Optimization Of Nonlinear Systems Research Articles

A Practical Analysis of Performance Optimization in OSTBC Based Nonlinear MIMO-OFDM Systems

This paper presents a practical performance analysis of an orthogonal space-time block code (OSTBC) based multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system in the presence of nonlinear power amplifiers (PAs). The equivalent single-input single-output (SISO) scalar model is introduced and this then is used to construct a model for the nonlinear MIMO-OFDM system. Based on an unique inter-modulation product (IMP) analysis, it is shown how the receiver signal-to-noise ratio (SNR) may be derived to a polynomial based function of the system operating point. It is also shown that expressions for the asymptotical behavior of this SNR, when the linear and highly nonlinear PA operations are applied, may also be derived. Based on these derivations, it is further shown that the optimal system operating point, which corresponds to the maximum receiver SNR and SEP lower bound, can be identified and be derived to a polynomial based expression. Additionally, a general expression for the different integral expressions of SEP for the phase shift keying (PSK) and quadrature amplitude modulation (QAM) signals is found. By means of these analytical results, it was found possible to advance analytical explanations of observed behaviour in simulations and also to provide a practical analysis of performance optimization of nonlinear MIMO-OFDM systems.

Impact of delay on robust stable optimization of a CSTR with recycle stream

We demonstrate that the normal vector method for robust optimization of nonlinear systems with uncertain parameters can be extended to systems with delays. A first-order exothermic irreversible reaction carried out in a CSTR with recycle stream serves as example for the broad class of nonlinear delay differential equations (DDE) with uncertain parameters. The stability boundaries that must be taken into account in the robust optimization consist of Hopf bifurcation points in this case. We show that (i) an unstable steady state of operation results if stability boundaries are neglected and (ii) a conservative optimal steady state results if the delay is ignored.

An analytical fuzzy-based approach to -gain optimal control of input-affine nonlinear systems using Newton-type algorithm

This paper is concerned with -gain optimisation of input-affine nonlinear systems controlled by analytic fuzzy logic system. Unlike the conventional fuzzy-based strategies, the non-conventional analytic fuzzy control method does not require an explicit fuzzy rule base. As the first contribution of this paper, we prove, by using the Stone–Weierstrass theorem, that the proposed fuzzy system without rule base is universal approximator. The second contribution of this paper is an algorithm for solving a finite-horizon minimax problem for -gain optimisation. The proposed algorithm consists of recursive chain rule for first- and second-order derivatives, Newton’s method, multi-step Adams method and automatic differentiation. Finally, the results of this paper are evaluated on a second-order nonlinear system.

LMI Based Sliding Mode Surface Design With Mixed H2/H∞ Optimization

In this paper sliding mode surface design is concerned with multi objective optimization for nonlinear continuous-time systems in the presence of matched and mismatched uncertainties and disturbances. In order to reduce the effect of uncertainties and disturbances on sliding motion, this problem is formulated as a well-motivated mixed H2/H∞ optimization problem and a constructive algorithm based on linear matrix inequality (LMI) is proposed. We also give an LMI-based sliding mode control law to direct the system trajectories onto the designed sliding surface. Finally, using a numerical example, we show the effectiveness of proposed method.

Fuzzy Based Multi-Objective Evolutionary Algorithm for Optimal Location of FACTS Devices in a Power System

This paper presents a Multi Objective Evolutionary Algorithm (MOEA) to solve nonlinear power system optimization problem. The optimization is done with three variables; choice, location and rating of FACTS devices. The targeted technical objectives are; to control the power flow, increase the transmission line capability to its maximum thermal limits, to keep the voltages within limits while minimizing losses. The parameters of objectives are optimized independently and then the formulation of a nonlinear constrained multi-objective optimization problem is done while carrying out concurrent optimization taking two and three objectives. A Fuzzy min max approach is incorporated to reduce the best solution out of non dominated Pareto optimal set. Assessments have been done on IEEE 14 and IEEE 30 bus system for different loading conditions with two devices SVC and TCSC modeled in steady state and the results affirm the potency of the propound approach.

Steady-state performance optimization for nonlinear control systems of Lur’e type

In this paper, we develop a methodology for the steady-state performance optimization, in terms of the sensitivity to disturbances, for Lur’e type nonlinear control systems. For linear systems, steady-state performance is well defined and related to frequency-domain characteristics. The definition and analysis of steady-state performance of nonlinear systems are, however, far from trivial. For a practically relevant class of nonlinear systems and disturbances, this paper provides a computationally efficient method for the computation of the steady-state responses and, therewith, for the efficient performance assessment of the nonlinear system. Based on these analysis tools, a strategy for performance optimization is proposed, which can be employed for the optimized tuning of system and controller parameters. The results are illustrated by application to a variable gain controlled short-stroke wafer stage of a wafer scanner.

An Effective Computational Algorithm for a Class of Linear Multiplicative Programming

In this paper, an effective computational algorithm is proposed for a class of linear multiplicative problem (P), which have broad applications in financial optimization, economic plan, engineering designs and stability analysis of nonlinear systems, and so on. By utilizing piecewise linearization technique underestimates the objective function, linear relaxation programming of the original linear multiplicative programming problem (P) is established, and the proposed global optimization algorithm is convergent to the global optimal solution of the original problem (P). And finally the numerical experiments are given to illustrate that the feasibility of proposed algorithm and can be used to globally solve the class of linear multiplicative programming problem (P).

Singular Value Decomposition-Based Method for Sliding Mode Control and Optimization of Nonlinear Neutral Systems

The sliding mode control and optimization are investigated for a class of nonlinear neutral systems with the unmatched nonlinear term. In the framework of Lyapunov stability theory, the existence conditions for the designed sliding surface and the stability boundα∗are derived via twice transformations. The further results are to develop an efficient sliding mode control law with tuned parameters to attract the state trajectories onto the sliding surface in finite time and remain there for all the subsequent time. Finally, some comparisons are made to show the advantages of our proposed method.

Introducing polynomial fuzzy time series

Using polynomial concept and non-liner optimization enhanced the performance of Chen's 1996 and Yu's 2005b methods as the two frequently used methods in fuzzy time series model. To this end, polynomial schemes were given to each fuzzy logical relationship groups that had been established through forecast process to establish non-linear optimization systems. The optimal solutions of this system were applied in corresponding steps of algorithms to obtain new weights. To validate model reliability and its effectiveness, the forecasts of two huge databases namely 5 years Taiwan's stock index and 2010 load data of Power Supply Company in Johor Bahru in Malaysia were then exposed to the proposed model. Next, the forecasts were compared with real values in testing datasets. The evaluation of measuring criteria namely RMSEs and MAPEs showed that the proposed model could produce accurate forecast compared with the Chen's and Yu's method in fuzzy time series. The implication of this study is to generalize the results to other fuzzy time series models.

Applying RBF Neural Networks and Genetic Algorithms to Nonlinear System Optimization

Nonlinear system optimization is always an issue that needs to be considered in engineering practices and management. In order to obtain optimal solutions without analysis formulas to nonlinear systems, we first construct a radial-base-function (RBF) neural network using the newrb() function in MALTAB 7.0, then train the neural network according to input and output, and finally obtain the solution using a genetic algorithm. Simulated experimental results show that the proposed algorithm is able to achieve optimal solutions with a relatively fast speed of convergence.

On Average Performance and Stability of Economic Model Predictive Control

Control performance and cost optimization can be conflicting goals in the management of industrial processes. Even when optimal or optimization-based control synthesis tools are applied, the economic cost associated with plant operation is often only optimized according to static criteria that pick, among all feasible steady states, those with minimal cost. In mathematical terms, an economic cost functional differs from stage costs commonly adopted in model predictive control (MPC) as it need not be minimal at its best equilibrium. This note collects and illustrates some recent advances in receding horizon optimization of nonlinear systems that allow the control designer to simultaneously and dynamically optimize transient and steady-state economic performance. In particular, we show that average performance of economic MPC is never worse than the optimal steady-state operation. We introduce a dissipation inequality and supply function that extend previous sufficient conditions for asymptotic stability of economic MPC. Dissipativity is also shown to be a sufficient condition for concluding that steady-state operation is optimal. We show how to modify an economic cost function so that steady-state operation is asymptotically stable when that feature is deemed desirable. Finally, for the case when steady-state operation is not optimal, we develop two modified MPC controllers that asymptotically guarantee 1) improved performance compared to optimal periodic control and 2) satisfaction of constraints on average values of states and inputs.

Robust optimization of nonlinear dynamic systems with application to a jacketed tubular reactor

We present robust optimization techniques for dynamic systems which are affected by time-varying uncertainties. After reviewing existing techniques from the field of reachability analysis and ellipsoidal calculus, we discuss how to over-estimate the influence of uncertainty in nonlinear dynamic systems. The corresponding strategies lead to a framework which can be used to solve min–max optimal control problems in a conservative approximation. The technique is illustrated by applying it to a robust optimal control problem for a nonlinear jacketed tubular reactor. Inside this reactor a highly nonlinear and exothermic chemical reaction takes place which is uncertain due to fouling at the reactor wall. We regard safety constraints on the temperature which must be satisfied for all possible scenarios.

Enhancing pose accuracy of space robot by improved differential evolution

Due to the intense vibration during launching and rigorous orbital temperature environment, the kinematic parameters of space robot may be largely deviated from their nominal parameters. The disparity will cause the real pose (including position and orientation) of the end effector not to match the desired one, and further hinder the space robot from performing the scheduled mission. To improve pose accuracy of space robot, a new self-calibration method using the distance measurement provided by a laser-ranger fixed on the end-effector is proposed. A distance-measurement model of the space robot is built according to the distance from the starting point of the laser beam to the intersection point at the declining plane. Based on the model, the cost function about the pose error is derived. The kinematic calibration is transferred to a non-linear system optimization problem, which is solved by the improved differential evolution (DE) algorithm. A six-degree of freedom (6-DOF) robot is used as a practical simulation example, and the simulation results show: 1) A significant improvement of pose accuracy of space robot can be obtained by distance measurement only; 2) Search efficiency is increased by improved DE; 3) More calibration configurations may make calibration results better.

Controlled Nonlinear Stochastic Delay Equations: Part II: Approximations and Pipe-Flow Representations

This is the second part of a work dealing with key issues that have not been addressed in the modeling and numerical optimization of nonlinear stochastic delay systems. We consider new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. Part I was concerned with issues concerning the class of admissible controls and their approximations, since the classical definitions are inadequate for our models. This part is concerned with transportation equation representations and their approximations. Such representations of nonlinear stochastic delay models have been crucial in the development of numerical algorithms with much reduced memory and computational requirements. The representations for the new models are not obvious and are developed. They also provide a template for the adaptation of the Markov chain approximation numerical methods.

Controlled Nonlinear Stochastic Delay Equations: Part I: Modeling and Approximations

This two-part paper deals with “foundational” issues that have not been previously considered in the modeling and numerical optimization of nonlinear stochastic delay systems. There are new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. There are two basic and interconnected themes for these models. The first, dealt with in this part, concerns the definition of admissible control. The classical definition of an admissible control as a nonanticipative relaxed control is inadequate for these models and needs to be extended. This is needed for the convergence proofs of numerical approximations for optimal controls as well as to have a well-defined model. It is shown that the new classes of admissible controls do not enlarge the range of the value functions, is closed (together with the associated paths) under weak convergence, and is approximatable by ordinary controls. The second theme, dealt with in Part II, concerns transportation equation representations, and their role in the development of numerical algorithms with much reduced memory and computational requirements.

Degrees of freedom analysis and parameter optimization of state feedback of first-order affine singular control for bioprocess systems

The state feedback optimization of first-order affine nonlinear singular control systems is formulated as a time-invariant parameter optimization problem. Degrees of freedom (DF) is applied to the differential balance equations with initial control or its time derivatives and switching times as parameters, and uncovered that the state feedback optimization problem has −2 DF, clarifying admissible singular control structures. Using these two novel concepts, we considered end-point optimization problems in fed-batch fermentation problem to illustrate the state feedback optimization of the feed flow rate.

Developing Methods and Computer Technologies for Learning, Identification and Optimization of Nonlinear Stochastic Systems

The learning methods for identification and optimization of stochastic systems, which based on Internet technologies and were developed in Yu.V. Kozhevnikov Department “Applied Mathematics and Informatics” of A.N. Tupolev Kazan National Research Technical University (KSTU-KAI), are presented.

Controller Parameter Optimization for Nonlinear Systems Using Enhanced Bacteria Foraging Algorithm

An enhanced bacteria foraging optimization (EBFO) algorithm-based Proportional + integral + derivative (PID) controller tuning is proposed for a class of nonlinear process models. The EBFO algorithm is a modified form of standard BFO algorithm. A multiobjective performance index is considered to guide the EBFO algorithm for discovering the best possible value of controller parameters. The efficiency of the proposed scheme has been validated through a comparative study with classical BFO, adaptive BFO, PSO, and GA based controller tuning methods proposed in the literature. The proposed algorithm is tested in real time on a nonlinear spherical tank system. The real-time results show that, EBFO tuned PID controller gives a smooth response for setpoint tracking performance.

Fuzzy Model Reference Adaptive Controller Design for Multivariable Nonlinear System

This paper describes the fuzzy model reference adaptive controller design for nonlinear system based on TSK model. The stability of closed-loop system can be assured by Lyapunov function and the adaptive law is developed. The parameters of the controller can be regulated by the adaptive rules and the control scheme is applied on the automatic gauge control system and spherical motor system as two examples. The analysis of dynamic performance for ordinary PID controller and fuzzy adaptive controller is performed in detail with simulation software. Simulation results verify the systems with strong adaptive ability and can adapt to the changes and disturbances of the controlled object. This study provides a theoretical guide for the configuration design, optimization and control research of multivariable nonlinear systems.

An efficient stochastic optimization framework for studying the impact of seasonal variation on the minimum water consumption of pulverized coal (PC) power plants

Coal-fired power plants use water in large amounts second only to agricultural irrigation. Water restrictions become more influential when water-expensive carbon capture technologies are added to the process. Therefore, national efforts to study the reduction of water withdrawal and consumption in existing and future plants have been intensified. Water consumption in these plants is strongly associated with the dry bulb temperature and humidity of air. There is significant variability in these parameters. In this work, we characterized the uncertainty and variability in these parameters in terms of probability distributions. These distributions change with seasons. We obtained optimal operating conditions for each season in the face of uncertainties using water minimization as the objective. It has been found that the water consumption is reduced from 3.2 to 15.4% depending on the season. In order to solve this large scale real world optimization problem, we had to resort to an efficient stochastic nonlinear programming (SNLP) algorithm called Better Optimization of Nonlinear Uncertain Systems (BONUS). It has been found that BONUS reduces the computationally intensity of this problem by 98.7%, making it possible to obtain optimal operating conditions in reasonable computational time.