that allows for highly efficient population transfer by accurately controlling the amplitude of a narrow-bandwidth pulse.To overcome fluctuations in control field parameters,we employ a frequency-domain quantum optimal control theory method to optimize the spectral phase of a single pulse with broad bandwidth while preserving the spectral amplitude.It is shown that this spectral-phase-only optimization approach can successfully identify robust and optimal control fields,leading to efficient population transfer to the target state while concurrently suppressing population transfer to undesired states.The method demonstrates resilience to fluctuations in control field parameters,making it a promising approach for reliable and efficient population transfer in practical applications.

Optimal Control for Age Distribution and Weighted Size Competitive Species in a Polluted Environment

In the paper,we study an optimal control for a system representing a competitive species model with fertility and mortality depending on a weighted size in a polluted environment.A fixed point theorem is applied to obtain the existence and uniqueness exhibited by a non-negative solution of above mentioned model.A maximum principle helps to carefully verify the existence of the optimal control policy,and tangent-normal cone techniques help to obtain the optimal condition specific to control issue.

Sequential Inverse Optimal Control of Discrete-Time Systems

This paper presents a novel sequential inverse optimal control(SIOC)method for discrete-time systems,which calculates the unknown weight vectors of the cost function in real time using the input and output of an optimally controlled discrete-time system.The proposed method overcomes the limitations of previous approaches by eliminating the need for the invertible Jacobian assumption.It calculates the possible-solution spaces and their intersections sequentially until the dimension of the intersection space decreases to one.The remaining one-dimensional vector of the possible-solution space’s intersection represents the SIOC solution.The paper presents clear conditions for convergence and addresses the issue of noisy data by clarifying the conditions for the singular values of the matrices that relate to the possible-solution space.The effectiveness of the proposed method is demonstrated through simulation results.

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.

Contract Mechanism of Water Environment Regulation for Small and Medium Sized Enterprises Based on Optimal Control Theory

The small and scattered enterprise pattern in the county economy has formed numerous sporadic pollution sources, hindering the centralized treatment of the water environment, increasing the cost and difficulty of treatment. How enterprises can make reasonable decisions on their water environment behavior based on the external environment and their own factors is of great significance for scientifically and effectively designing water environment regulation mechanisms. Based on optimal control theory, this study investigates the design of contractual mechanisms for water environmental regulation for small and medium-sized enterprises. The enterprise is regarded as an independent economic entity that can adopt optimal control strategies to maximize its own interests. Based on the participation of multiple subjects including the government, enterprises, and the public, an optimal control strategy model for enterprises under contractual water environmental regulation is constructed using optimal control theory, and a method for calculating the amount of unit pollutant penalties is derived. The water pollutant treatment cost data of a paper company is selected to conduct empirical numerical analysis on the model. The results show that the increase in the probability of government regulation and public participation, as well as the decrease in local government protection for enterprises, can achieve the same regulatory effect while reducing the number of administrative penalties per unit. Finally, the implementation process of contractual water environmental regulation for small and medium-sized enterprises is designed.

Multi-Time Scale Optimal Scheduling of a Photovoltaic Energy Storage Building System Based on Model Predictive Control

Building emission reduction is an important way to achieve China’s carbon peaking and carbon neutrality goals.Aiming at the problem of low carbon economic operation of a photovoltaic energy storage building system,a multi-time scale optimal scheduling strategy based on model predictive control(MPC)is proposed under the consideration of load optimization.First,load optimization is achieved by controlling the charging time of electric vehicles as well as adjusting the air conditioning operation temperature,and the photovoltaic energy storage building system model is constructed to propose a day-ahead scheduling strategy with the lowest daily operation cost.Second,considering inter-day to intra-day source-load prediction error,an intraday rolling optimal scheduling strategy based on MPC is proposed that dynamically corrects the day-ahead dispatch results to stabilize system power fluctuations and promote photovoltaic consumption.Finally,taking an office building on a summer work day as an example,the effectiveness of the proposed scheduling strategy is verified.The results of the example show that the strategy reduces the total operating cost of the photovoltaic energy storage building system by 17.11%,improves the carbon emission reduction by 7.99%,and the photovoltaic consumption rate reaches 98.57%,improving the system’s low-carbon and economic performance.

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.

Trigonometric Regularization and Continuation Method Based Time-Optimal Control of Hypersonic Vehicles

Aiming at the time-optimal control problem of hypersonic vehicles(HSV)in ascending stage,a trigonometric regularization method(TRM)is introduced based on the indirect method of optimal control.This method avoids analyzing the switching function and distinguishing between singular control and bang-bang control,where the singular control problem is more complicated.While in bang-bang control,the costate variables are unsmooth due to the control jumping,resulting in difficulty in solving the two-point boundary value problem(TPBVP)induced by the indirect method.Aiming at the easy divergence when solving the TPBVP,the continuation method is introduced.This method uses the solution of the simplified problem as the initial value of the iteration.Then through solving a series of TPBVP,it approximates to the solution of the original complex problem.The calculation results show that through the above two methods,the time-optimal control problem of HSV in ascending stage under the complex model can be solved conveniently.

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.

A new optimal adaptive backstepping control approach for nonlinear systems under deception attacks via reinforcement learning

In this paper,a new optimal adaptive backstepping control approach for nonlinear systems under deception attacks via reinforcement learning is presented in this paper.The existence of nonlinear terms in the studied system makes it very difficult to design the optimal controller using traditional methods.To achieve optimal control,RL algorithm based on critic–actor architecture is considered for the nonlinear system.Due to the significant security risks of network transmission,the system is vulnerable to deception attacks,which can make all the system state unavailable.By using the attacked states to design coordinate transformation,the harm brought by unknown deception attacks has been overcome.The presented control strategy can ensure that all signals in the closed-loop system are semi-globally ultimately bounded.Finally,the simulation experiment is shown to prove the effectiveness of the strategy.

Stochastic Maximum Principle for Optimal Advertising Models with Delay and Non-Convex Control Spaces

In this paper we study optimal advertising problems that model the introduction of a new product into the market in the presence of carryover effects of the advertisement and with memory effects in the level of goodwill. In particular, we let the dynamics of the product goodwill to depend on the past, and also on past advertising efforts. We treat the problem by means of the stochastic Pontryagin maximum principle, that here is considered for a class of problems where in the state equation either the state or the control depend on the past. Moreover the control acts on the martingale term and the space of controls U can be chosen to be non-convex but now the space of controls U can be chosen to be non-convex. The maximum principle is thus formulated using a first-order adjoint Backward Stochastic Differential Equations (BSDEs), which can be explicitly computed due to the specific characteristics of the model, and a second-order adjoint relation.

Transmission Dynamics and Optimal Control Strategies of a Hand-Foot-Mouth Disease Model with Treatment and Vaccination Interventions

In this article, the transmission dynamics of a Hand-Foot-Mouth disease model with treatment and vaccination interventions are studied. We calculated the basic reproduction number and proved the global stability of disease-free equilibrium when R0 R0 > 1. Meanwhile, we obtained the optimal control strategies minimizing the cost of intervention and minimizing the infected person. We also give some numerical simulations to verify our theoretical results.

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.

Gradient Recovery Based Two-Grid Finite Element Method for Parabolic Integro-Differential Optimal Control Problems

In this paper, the optimal control problem of parabolic integro-differential equations is solved by gradient recovery based two-grid finite element method. Piecewise linear functions are used to approximate state and co-state variables, and piecewise constant function is used to approximate control variables. Generally, the optimal conditions for the problem are solved iteratively until the control variable reaches error tolerance. In order to calculate all the variables individually and parallelly, we introduce a gradient recovery based two-grid method. First, we solve the small scaled optimal control problem on coarse grids. Next, we use the gradient recovery technique to recover the gradients of state and co-state variables. Finally, using the recovered variables, we solve the large scaled optimal control problem for all variables independently. Moreover, we estimate priori error for the proposed scheme, and use an example to validate the theoretical results.

A Priori Error Analysis for NCVEM Discretization of Elliptic Optimal Control Problem

In this paper, we propose the nonconforming virtual element method (NCVEM) discretization for the pointwise control constraint optimal control problem governed by elliptic equations. Based on the NCVEM approximation of state equation and the variational discretization of control variables, we construct a virtual element discrete scheme. For the state, adjoint state and control variable, we obtain the corresponding prior estimate in H1 and L2 norms. Finally, some numerical experiments are carried out to support the theoretical results.

Deterministic Time-inconsistent Optimal Control Problems - an Essentially Cooperative Approach

A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control, a non-cooperative N-person differential game （but essentially cooperative in some sense） is introduced. Under certain conditions, it is proved that the open-loop Nash equilibrium value function of the N-person differential game converges to a time-consistent equilibrium value function of the original problem, which is the value function of a time-consistent optimal control problem. Moreover, it is proved that any optimal control of the time-consistent limit problem is a time-consistent equilibrium control of the original problem.

Wellbore-heat-transfer-model-based optimization and control for cooling downhole drilling fluid

To address the two critical issues of evaluating the necessity of implementing cooling techniques and achieving real-time temperature control of drilling fluids underground in the current drilling fluid cooling technology,we first established a temperature and pressure coupled downhole heat transfer model,which can be used in both water-based and oil-based drilling fluid.Then,fourteen factors,which could affect wellbore temperature,were analyzed.Based on the standard deviation of the downhole temperature corresponding to each influencing factor,the influence of each factor was quantified.The influencing factors that can be used to guide the drilling fluid's cooling technology were drilling fluid thermal conductivity,drilling fluid heat capacity,drilling fluid density,drill strings rotation speed,pump rate,viscosity,ROP,and injection temperature.The nondominated sorting genetic algorithm was used to optimize these six parameters,but the optimization process took 182 min.Combining these eight parameters'influence rules with the nondominated sorting genetic algorithm can reduce the optimization time to 108 s.Theoretically,the downhole temperature has been demonstrated to increase with the inlet temperature increasing linearly under quasi-steady states.Combining this law and PID,the downhole temperature can be controlled,which can reduce the energy for cooling the surface drilling fluid and can ensure the downhole temperature reaches the set value as soon as possible.

Vibration Control of the Rail Grinding Vehicle with Abrasive Belt Based on Structural Optimization and Lightweight Design

As a new grinding and maintenance technology,rail belt grinding shows significant advantages in many applications The dynamic characteristics of the rail belt grinding vehicle largely determines its grinding performance and service life.In order to explore the vibration control method of the rail grinding vehicle with abrasive belt,the vibration response changes in structural optimization and lightweight design are respectively analyzed through transient response and random vibration simulations in this paper.Firstly,the transient response simulation analysis of the rail grinding vehicle with abrasive belt is carried out under operating conditions and non-operating conditions.Secondly,the vibration control of the grinding vehicle is implemented by setting vibration isolation elements,optimizing the structure,and increasing damping.Thirdly,in order to further explore the dynamic characteristics of the rail grinding vehicle,the random vibration simulation analysis of the grinding vehicle is carried out under the condition of the horizontal irregularity of the American AAR6 track.Finally,by replacing the Q235 steel frame material with 7075 aluminum alloy and LA43M magnesium alloy,both vibration control and lightweight design can be achieved simultaneously.The results of transient dynamic response analysis show that the acceleration of most positions in the two working conditions exceeds the standard value in GB/T 17426-1998 standard.By optimizing the structure of the grinding vehicle in three ways,the average vibration acceleration of the whole car is reduced by about 55.1%from 15.6 m/s^(2) to 7.0 m/s^(2).The results of random vibration analysis show that the grinding vehicle with Q235 steel frame does not meet the safety conditions of 3σ.By changing frame material,the maximum vibration stress of the vehicle can be reduced from 240.7 MPa to 160.0 MPa and the weight of the grinding vehicle is reduced by about 21.7%from 1500 kg to 1175 kg.The modal analysis results indicate that the vibration control of the grinding vehicle can be realized by optimizing the structure and replacing the materials with lower stiffness under the premise of ensuring the overall strength.The study provides the basis for the development of lightweight,diversified and efficient rail grinding equipment.