利用干扰信号二阶差分进行最优预见伺服系统设计

本文研究从偏差系统出发，利用干扰信号的二阶差分进行最优预见伺服系统设计的方法．这种设计方法适用于有输入时间滞后的线性控制系统．     

财政收支平衡控制模型及其应用

本文运用现代控制论的原理与方法研究了地区（或县、市）一级财政收支平衡的控制问题。把财政收支平衡的控制问题置于国民经济系统之中，运用最优控制论建立了最优积累率控制模型；进而，从所求得的最优积累率为出发点，讨论了财政收支的平衡控制，并建立了相应的控制模型。     

Optimal control problem for viscous Cahn-Hilliard equation

This paper is concerned with the viscous Cahn-Hilliard equation, which arises in the dynamics of viscous first order phase transitions in cooling binary solutions. The optimal control under boundary condition is given and the existence of optimal solution to the equation is proved.     

Optimal vaccination and control strategies against dengue

This article focuses on the mathematical modelling of a disease outbreak of dengue fever. A cost‐efficient fighting strategy, which simultaneously uses vaccination, application of insecticides to adult and aquatic mosquitoes, and an approach to decrease the number of man‐made breeding places for the mosquitoes, is computed using optimal control. Vaccination includes a paediatric vaccination and an imperfect random mass vaccination with waning immunity.     

具有终端不等式约束的线性二次控制问题

本文研究具有终端不等式约束的线性二次控制问题,得到了最优控制的反馈形式.所得到的反馈形式与相应的无约束问题的Riccati微分方程和一个函数矩阵的线性方程的解有关.     

On the optimal control of a single-server queueing system: Reply

This comment replies to a criticism due to Klein and Gruver (Ref. 1) of our earlier paper (Ref. 2) on the application of control theory to a queueing system. The criticism concerns the state-space diagram and the table which we inadvertently gave for the terminal-reward problem, albeit incorrectly labeled, rather than for the free-endpoint problem considered in our paper. We show that the solution given by Klein and Gruver is itself incorrect and nonoptimal.     

Optimal control of unilateral obstacle problem with a source term

We consider an optimal control problem for the obstacle problem with an elliptic variational inequality. The obstacle function which is the control function is assumed in H². We use an approximate technique to introduce a family of problems governed by variational equations. We prove optimal solutions existence and give necessary optimality conditions. The author is grateful to Prof. M. Bergounioux for her instructive suggestions.     

Optimal Control of Linear Time-Varying Systems via Haar Wavelets

This paper introduces the application of Haar wavelets to the optimal control synthesis for linear time-varying systems. Based upon some useful properties of Haar wavelets, a special product matrix, a related coefficient matrix, and an operational matrix of backward integration are proposed to solve the adjoint equation of optimization. The results obtained by the proposed Haar approach are almost the same as those obtained by the conventional Riccati method.     

On a Problem of Optimal Stochastic Control with Incomplete Information

We study a problem of Bayesian adaptive control arising in mathematical finance. For this particular problem, we obtain explicit formulas for the value function and the optimal control policy.     

Conditions implying the vanishing of the Hamiltonian at infinity in optimal control problems

In an infinite horizon optimal control problem the Hamiltonian vanishes at infinity when the differential equation is autonomous and the integrand in the criterion satisfies some weak integrability conditions. A generalization of Michel’s result (in Econometrica 50:975–985, 1982) is obtained.     

Dynamics for controlled 2-D Boussinesq systems with distributed controls

The long-time behavior of solutions for an optimal distributed control problem associated with the Boussinesq equations is studied. First, a quasi-optimal solution for the Boussinesq equations is constructed; this quasi-optimal solution possesses the decay (in time) properties. Then, some preliminary estimates for the long-time behavior of all solutions of the Boussinesq equations are derived. Next, the existence of a solution for the optimal control problem is proved. Finally, the long-time decay properties for the optimal solutions is established.     

Finding candidate singular optimal controls: A state of the art survey

Pontryagin's maximum principle gives no information about a singular optimal control if the problem is linear. This survey shows how candidate singular optimal controls may be found for linear and nonlinear problems. A theorem is given on the maximum order of a linear singular problem.This paper is based in part on the research undertaken by the author at the Hatfield Polytechnic, Hatfield, Hertfordshire, England, for the Ph.D. Degree.     

Optimal control of the viscous weakly dispersive Degasperis-Procesi equation

In this paper, we study the optimal control problem for the viscous weakly dispersive Degasperis-Procesi equation. We deduce the existence and uniqueness of a weak solution to this equation in a short interval by using the Galerkin method. Then, according to optimal control theories and distributed parameter system control theories, the optimal control of the viscous weakly dispersive Degasperis-Procesi equation under boundary conditions is given and the existence of an optimal solution to the viscous weakly dispersive Degasperis-Procesi equation is proved.     

Optimal control of random evolutions

We consider a stochastic control problem for a random evolution. We study the Bellman equation of the problem and we prove the existence of an optimal stochastic control which is Markovian. This problem enables us to approximate the general problem of the optimal control of solutions of stochastic differential equations.     

Optimal feedback control laws using nonlinear programming

A procedure of parametrizing feedback controls when solving the optimal control problem using nonlinear programming is considered. The maximum principle is utilized to determine the forms of the parametrized feedback control. Applications are demonstrated by numerical examples.     

Time-Varying Linear-Quadratic Control

This paper discusses the performance of controlled linear dynamic systems that use time-varying feedforward signals and time-varying linear-quadratic (LQ) feedback gains. Such a time-varying LQ controller can bring a dynamic system to a desired final state in roughly half the time required by a time-invariant LQ controller, since it pushes at both ends, i.e., it uses significant control effort near the end of the maneuver, as well as at the beginning, to meet the specified end conditions; there is no overshoot and no settling time. This requires a more complex controller and some care with the high gains near the final time. A MATLAB³ code is listed that synthesizes and simulates zero-order-hold time-varying LQ controllers. The precision landing of a helicopter using four controls is treated as an example.