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.     

Stochastic model predictive control: Insights and performance comparisons for linear systems

In this paper, we define several instances of model predictive control (MPC) for linear systems, including both deterministic and stochastic formulations. We show by explicit computation of the associated control laws that, under certain conditions, different formulations lead to identical results. This paper provides insights into the performance of stochastic MPC. Amongst other things, it shows that stochastic MPC and traditional MPC can give identical results in special cases. In cases where the solutions are different, we show that the explicit formulation of the problem can give insight into the performance gap.     

Chaotic differential evolution methods for dynamic economic dispatch with valve-point effects

The dynamic economic dispatch (DED), with the consideration of valve-point effects, is a complicated non-linear constrained optimization problem with non-smooth and non-convex characteristics. In this paper, three chaotic differential evolution (CDE) methods are proposed based on the Tent equation to solve DED problem with valve-point effects. In the proposed methods, chaotic sequences are applied to obtain the dynamic parameter settings in DE. Meanwhile, a chaotic local search (CLS) operation for solving DED problem is designed to help DE avoiding premature convergence effectively. Finally, in order to handle the complicated constraints with efficiency, new heuristic constraints handling methods and feasibility based selection strategy are embedded into the proposed CDE methods. The feasibility and effectiveness of the proposed CDE methods are demonstrated for two test systems. The simulation results reveal that, compared with DE and those other methods reported in literatures recently, the proposed CDE methods are capable of obtaining better quality solutions with higher efficiency.     

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.     

Dynamic economic load dispatch using hybrid swarm intelligence based harmony search algorithm

This paper presents the hybrid harmony search algorithm with swarm intelligence (HHS) to solve the dynamic economic load dispatch problem. Harmony Search (HS) is a recently developed derivative-free, meta-heuristic optimization algorithm, which draws inspiration from the musical process of searching for a perfect state of harmony. This work is an attempt to hybridize the HS algorithm with the powerful population based algorithm PSO for a better convergence of the proposed algorithm. The main aim of dynamic economic load dispatch problem is to find out the optimal generation schedule of the generators corresponding to the most economical operating point of the system over the considered timing horizon. The proposed algorithm also takes care of different constraints like power balance, ramp rate limits and generation limits by using penalty function method. Simulations were performed over various standard test systems with 5 units, 10 units and 30 units and a comparative study is carried out with other recently reported results. The findings affirmed the robustness and proficiency of the proposed methodology over other existing techniques.     

Reinforcement Learning Versus Model Predictive Control: A Comparison on a Power System Problem

This paper compares reinforcement learning (RL) with model predictive control (MPC) in a unified framework and reports experimental results of their application to the synthesis of a controller for a nonlinear and deterministic electrical power oscillations damping problem. Both families of methods are based on the formulation of the control problem as a discrete-time optimal control problem. The considered MPC approach exploits an analytical model of the system dynamics and cost function and computes open-loop policies by applying an interior-point solver to a minimization problem in which the system dynamics are represented by equality constraints. The considered RL approach infers in a model-free way closed-loop policies from a set of system trajectories and instantaneous cost values by solving a sequence of batch-mode supervised learning problems. The results obtained provide insight into the pros and cons of the two approaches and show that RL may certainly be competitive with MPC even in contexts where a good deterministic system model is available.      

城市煤气供应系统优化调度

本文提出城市煤气供应系统优化调度的两级算法。首先，根据分解－协调原理，提出求解中压分配系统优化调度问题的一种算法；其次推导出低压分配系统优化调度问题的解析解，并提出相应算法。实例计算表明，其结果比较满意。     

Model predictive control with robust feasibility

This paper presents a new model predictive control (MPC) method that provides robust feasibility with tractable, real-time computation. The method optimizes the closed-loop system dynamics, which involves models of the process (with parametric uncertainty) and controller at each step in the prediction horizon. Such problems are often formulated as a multi-stage stochastic program that suffers from the curse of dimensionality. This paper presents an alternative formulation that yields a bilevel stochastic optimization problem that is transformed by a series of reformulation steps into a tractable problem such that it can be solved through a limited number of second order cone programming sub-problems. The method addresses robust feasibility, manipulated saturation, state and output soft constraints, exogenous and endogenous uncertainty, and uncertainty in the state estimation in an integrated manner. Case study results demonstrate the advantages of the proposed robust MPC over nominal MPC and several other robust MPC formulations.     

Reserve-constrained multiarea environmental/economic dispatch based on particle swarm optimization with local search

The objective of economic dispatch (ED) is to minimize the total operational cost while satisfying the operational constraints of power systems. Multiarea economic dispatch (MAED) deals with the optimal power dispatch of multiple areas. In this investigation, multiarea environmental/economic dispatch (MAEED) is proposed to address the environmental issue during the ED. Its target is to dispatch the power among different areas by simultaneously minimizing the operational costs and pollutant emissions. In this paper, the MAEED problem is first formulated and then an improved multiobjective particle swarm optimization (MOPSO) algorithm is developed to derive a set of Pareto-optimal solutions. In the proposed version of MOPSO, local search is used to increase its search efficiency. To ensure the system security, tie-line transfer limits between different areas are incorporated as a set of constraints in the optimization process. Moreover, the reserve-sharing scheme is applied to ensure that each area is able to fulfill its reserve requirement. Numerical studies based on a four-area test power generation system are carried out to demonstrate the validity of the proposed optimization method as well as the results from different problem formulations. Comparative results with respect to other optimization methods are also presented.     

基于仿射控制输入的输入状态稳定非线性预测控制

针对有扰动的约束非线性系统,提出了一种基于仿射控制输入的反馈预测控制策略.采用无穷范数定义有限时域代价函数,对其进行极大极小优化得到预测控制律,并应用输入状态稳定分析了闭环系统的鲁棒稳定性,同时还给出了确定容许扰动上界的方法.最后,数值仿真说明本文的预测控制策略是有效的.     

Latent‐variable Nonlinear Model Predictive Control Strategy for a pH Neutralization Process

Linear model predictive control (MPC) is a widely‐used control strategy in chemical processes. Its extension to nonlinear MPC (NMPC) has drawn increasing attention since many process systems are inherently nonlinear. When implementing the NMPC based on a nonlinear predictive model, a nonlinear dynamic optimization problem must be calculated. For the sake of solving this optimization problem efficiently, a latent‐variable dynamic optimization approach is proposed. Two kinds of constraint formulations, original variable constraint and Hotelling T² statistic constraint, are also discussed. The proposed method is illustrated in a pH neutralization process. The results demonstrate that the latent‐variable dynamic optimization based the NMPC strategy is efficient and has good control performance.     

Symbiotic organisms search algorithm for dynamic economic dispatch with valve-point effects

Abstract

In this study, symbiotic organisms search (SOS) algorithm is proposed to solve the dynamic economic dispatch with valve-point effects problem, which is one of the most important problems of the modern power system. Some practical constraints like valve-point effects, ramp rate limits and prohibited operating zones have been considered as solutions. Proposed algorithm was tested on five different test cases in 5 units, 10 units and 13 units systems. The obtained results have been compared with other well-known metaheuristic methods reported before. Results show that proposed algorithm has a good convergence and produces better results than other methods.     

Water cycle algorithm-based economic dispatcher for sequential and simultaneous objectives including practical constraints

The article presents an efficient methodology based-on water cycle algorithm (WCA) to solve single and multiple objectives of economic load dispatch (ELD) aiming to generate the optimal value of the active generated power for each unit. Three objectives are adopted for optimisation either sequentially or concurrently; they are: (i) fuel cost considering valve-ripple effect, (ii) emission rate, and (iii) total network loss. The generating unit prohibited zones along with ramp rate limits and generating unit power limits specify the inequality constraints of the problem while maintaining system power balance. Usually, optimisation of simultaneous multiple objectives produces set of non-dominated Pareto-front solutions. To help the decision maker, the best compromise solution is carefully picked among optimal Pareto-front points. The proposed WCA-based methodology is demonstrated on three test cases with various complexities and under number of objective scenarios. Numerical results and further subsequent comparisons to other challenging optimisers indicate the viability and confirm the strength of the proposed WCA-based ELD method.     

Robust economic model predictive control based on a periodicity constraint

This paper proposes robust economic model predictive control based on a periodicity constraint for linear systems subject to unknown‐but‐bounded additive disturbances. In this economic MPC design, a periodic steady‐state trajectory is not required and thus assumed unknown, which precludes the use of enforcing terminal state constraints as in other standard economic formulations. Instead, based on the desired periodicity of system operation, we optimize the economic performance over a set of periodic trajectories that include the current state. To achieve robust constraint satisfaction, we use a tube‐based technique in the economic MPC formulation. The mismatches between the nominal model and the closed‐loop system with perturbations are limited using a local control law. With the proposed robust tube‐based strategy, recursive feasibility is guaranteed. Moreover, under a convexity assumption, the closed‐loop convergence of the closed‐loop system is analyzed, and an optimality certificate is provided to check if the closed‐loop trajectory reaches a neighborhood of the optimal nominal periodic steady trajectory using Karush‐Kuhn‐Tucker optimality conditions. Finally, through numerical examples, we show the effectiveness of the proposed approach.     

Uncertainty management in multiobjective hydro-thermal self-scheduling under emission considerations

In this paper, a stochastic multiobjective framework is proposed for a day-ahead short-term Hydro Thermal Self-Scheduling (HTSS) problem for joint energy and reserve markets. An efficient linear formulations are introduced in this paper to deal with the nonlinearity of original problem due to the dynamic ramp rate limits, prohibited operating zones, operating services of thermal plants, multi-head power discharge characteristics of hydro generating units and spillage of reservoirs. Besides, system uncertainties including the generating units’ contingencies and price uncertainty are explicitly considered in the stochastic market clearing scheme. For the stochastic modeling of probable multiobjective optimization scenarios, a lattice Monte Carlo simulation has been adopted to have a better coverage of the system uncertainty spectrum. Consequently, the resulting multiobjective optimization scenarios should concurrently optimize competing objective functions including GENeration COmpany's (GENCO's) profit maximization and thermal units’ emission minimization. Accordingly, the ɛ-constraint method is used to solve the multiobjective optimization problem and generate the Pareto set. Then, a fuzzy satisfying method is employed to choose the most preferred solution among all Pareto optimal solutions. The performance of the presented method is verified in different case studies. The results obtained from ɛ-constraint method is compared with those reported by weighted sum method, evolutionary programming-based interactive Fuzzy satisfying method, differential evolution, quantum-behaved particle swarm optimization and hybrid multi-objective cultural algorithm, verifying the superiority of the proposed approach.     

Lateral buckling analysis of beams by the fem

Two new finite element formulations for the calculation of the lateral buckling load for elastic straight prismatic thin-walled open beams under conservative static loads, are presented. The stability criterion used is based on the positive definiteness of the second variation of the total potential energy. One formulation is suitable for sections where the initial bending is about a dominant major axis. The other finite element formulation takes account of initial bending curvature and essentially takes the form of a quadratic eigenvalue problem. Both formulations are tested with problems that have classical solutions or experimentally determined results and are shown to be accurate.     

Online optimal tracking control of continuous-time linear systems with unknown dynamics by using adaptive dynamic programming

In this paper, a novel theoretic formulation based on adaptive dynamic programming (ADP) is developed to solve online the optimal tracking problem of the continuous-time linear system with unknown dynamics. First, the original system dynamics and the reference trajectory dynamics are transformed into an augmented system. Then, under the same performance index with the original system dynamics, an augmented algebraic Riccati equation is derived. Furthermore, the solutions for the optimal control problem of the augmented system are proven to be equal to the standard solutions for the optimal tracking problem of the original system dynamics. Moreover, a new online algorithm based on the ADP technique is presented to solve the optimal tracking problem of the linear system with unknown system dynamics. Finally, simulation results are given to verify the effectiveness of the theoretic results.     

Allocation of freeway ramp metering volumes to optimize corridor performance

A simple macroscopic freeway traffic corridor model is formulated for the purpose of developing optimal allocations of freeway on-ramp metering volumes. The model represents a freeway and a single parallel "equivalent surface street," both unidirectional, which are interconnected by freeway on-ramps. Since a choice of routes is included in the problem formulation, the fairly standard methodology of "traffic assignment" is employed to predict how drivers will react to the on-ramp metering. An explicit traffic assignment algorithm which includes ramp queueing is developed. Both the corridor and traffic assignment models are restricted to stationary traffic patterns. Two specific corridor performance criteria, freeway travel rate and total travel-time rate, are formulated in terms of the model variables. Then the problem of choosing ramp metering volumes to optimize a performance criterion is posed. A computationally efficient suboptimal dynamic programming scheme is developed and illustrated by an example.     

Predictive control of hybrid systems: Input-to-state stability results for sub-optimal solutions

This article presents a novel model predictive control (MPC) scheme that achieves input-to-state stabilization of constrained discontinuous nonlinear and hybrid systems. Input-to-state stability (ISS) is guaranteed when an optimal solution of the MPC optimization problem is attained. Special attention is paid to the effect that sub-optimal solutions have on ISS of the closed-loop system. This issue is of interest as firstly, the infimum of MPC optimization problems does not have to be attained and secondly, numerical solvers usually provide only sub-optimal solutions. An explicit relation is established between the deviation of the predictive control law from the optimum and the resulting deterioration of the ISS property of the closed-loop system. By imposing stronger conditions on the sub-optimal solutions, ISS can even be attained in this case.     

A hybrid differential evolution algorithm based on particle swarm optimization for nonconvex economic dispatch problems

This paper presents the design and application of an efficient hybrid heuristic search method to solve the practical economic dispatch problem considering many nonlinear characteristics of power generators, and their operational constraints, such as transmission losses, valve-point effects, multi-fuel options, prohibited operating zones, ramp rate limits and spinning reserve. These practical operation constraints which can usually be found at the same time in realistic power system operations make the economic load dispatch problem a nonsmooth optimization problem having complex and nonconvex features with heavy equality and inequality constraints.The proposed approach combines in the most effective way the properties of two of the most popular evolutionary optimization techniques now in use for power system optimization, the Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms. To improve the global optimization property of DE, the PSO procedure is integrated as additional mutation operator.The effectiveness of the proposed algorithm (termed DEPSO) is demonstrated by solving four kinds of ELD problems with nonsmooth and nonconvex solution spaces. The comparative results with some of the most recently published methods confirm the effectiveness of the proposed strategy to find accurate and feasible optimal solutions for practical ELD problems.