A simulated annealing algorithm for prioritized multiobjective optimization--implementation in an adaptive model predictive control configuration.

This paper presents a new stochastic algorithm for solving hierarchical multiobjective optimization problems. The algorithm is based on the simulated annealing concept and returns a single solution that corresponds to the lexicographic ordering approach. The algorithm optimizes simultaneously the multiple objectives by assigning a different initial temperature to each one, according to its position in the hierarchy. A major advantage of the proposed method is its low computational cost. This is very critical, particularly, for online applications, where the time that is available for decision making is limited. The method is tested in a number of benchmark problems, which illustrate its ability to find near-optimal solutions even in nonconvex multiobjective optimization problems. The results are comparable with those that are produced by state-of-the-art multiobjective evolutionary algorithms, such as the Nondominated Sorting Genetic Algorithm II. The algorithm is further applied to the solution of a large-scale problem that is formulated online, when a multiobjective adaptive model predictive control (MPC) configuration is adopted. This particular control scheme involves an adaptive discrete-time model of the system, which is developed using the radial-basis-function neural-network architecture. A key issue in the success of the adaptation strategy is the introduction of a persistent excitation constraint, which is transformed to a top-priority objective. The overall methodology is applied to the control problem of a pH reactor and proves to be superior to conventional MPC configurations.     

Adaptive air-fuel ratio control with MLP network

This paper presents an application of adaptive neural network model-based predictive control (MPC) to the air-fuel ratio of an engine simulation. A multi-layer perceptron (MLP) neural network is trained using two on-line training algorithms: a back propagation algorithm and a recursive least squares (RLS) algorithm. It is used to model parameter uncertainties in the nonlinear dynamics of internal combustion (IC) engines. Based on the adaptive model, an MPC strategy for controlling air-fuel ratio is realized, and its control performance compared with that of a traditional PI controller. A reduced Hessian method, a newly developed sequential quadratic programming (SQP) method for solving nonlinear programming (NLP) problems, is implemented to speed up nonlinear optimization in the MPC.     

Multiobjective model predictive control

This paper proposes a novel model predictive control (MPC) scheme based on multiobjective optimization. At each sampling time, the MPC control action is chosen among the set of Pareto optimal solutions based on a time-varying, state-dependent decision criterion. Compared to standard single-objective MPC formulations, such a criterion allows one to take into account several, often irreconcilable, control specifications, such as high bandwidth (closed-loop promptness) when the state vector is far away from the equilibrium and low bandwidth (good noise rejection properties) near the equilibrium. After recasting the optimization problem associated with the multiobjective MPC controller as a multiparametric multiobjective linear or quadratic program, we show that it is possible to compute each Pareto optimal solution as an explicit piecewise affine function of the state vector and of the vector of weights to be assigned to the different objectives in order to get that particular Pareto optimal solution. Furthermore, we provide conditions for selecting Pareto optimal solutions so that the MPC control loop is asymptotically stable, and show the effectiveness of the approach in simulation examples.     

基于目标空间划分的自适应多目标进化算法

目前,多目标进化算法在众多领域具有极高的应用价值,是优化领域的研究热点之一.分析已有多目标进化算法在保持种群多样性方面的不足并提出一种基于解空间划分的自适应多目标进化算法（space division basedadaptive multiobjective evolutionary algorithm,简称SDA-MOEA）来解决多目标优化问题.该方法首先将多目标优化问题的解空间划分为大量子空间,在算法进化过程中,每个子空间都保留一个非支配解集,以保证种群的多样性.另外,该方法根据每个子空间推进种群前进的距离,自适应地为每个子空间分配进化机会,以提高种群的进化速度.最后,利用3组共14个多目标优化问题检验SDA-MOEA的性能,并将SDA-MOEA与其他5个已有多目标进化算法进行对比分析.实验结果表明：在10个问题上,算法SDA-MOEA显著优于其他对比算法.     

Adaptive control Lyapunov function based model predictive control for continuous nonlinear systems

A design of adaptive model predictive control (MPC) based on adaptive control Lyapunov function (aCLF) is proposed in this article for nonlinear continuous systems with part of its dynamics being unknown at the starting time. Specifically, to guarantee the convergence of the closed-loop system with online predictive model updating, a stability constraint is designed. It limits the aCLF of the system under the MPC to be less than that under an online updated auxiliary adaptive control. The auxiliary adaptive control which implements in a sampling-hold fashion can guarantee the convergence of the controlled system. The sufficient conditions that guarantee the states to be steered to a small region near the equilibrium by the proposed MPC are provided. The calculation of the proposed algorithm does not depend on the model mismatch at the starting time. And it does not require the Lyapunov function of the state of the real system always to be reduced at each time. These provide the potential to improve the performance of the closed-loop system. The effectiveness of the proposed method is illustrated through a chemical process example.     

Tuning of PID controller based on a multiobjective genetic algorithm applied to a robotic manipulator

Most controllers optimization and design problems are multiobjective in nature, since they normally have several (possibly conflicting) objectives that must be satisfied at the same time. Instead of aiming at finding a single solution, the multiobjective optimization methods try to produce a set of good trade-off solutions from which the decision maker may select one. Several methods have been devised for solving multiobjective optimization problems in control systems field. Traditionally, classical optimization algorithms based on nonlinear programming or optimal control theories are applied to obtain the solution of such problems. The presence of multiple objectives in a problem usually gives rise to a set of optimal solutions, largely known as Pareto-optimal solutions. Recently, Multiobjective Evolutionary Algorithms (MOEAs) have been applied to control systems problems. Compared with mathematical programming, MOEAs are very suitable to solve multiobjective optimization problems, because they deal simultaneously with a set of solutions and find a number of Pareto optimal solutions in a single run of algorithm. Starting from a set of initial solutions, MOEAs use iteratively improving optimization techniques to find the optimal solutions. In every iterative progress, MOEAs favor population-based Pareto dominance as a measure of fitness. In the MOEAs context, the Non-dominated Sorting Genetic Algorithm (NSGA-II) has been successfully applied to solving many multiobjective problems. This paper presents the design and the tuning of two PID (Proportional–Integral–Derivative) controllers through the NSGA-II approach. Simulation numerical results of multivariable PID control and convergence of the NSGA-II is presented and discussed with application in a robotic manipulator of two-degree-of-freedom. The proposed optimization method based on NSGA-II offers an effective way to implement simple but robust solutions providing a good reference tracking performance in closed loop.     

Adaptive model predictive control for a class of constrained linear systems based on the comparison model

This paper proposes an adaptive model predictive control (MPC) algorithm for a class of constrained linear systems, which estimates system parameters on-line and produces the control input satisfying input/state constraints for possible parameter estimation errors. The key idea is to combine the robust MPC method based on the comparison model with an adaptive parameter estimation method suitable for MPC. To this end, first, a new parameter update method based on the moving horizon estimation is proposed, which allows to predict an estimation error bound over the prediction horizon. Second, an adaptive MPC algorithm is developed by combining the on-line parameter estimation with an MPC method based on the comparison model, suitably modified to cope with the time-varying case. This method guarantees feasibility and stability of the closed-loop system in the presence of state/input constraints. A numerical example is given to demonstrate its effectiveness.     

Robust explicit MPC based on approximate multiparametric convex programming

Many robust model predictive control (MPC) schemes require the online solution of a computationally demanding convex program. For deterministic MPC schemes, multiparametric programming was successfully applied to move offline most of the computation. In this paper, we adopt a general approximate multiparametric algorithm recently suggested for convex problems and propose to apply it to a classical robust MPC scheme. This approach enables one to implement a robust MPC controller in real time for systems with polytopic uncertainty, ensuring robust constraint satisfaction and robust convergence to a given bounded set.     

Online linearization-based neural predictive control of air–fuel ratio in SI engines with PID feedback correction scheme

Model predictive control (MPC) frequently uses online identification to overcome model mismatch. However, repeated online identification does not suit the real-time controller, due to its heavy computational burden. This work presents a computationally efficient constrained MPC scheme using nonlinear prediction and online linearization based on neural models for controlling air–fuel ratio of spark ignition engine to its stoichiometric value. The neural model for AFR identification has been trained offline. The model mismatch is taken care of by incorporating a PID feedback correction scheme. Quadratic programming using active set method has been applied for nonlinear optimization. The control scheme has been tested on mean value engine model simulations. It has been shown that neural predictive control with online linearization using PID feedback correction gives satisfactory performance and also adapts to the change in engine systems very quickly.     

Adaptive genetic algorithms applied to dynamic multiobjective problems

This paper describes an adaptive genetic algorithm (AGA) with dynamic fitness function for multiobjective problems (MOPs) in a dynamic environment. In order to see performance of the algorithm, AGA was applied to two kinds of MOPs. Firstly, the algorithm was used to find an optimal force allocation for a combat simulation. The paper discusses four objectives that need to be optimized and presents a fuzzy inference system that forms an aggregation of the four objectives. A second fuzzy inference system is used to control the crossover and mutation rates based on statistics of the aggregate fitness. In addition to dynamic force allocation optimization problem, a simple example of a dynamic multiobjective optimization problem taken from Farina et al. [M. Farina, K. Deb, P. Amato, Dynamic multiobjective optimization problems: test cases, approximations, and applications, IEEE Trans. Evol. Comput. 8 (5) (2004) 425–442] is presented and solved with the proposed algorithm. The results obtained here indicate that performance of the fuzzy-augmented GA is better than a standard GA method in terms of improvement of convergence to solutions of dynamic MOPs.     

RBF-ARX model-based MPC strategies with application to a water tank system

A hybrid pseudo-linear RBF-ARX model that combines Gaussian radial basis function (RBF) networks and linear ARX model structure is utilized for representing the dynamic behavior of a class of smooth nonlinear and non-stationary systems. This model is locally linear at each working point and globally nonlinear within whole working range. Based on the structural characteristics of the RBF-ARX model, three receding horizon predictive control (RBF-ARX-MPC) strategies are designed: (1) the RBF-ARX-MPC algorithm based on single-point linearization (MPC-SPL); (2) the RBF-ARX-MPC algorithm based on multi-point linearization (MPC-MPL); and (3) the RBF-ARX-MPC algorithm based on globally nonlinear optimization (MPC-GNO). In the MPC-SPL, the future multi-step-ahead predictive output of the system is obtained based on the local linearization of the RBF-ARX model at only current working-point, while in the MPC-MPL the future long-term output prediction is obtained according to the future local characteristics from previous online optimization results of the RBF-ARX model based MPC. In the MPC-GNO, the globally nonlinear characteristics of the RBF-ARX model are fully used for online getting control variables of the MPC. Real-time control experiments for the three type MPCs are carried out on a water tank system, which are also compared with a classical PID control and a traditional linear ARX model-based MPC. The results verify that the modeling method and the model-based predictive control strategies are realizable and effective for the nonlinear and unstable system. Moreover, it is also shown that the MPC-GNO can obtain better control performance but need more computation time compared to the other MPCs, which makes it possible to be applied into some slowly varying processes.     

Reconstruction of cylinder pressure for SI engine using recurrent neural network

Model predictive control (MPC) frequently uses online identification to overcome model mismatch. However, repeated online identification does not suit the real-time controller, due to its heavy computational burden. This work presents a computationally efficient constrained MPC scheme using nonlinear prediction and online linearization based on neural models for controlling air–fuel ratio of spark ignition engine to its stoichiometric value. The neural model for AFR identification has been trained offline. The model mismatch is taken care of by incorporating a PID feedback correction scheme. Quadratic programming using active set method has been applied for nonlinear optimization. The control scheme has been tested on mean value engine model simulations. It has been shown that neural predictive control with online linearization using PID feedback correction gives satisfactory performance and also adapts to the change in engine systems very quickly.     

Online set-point optimisation cooperating with predictive control of a yeast fermentation process: A neural network approach

Online set-point optimisation which cooperates with model predictive control (MPC) and its application to a yeast fermentation process are described. A computationally efficient multilayer control system structure with adaptive steady-state target optimisation (ASSTO) and a suboptimal MPC algorithm are presented in which two neural models of the process are used. For set-point optimisation, a steady-state neural model is linearised online and the set-point is calculated from a linear programming problem. For MPC, a dynamic neural model is linearised online and the control policy is calculated from a quadratic programming problem. In consequence of linearisation of neural models, the necessity of online nonlinear optimisation is eliminated. Results obtained in the proposed structure are comparable with those achieved in a computationally demanding structure with nonlinear optimisation used for set-point optimisation and MPC.     

三相脉宽调制整流器的约束预测控制

本文将基于并行神经网络优化的约束模型预测控制(MPC)应用于脉宽调制(PWM)整流器中,提高了电网的质量.在三相静止坐标系下,建立了三相PWM整流器的解耦数学模型,采用约束模型预测控制策略,突破了有限集和无约束条件下预测控制的局限性.为了提高单步优化的速度,采用神经网络优化算法求解模型预测控制的在线优化.在保证系统单位功率因数的前提下,当系统负载突然变化时,具有快速动态响应稳定输出直流电压的性能.采用FPGA控制器实现并行计算,减少了预测控制算法的计算时间.最后,通过仿真和实验结果得到,采用本文的控制策略,总谐波失真(THD)降低了2.5%,达到稳态的时间大约是PI控制算法的五分之一,为12 ms,验证了该方法的可行性和有效性.     

A model predictive control approach to the periodic implementation of the solutions of the optimal dynamic resource allocation problem

This paper proposes a model predictive control (MPC) approach to the periodic implementation of the optimal solutions of a class of resource allocation problems in which the allocation requirements and conditions repeat periodically over time. This special class of resource allocation problems includes many practical energy optimization problems such as load scheduling and generation dispatch. The convergence and robustness of the MPC algorithm is proved by invoking results from convex optimization. To illustrate the practical applications of the MPC algorithm, the energy optimization of a water pumping system is studied.     

GPU-based model predictive control for continuous casting spray cooling control system using particle swarm optimization

Model predictive control (MPC) for spray cooling control system requires a repeated online solution of an optimization problem that includes partial differential equations (PDEs). To simulate the future temperature behavior of steel billets, 3D dynamic heat transfer model is used. The special solution domain of PDEs has led to large computation cost, which is the main challenge in the real-time practical application of spray cooling control system. Meanwhile, the heat transfer coefficients need to be identified using the measured surface temperature. This work presents a two-level parallel solution method implemented on a Graphics processing unit (GPU) for MPC of spray cooling control systems and a weighted least squares modified conjugate gradient method (WLS–MCG) for identification of heat transfer coefficients. Two-level parallel solution method consists of parallel-based heat transfer model and stream parallel particle swarm optimization (PSO). PSO is used to solve the optimization problem. WLS–MCG consists of the weighted least squares (WLS) and modified conjugate gradient method (MCG). The experimental results show that the two-level parallel solution method has good computational performance and achieves satisfactory control performance.     

A novel adaptive fuzzy predictive control for hybrid systems with mixed inputs

This paper proposes a new adaptive nonlinear model predictive control (NMPC) methodology for a class of hybrid systems with mixed inputs. For this purpose, an online fuzzy identification approach is presented to recursively estimate an evolving Takagi–Sugeno (eTS) model for the hybrid systems based on a potential clustering scheme. A receding horizon adaptive NMPC is then devised on the basis of the online identified eTS fuzzy model. The nonlinear MPC optimization problem is solved by a genetic algorithm (GA). Diverse sets of test scenarios have been conducted to comparatively demonstrate the robust performance of the proposed adaptive NMPC methodology on the challenging start-up operation of a hybrid continuous stirred tank reactor (CSTR) benchmark problem.     

基于可达集的鲁棒模型预测控制

设计了一种基于可达集的鲁棒模型预测控制算法.首先确定了一个鲁棒不变集,并将此不变集用作模型预测控制的终端约束集;接着采用终端约束集对可达集的包含度作为优化指标;最后,采用预测时域逐渐减小的控制策略以保证在线优化存在可行解.从理论上证明了吸引域内的任意点在有限时域内都会被引导至终端约束集并始终停留在此集之内,并由仿真算例验证了本文所设计鲁棒模型预测控制算法的可行性.     

Analytical expression of explicit MPC solution via lattice piecewise-affine function

An analytical expression of the explicit solution to linear model predictive control (MPC) is proposed by the introduction of a lattice piecewise-affine (PWA) function. A systematic procedure is developed for building a lattice PWA representation from a continuous explicit MPC solution obtained by a multi-parametric program. A simple method is presented to remove the redundant parameters in the lattice expression of MPC control laws. The effectiveness of this approach is supported by the study of three benchmark MPC problems. The proposed analytical expression provides a very efficient and practically viable method for implementing the explicit MPC solutions regarding its online calculation and memory space requirements.     

Multiobjective optimization using population-based extremal optimization

In recent years, a general-purpose local-search heuristic method called Extremal Optimization (EO) has been successfully applied in some NP-hard combinatorial optimization problems. In this paper, we present a novel Pareto-based algorithm, which can be regarded as an extension of EO, to solve multiobjective optimization problems. The proposed method, called Multiobjective Population-based Extremal Optimization (MOPEO), is validated by using five benchmark functions and metrics taken from the standard literature on multiobjective evolutionary optimization. The experimental results demonstrate that MOPEO is competitive with the state-of-the-art multiobjective evolutionary algorithms. Thus MOPEO can be considered as a viable alternative to solve multiobjective optimization problems.