A distributionally robust optimization model for batch nonlinear switched time-delay system considering uncertain output measurements

In this paper, we consider a nonlinear switched time-delay (NSTD) system with unknown switching times and unknown system parameters, where the output measurement is uncertain. This system is the underling dynamical system for the batch process of glycerol bioconversion to 1,3-propanediol induced by Klebsiella pneumoniae. The uncertain output measurement is regarded as a stochastic vector (whose components are stochastic variables) and the only information about its distribution is the first-order moment. The objective of this paper is to identify the unknown quantities of the NSTD system. For this, a distributionally robust optimization problem (a bi-level optimization problem) governed by the NSTD system is proposed, where the relative error under the environment of uncertain output measurements is involved in the cost functional. The bi-level optimization problem is transformed into a single-level optimization problem with non-smooth term through the application of duality theory in probability space. By applying the smoothing technique, the non-smooth term is approximated by a smooth term and the convergence of the approximation is established. Then, the gradients of the cost functional with respect to switching times and system parameters are derived. A hybrid optimization algorithm is developed to solve the transformed problem. Finally, we verify the obtained switching times and system parameters, as well as the effectiveness of the proposed algorithm, by solving this distributionally robust optimization problem.     

Robust parameter identification using parallel global optimization for a batch nonlinear enzyme-catalytic time-delayed process presenting metabolic discontinuities

In this paper, a nonlinear enzyme-catalytic time-delayed switched dynamical system is considered to describe batch culture of glycerol bioconversion to 1,3-propanediol induced by Klebsiella pneumoniae. This system can not only predict the exponential growth phase but also the lag and the stationary growth phases of batch culture since it contains two switching times for representing the starting moment of lag growth phase and the time when the cell specified growth rate reaches the maximum. The biological robustness is expressed in terms of the expectation and variance of the relative deviation. Our aim is to identify the switching times. To this end, a robust parameter identification problem is formulated, where the switching times are decision variables to be chosen such that the biological robustness measure is optimized. This problem, which is governed by the nonlinear system, is subject to a quality constraint and continuous state inequality constraints. Using a hybrid time-scaling transformation to parameterize the switching times into new parameters, an equivalently robust parameter identification problem is investigated. The continuous state inequality constraints are approximated by a conventional inequality constraint, yielding a sequence of approximate robust parameter identification subproblems. The convergence analysis of this approximation is also investigated. Owing to the highly complex nature of these subproblems, a parallel algorithm, based on simulated annealing, is proposed to solve these subproblems. From an extensive simulation study, it is observed that the obtained optimal switching times are satisfactory.     

Adaptive-observer-based output-constrained tracking of a class of arbitrarily switched uncertain non-affine nonlinear systems

This paper addresses an adaptive output-feedback tracking problem of arbitrarily switched pure-feedback nonlinear systems with time-varying output constraints and unknown control directions. In this work, the tracking problem of switched non-affine nonlinear systems with output constraints is transformed into the stabilization problem of switched unconstrained affine systems. The main contribution of this paper is to present a universal formula for constructing an adaptive state-observer-based tracking controller with only two adaptive parameters by using the common Lyapunov function method. These adaptive parameters in the proposed control scheme are derived using the function approximation technique and a priori knowledge of the signs of control gain functions is not required. The theoretical analysis is presented for the Lyapunov stability and the constraint satisfaction of the resulting closed-loop system in the presence of arbitrary switchings.     

基于小波包分解的非线性时变系统辩识

在实际应用中,经常会碰到非线性时变系统,它们的辨识和建模比较困难．本文采用时变Hammerstein模型描述时变非线性系统．该模型可以以较简单的方式刻划系统的时变特性和非线性特性．然后用小波包对时变系数进行展开,把时变系统的辨识转化为对时不变系数的辨识．     

Procedure for asymptotic state and parameter estimation of nonlinear distributed parameter bioreactors

Due to measurement problem in biological variables, such as the biomass concentration and its specific growth rate, the on-line measurement of these variables is not ensured and this presents a great difficulty, especially when we consider the control problem. This paper presents and analyses an approach for estimating these biological variables through an example of a nonlinear distributed parameter bioreactor. An orthogonal collocation method is applied in the distributed system to obtain a system of ordinary differential equations. A simulation study shows the feasibility and the robustness of the estimator used for this nonlinear process.     

On the fractional-order extended Kalman filter and its application to chaotic cryptography in noisy environment

In this paper via a novel method of discretized continuous-time Kalman filter, the problem of synchronization and cryptography in fractional-order systems has been investigated in presence of noisy environment for process and output signals. The fractional-order Kalman filter equation, applicable for linear systems, and its extension called the extended Kalman filter, which can be used for nonlinear systems, are derived. The result is utilized for chaos synchronization with the aim of cryptography while the transmitter system is fractional-order, and both the transmitter and transmission channel are noisy. The fractional-order stochastic chaotic Chen system is then presented to apply the proposed method for chaotic signal cryptography. The results show the effectiveness of the proposed method.     

Column enumeration based decomposition techniques for a class of non-convex MINLP problems

We propose a decomposition algorithm for a special class of nonconvex mixed integer nonlinear programming problems which have an assignment constraint. If the assignment decisions are decoupled from the remaining constraints of the optimization problem, we propose to use a column enumeration approach. The master problem is a partitioning problem whose objective function coefficients are computed via subproblems. These problems can be linear, mixed integer linear, (non-)convex nonlinear, or mixed integer nonlinear. However, the important property of the subproblems is that we can compute their exact global optimum quickly. The proposed technique will be illustrated solving a cutting problem with optimum nonlinear programming subproblems.     

Multi-Path Approach for Reliability-Redundancy Allocation Using a Scaling Method

The reliability-redundancy allocation problem is an optimization problem that achieves better system reliability by determining levels of component redundancies and reliabilities simultaneously. The problem is classified with the hardest problems in the reliability optimization field because the decision variables are mixed-integer and the system reliability function is nonlinear, non-separable, and non-convex. Thus, iterative heuristics are highly recommended for solving the problem due to their reasonable solution quality and relatively short computation time. At present, most iterative heuristics use sensitivity factors to select an appropriate variable which significantly improves the system reliability. The sensitivity factor represents the impact amount of each variable to the system reliability at a designated iteration. However, these heuristics are inefficient in terms of solution quality and computation time because the sensitivity factor calculations are performed only at integer variables. It results in degradation of the exploration and growth in the number of subsequent continuous nonlinear programming (NLP) subproblems. To overcome the drawbacks of existing iterative heuristics, we propose a new scaling method based on the multi-path iterative heuristics introduced by Ha (2004). The scaling method is able to compute sensitivity factors for all decision variables and results in a decreased number of NLP subproblems. In addition, the approximation heuristic for NLP subproblems helps to avoid redundant computation of NLP subproblems caused by outlined solution candidates. Numerical experimental results show that the proposed heuristic is superior to the best existing heuristic in terms of solution quality and computation time.     

Output feedback regulation control for a class of cascade nonlinear systems and its application to fan speed control

The output feedback regulation problem is considered for a class of nonlinear systems with integral input-to-state stable (iISS) inverse dynamics and unknown control direction. The system output together with the complete unmeasured state components appears in the system uncertainties. A systematic output feedback control scheme is presented with the help of a dynamic observer, whose gain comes from an off-line time-varying Riccati matrix differential equation. The proposed scheme can be applied to the analysis of the speed tracking control of a fan. The simulation results demonstrate the validity of the presented algorithm.     

Complex metabolic network of glycerol fermentation by Klebsiella pneumoniae and its system identification via biological robustness

The bioconversion of glycerol to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae (K. pneumoniae) can be characterized by an intricate metabolic network of interactions among biochemical fluxes, metabolic compounds, key enzymes and genetic regulation. Since there are some uncertain factors in the fermentation, especially the transport mechanisms of substances across cell membrane, the metabolic network contains multiple possible metabolic systems. In this paper, we establish a complex metabolic network and the corresponding nonlinear hybrid dynamical system aiming to determine the most possible metabolic system. The existence, uniqueness and continuity of solutions are discussed. We quantitatively describe biological robustness and present a system identification model on the basis of robustness performance. The identification problem is decomposed into two subproblems and a procedure is constructed to solve them. Numerical results show that it is most possible that both glycerol and 1,3-PD pass the cell membrane by active transport coupling with passive diffusion under substrate-sufficient conditions, whereas, under substrate-limited conditions, glycerol passes cell membrane by active transport coupling with passive diffusion and 1,3-PD by active transport.     

Reliable amplitude and frequency estimation for biased and noisy signals

Robust estimation of the amplitude, frequency and bias of unknown noisy sinusoidal signals is considered in this paper. It is only assumed that the measurements noise is bounded without any additional information such as stationarity, uncorrelation or type of distribution. In this context, the aim is to compute the set of all admissible values that are consistent with the measurements and with the error bound. The estimation problem is formulated as a Constraint Satisfaction Problem (CSP) where the amplitude, frequency and bias constitute the variables and a function relating them to the output is the constraint. Interval constraint propagation techniques are used to solve, in a guaranteed way, this problem. In order to illustrate the principle and the efficiency of the approach, numerical simulations are provided.     

Optimal estimation of sensor biases for asynchronous multi-sensor data fusion

An important step in a multi-sensor surveillance system is to estimate sensor biases from their noisy asynchronous measurements. This estimation problem is computationally challenging due to the highly nonlinear transformation between the global and local coordinate systems as well as the measurement asynchrony from different sensors. In this paper, we propose a novel nonlinear least squares formulation for the problem by assuming the existence of a reference target moving with an (unknown) constant velocity. We also propose an efficient block coordinate decent (BCD) optimization algorithm, with a judicious initialization, to solve the problem. The proposed BCD algorithm alternately updates the range and azimuth bias estimates by solving linear least squares problems and semidefinite programs. In the absence of measurement noise, the proposed algorithm is guaranteed to find the global solution of the problem and the true biases. Simulation results show that the proposed algorithm significantly outperforms the existing approaches in terms of the root mean square error.     

On Observer Design for a Class of Nonlinear Systems Including Unknown Time-Delay

The observer design for nonlinear systems with unknown, bounded, time-varying delays, on both input and state, is still an open problem for researchers. In this paper, a new observer design for a class of nonlinear system with unknown, bounded, time-varying delay was presented. For the proof of the observer stability, a Lyapunov–Krasovskii function was chosen. Sufficient assumptions are provided to prove the practical stability of the proposed observer. Furthermore, the exponential convergence of the observer was proved in the case of a constant time delay. Simulation results were shown to illustrate the feasibility of the proposed strategy.

     

Adaptive neural dynamic surface control with fixed-time prescribed performance for uncertain nonstrict-feedback stochastic switched systems

An adaptive neural dynamic surface control (DSC) problem with fixed-time prescribed performance (FTPP) is investigated for a class of nonstrict-feedback stochastic switched systems. Differently from the existing works for FTPP problem, the stochastic switched systems with nonstrict-feedback form and completely unknown systems are considered in this paper, and the unknown functions are approximated by some radial basis function (RBF) neural networks (NNs). The desired adaptive neural controller is designed by using common Lyapunov function method and defining fixed-time prescribed performance function (PPF). And based on the adaptive DSC scheme with the nonlinear filter, the “explosion of complexity” problem is avoided. Besides, the constructed fixed-time PPF just need to meet the requirement of second derivative exists. According to the Lyapunov stability theory, the FTPP of output tracking error is achieved, and all signals of closed-loop system remain bounded in probability. Finally, simulation results are presented to verify the availability of the designed control strategy.     

Prices stabilization for inexact unit-commitment problems

A widespread and successful approach to tackle unit-commitment problems is constraint decomposition: by dualizing the linking constraints, the large-scale nonconvex problem decomposes into smaller independent subproblems. The dual problem consists then in finding the best Lagrangian multiplier (the optimal “price”); it is solved by a convex nonsmooth optimization method. Realistic modeling of technical production constraints makes the subproblems themselves difficult to solve exactly. Nonsmooth optimization algorithms can cope with inexact solutions of the subproblems. In this case however, we observe that the computed dual solutions show a noisy and unstable behaviour, that could prevent their use as price indicators. In this paper, we present a simple and easy-to-implement way to stabilize dual optimal solutions, by penalizing the noisy behaviour of the prices in the dual objective. After studying the impact of a general stabilization term on the model and the resolution scheme, we focus on the penalization by discrete total variation, showing the consistency of the approach. We illustrate our stabilization on a synthetic example, and real-life problems from EDF (the French Electricity Board).     

Optimal estimation of parameters and states in stochastic time-varying systems with time delay

In this study estimation of parameters and states in stochastic linear and nonlinear delay differential systems with time-varying coefficients and constant delay is explored. The approach consists of first employing a continuous time approximation to approximate the stochastic delay differential equation with a set of stochastic ordinary differential equations. Then the problem of parameter estimation in the resulting stochastic differential system is represented as an optimal filtering problem using a state augmentation technique. By adapting the extended Kalman–Bucy filter to the resulting system, the unknown parameters of the time-delayed system are estimated from noise-corrupted, possibly incomplete measurements of the states.     

Fuzzy Bayesian system reliability assessment based on exponential distribution

The Bayesian system reliability assessment under fuzzy environments is proposed in this paper. In order to apply the Bayesian approach, the fuzzy parameters are assumed as fuzzy random variables with fuzzy prior distributions. The (conventional) Bayesian estimation method will be used to create the fuzzy Bayes point estimator of system reliability based on Exponential distribution by invoking the well-known theorem called “Resolution Identity” in fuzzy sets theory. On the other hand, we also provide the computational procedures to evaluate the membership degree of any given Bayes point estimate of system reliability. In order to achieve this purpose, we transform the original problem into a nonlinear programming problem. This nonlinear programming problem is then divided into four subproblems for the purpose of simplifying computation. Finally, the subproblems can be solved by using any commercial optimizers, e.g., GAMS or LINGO (LINDO).     

Adaptive Stabilization of Nonlinear Stochastic Systems

The purpose of this paper is to study the problem of asymptotic stabilization in probability of nonlinear stochastic differential systems with unknown parameters. With this aim, we introduce the concept of an adaptive control Lyapunov function for stochastic systems and we use the stochastic version of Artstein's theorem to design an adaptive stabilizer. In this framework the problem of adaptive stabilization of a nonlinear stochastic system is reduced to the problem of asymptotic stabilization in probability of a modified system. The design of an adaptive control Lyapunov function is illustrated by the example of adaptively quadratically stabilizable in probability stochastic differential systems. Accepted 9 December 1996     

块循环矩阵方程组的新算法

1　基本概念形如 A=a1 a2 … a Na N a1 … a N- 1?彙?廰2 a3 … a1的矩阵称为由 a1 ,a2 ,… ,a N 生成的循环矩阵 .力学和工程中的轴对称结构的计算产生上述循环矩阵 [2 - 3] .以循环矩阵A为系数矩阵的方程组 ,称为循环矩阵方程组 .已有的求解循环矩阵方程组的办法主要是各种迭代法 ,如递推法及 SOR,SSOR,SAOR超松弛迭代法[2 - 6] 等 .定义 1　形如A =A1 A2 … ANAN A1… AN- 1?彙?廇2 A3… A1　 (Ai,i =1 ,2 ,… ,N为 m阶矩阵 )的矩阵称为由 A1 ,A2 ,… ,AN 生成的块循环矩阵 .定义 2　系数矩阵 A为块循环矩阵的方程组AX …     

多周期公用工程系统运行的模型,优化方法与应用

针对多周期公用工程系统的运行优化问题，考虑了设备的启停费用的情况下。建立了混合整数非线性规划模型并证明了最优解的存在性。针对该运行优化问题本将其分解成若干子问题，然后利用改进的Hooke-Jeeves优化算法求解每个子问题。应用于具体实例，其数值结果与其它方法得到的相比。运行时间短，且更适合多周期公用工程问题的求解。