Optimal piecewise constant control of continuous time systems with time-varying delay

Necessary conditions are presented for the optimal piecewise constant control of continuous time systems with time-varying delay. The conventional Hamiltonian is used; the effect of the delay is included in the costate equation. A fixed endpoint problem is formulated for a scalar system. Restricting the control to be piecewise constant results in a condition on the Hamiltonian integrated between switching instants. The extension to more general terminal constraints for multivariable systems is straight-forward.     

Input delay compensation of nonlinear stochastic systems with both state and input delays by prediction approach

In this study, we present an extension of the prediction scheme (dynamic control) for nonlinear stochastic systems with both input and state delays. The stochastic system includes multiplicative noise and it is modelled as Ito stochastic differential equation. Input delay is considered to be equal or less than state delay and both delays are considered to be constant. At first, a new formula for prediction of the system's state is presented and then by means of this prediction vector, control input is constructed. To calculate the stabilising gain of the predictive controller, some sufficient delay-independent conditions in the form of linear matrix inequality are presented. Finally, simulation examples are given to illustrate the effectiveness of the proposed approach.     

A quasilinearization algorithm and its application to a manipulator problem

A quasilinearization algorithm is proposed for the computation of optimal control of a class of constrained problem. The constraints are inequality constraints on functions of the state and control variables, and bounds on the values of the control variables. Necessary conditions for optimal control of the control problem are derived. In the iterative procedure, no prior information is required regarding the sequence of constrained and unconstrained arcs and the inequality constraints which are on their boundaries along a specific constrained arc of the optimal trajectory. All this information will be determined within the iterative procedure using some necessary conditions for optimal control. The ability of the proposed algorithm to solve practical problems is demonstrated by its application to several variations of two problems, one of which is a common manipulator problem in industry where transportation of open vessels of liquid is to be performed in a specified period of time. It is shown that the proposed quasilinearization algorithm is an effective tool in deriving optimal control policies for a common type of manipulator operation in industry.     

Necessary conditions for optimality of stochastic systems with uncontrollable flow of failures and constraints of the equality and inequality type

Consideration was given to the necessary conditions for optimal control of the nonlinear random-structure stochastic systems conditioned by the uncontrollable flow of failures with constraints of the equality and inequality on the system parameters, control functions, and state vector describing various requirements on the system.     

Time optimal control of linear systems with delay†

Necessary conditions, analogous to those of Pontryagin's maximum principle are developed for the problem of reducing the state, of linear systems with delay, to zero in minimum time. An example is presented that demonstrates the technique of finding the time optimal control.     

Approximate optimal controls for a class of Volterra systems with nonlinear delay

Necessary and sufficient conditions of approximate optimal controls for integral linear in state Volterra systems with nonlinear delays are derived. They are used for studying approximate optimal controls obtained by the control parameterization method as an important application.     

Optimal discrete systems with pure delays

Necessary and sufficient conditions for the optimization of multivariable discrete systems containing pure delays in dynamics, in performance index, and in constraints are investigated. Using nonlinear programming, it is shown that a discrete maximum principle similar to the one derived by Pearson and Sridhar [1] is valid for a subclass of these problems, that is, systems with linear dynamics, convex inequality constraints, and convex performance index.     

Adaptive Fault-Delay Accommodation for a Class of State-Delay Systems With Actuator Faults

Fault and delay accommodating simultaneously for a class of linear systems subject to state delays, actuator faults and disturbances is investigated in this work. A matrix norm minimization technique is applied to minimize the norms of coefficient matrix on time delay terms of the system in consideration. Compared with the matrix inequality scaling technique, the minimization technique can relax substantially the obtained stability conditions for state delay systems, especially, when the coefficient matrices of time delay terms have a large order of magnitudes.An output feedback adaptive fault-delay tolerant controller(AFDTC) is designed subsequently to stabilize the plant with state delays and actuator faults. Compared with the conventional fault tolerant controller(FTC), the designed output feedback AFDTC can be updated on-line to compensate the effect of both faults and delays on systems. Simulation results under two numerical examples exhibit the effectiveness and merits of the proposed method.     

Stability conditions of constrained delay systems via positive invariance

A delay system is represented by a linear difference equation. The system parameters and the delays are assumed to be imperfectly known. The output vector is perturbed by an external disturbance vector. The addressed problem is to characterize conditions which guarantee that the output vector remains in a given domain defined by a set of symmetrical linear constraints. This problem is solved by imposing positive invariance conditions. These conditions also imply delay independent asymptotic stability of the associated deterministic system. The possible use of these new robust stability conditions for controlling an input–output delay model is then presented. An application is finally proposed; it concerns an inventory control problem for a simple production loop subject to constraints on inventory levels. © 1998 John Wiley & Sons, Ltd.     

带饱和执行器的不确定时滞系统的 鲁棒控制

研究了一类具有饱和执行器约束的不确定时滞系统时滞依赖型无记忆鲁棒控制问题 .所考虑的时滞系统包括时变未知但有界的不确定参数以及状态和控制的时滞项 .文中应用了 Lyapunov定理以及线性矩阵不等式 ( LMI)方法来研究该系统的分析和综合问题 ,导出了一个新的鲁棒可镇定判据和相应的无记忆鲁棒镇定控制律设计方法 .所得的基于一组LMIs的结果是与时滞相关的     

A new approach to differential dynamic programming for discrete time systems

This paper proposes a new differential dynamic programming algorithm for solving discrete time optimal control problems with equality and inequality constraints on both control and state variables and proves its convergence. The present algorithm is different from differential dynamic programming algorithms developed in [10]-[15], which can hardly solve optimal control problems with inequality constraints on state variables and whose convergence has not been proved. Composed of iterative methods for solving systems of nonlinear equations, it is based upon Kuhn-Tucker conditions for recurrence relations of dynamic programming. Numerical examples show file efficiency of the present algorithm.     

Robust stability and stabilization for singular systems with statedelay and parameter uncertainty

Considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay. The parametric uncertainty is assumed to be norm bounded. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties, while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed-loop system is robustly stable. These problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization, respectively. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived. A strict linear matrix inequality (LMI) design approach is developed. An explicit expression for the desired robust state feedback control law is also given. Finally, a numerical example is provided to demonstrate the application of the proposed method     

Design of networked control systems with bounded arbitrary time delays

This paper is mainly concerned with the model predictive control (MPC) of networked control systems (NCSs) with uncertain time delay and data packets disorder. The network-induced time delay is described as bounded and arbitrary process. For the usual state feedback controller, by considering all the possibilities of delays, an augmented state space model of the closed-loop system, which characterizes all the delay cases, is obtained. The stability conditions are given according to the Lyapunov method based on this augmented model. The stability property is inherited in MPC which explicitly considers the physical constraints. A numerical example is given to demonstrate the effectiveness of the proposed MPC.     

多时滞线性系统的控制参数优化方法

采用控制参数化方法研究具有连续状态不等式约束和多重状态及控制时滞的线性系统优化控制问题．通过把时滞系统动态模型中的控制量表示成关于时间的分段常数函数,把每个控制参数看作决策变量,将多时滞系统的控制问题转化为数学规划问题．推导出在连续状态不等式约束条件下的目标函数和约束函数对于待求参数的梯度公式,并用序列二次规划算法求出其最优控制量．最后,将该优化算法应用于湿法炼锌净化过程中．仿真结果表明,锌粉的添加量可以有效地减少,从而避免了资源的浪费．     

Design of reduced-order observers without internal delays

This paper provides a simple and systematic design method of reduced-order observers without internal delays for systems having a time delay in the state variables. Necessary and sufficient conditions for the existence of these observers are given     

Optimal guaranteed cost control of a class of hybrid systems with mode-dependent mixed time delays

In this paper, the guaranteed cost control problem is investigated for a class of nonlinear systems with Markovian jumping parameters and mixed time delays. The time delays involved consist of the mode-dependent discrete time delay and the distributed time delay with mode-dependent upper and lower boundaries; the associated cost function is a quadratic function, and nonlinear functions are assumed to satisfy sector-bounded conditions. By introducing new Lyapunov–Krasovskii functionals and some analytic techniques, the sufficient conditions for the existence of guaranteed cost controllers are derived for the systems and related cost function. Moreover, a linear matrix inequality (LMI) based approach to design the optimal guaranteed cost controller is formulated to minimise the guaranteed cost of the closed-loop system. Numerical simulation is further carried out to demonstrate the effectiveness of the proposed methods.     

Improved robust stability criteria and design of robust stabilizing controller for uncertain linear time‐delay systems

In this paper, an improved linear matrix inequality (LMI)‐based robust delay‐dependent stability test is introduced to ensure a larger upper bound for time‐varying delays affecting the state vector of an uncertain continuous‐time system with norm‐bounded‐type uncertainties. A quasi‐full‐size Lyapunov–Krasovskii functional is chosen and free‐weighting matrix approach is employed. Less restrictive sufficient conditions are derived for robust stability of time‐varying delay systems with norm‐bounded‐type uncertainties. Moreover, the investigation of the stabilization problem with memoryless state‐feedback control is presented such that the stabilizability criteria are obtained in terms of matrix inequalities, which can be solved via utilizing a cone complementarity minimization algorithm. Finally, the problem of output feedback stabilization for square systems is also taken into consideration. The output feedback stabilizability criteria are derived in the form of linear matrix inequalities, which are convex and can be easily solved using interior point algorithms. A plenty of numerical examples are presented indicating that the proposed stability and stabilization methods effectively improve the existing results. Copyright © 2006 John Wiley & Sons, Ltd.     

Multistage linear programming for discrete optimal control with distributed-lags

A multistage decomposition scheme is developed for optimizing discrete-time dynamic systems, which include distributed and/or multiple pure delays. The discrete optimal control problem in this paper consists of a system dynamics described by a multidimensional linear difference equation of high-order which is called the distributed-lag model, a linear objective function, and linear state and control constraints. This problem may be solved as a linear program by, for example, a revised simplex method. However, this leads to excessive storage requirement for large problems. Instead, by taking advantage of the staircase-structure of equality constraints (system equation), Dantzig-Wolfe decomposition principle is applied repeatedly in each stage, and an effective multistage decomposition algorithm for distributed-lag models is obtained. Significant advantage of the optimization technique in this paper is that it can handle any number of delay terms in the system without reducing the multidimensional high-order system equation to a conventional larger dimensional first-order system equation (state equation of normal form). Therefore, a substantial reduction of computational burden, the so called curse of dimensionality, in the existing discrete optimal control algorithms, is obtained. A numerical example of a congested urban road traffic control problem with many delays is included.     

Observer‐based fault estimators using iterative learning scheme for nonlinear time‐delay systems with intermittent faults

This paper deals with the intermittent fault estimation problem for a class of nonlinear time‐delay systems with measurement noise. The time delays are assumed to occur in state vector, nonlinear term as well as output vector, thus reflecting the time delays influence in reality more closely. The aim of the problem is to estimate the intermittent fault by using iterative learning scheme, with the property of index, hence attenuating the influence from measurement noise. Different from existing fault estimating schemes, the state error information and fault estimating information in the previous iteration are used in the current iteration to improve the estimating results. The stability and convergence of iterative learning observer and uniform boundedness of dynamic error system are achieved by using Lyapunov function and optimal function design. Simultaneously, an improved sufficient condition for the existence of such an estimator is established in terms of the linear matrix inequality by the Schur complements and Young relations. Furthermore, the results are both suited for the systems with time‐varying delay and the systems with constant delay. Finally, two numerical examples are proposed to illustrate the effectiveness of the proposed method, and a comparability example is presented to demonstrate its superiority. Copyright © 2017 John Wiley & Sons, Ltd.