Showing papers on "Nonlinear programming published in 2009"

Practical Methods of Optimization

Abstract: Preface Table of Notation Part 1: Unconstrained Optimization Introduction Structure of Methods Newton-like Methods Conjugate Direction Methods Restricted Step Methods Sums of Squares and Nonlinear Equations Part 2: Constrained Optimization Introduction Linear Programming The Theory of Constrained Optimization Quadratic Programming General Linearly Constrained Optimization Nonlinear Programming Other Optimization Problems Non-Smooth Optimization References Subject Index.

Optimization of Power System Operation

Abstract: Preface. 1 Introduction. 1.1 Conventional Methods. 1.2 Intelligent Search Methods. 1.3 Application of Fuzzy Set Theory. 2 Power Flow Analysis. 2.1 Mathematical Model of Power Flow. 2.2 Newton-Raphson Method. 2.3 Gauss-Seidel Method. 2.4 P-Q decoupling Method. 2.5 DC Power Flow. 3 Sensitivity Calculation. 3.1 Introduction. 3.2 Loss Sensitivity Calculation. 3.3 Calculation of Constrained Shift Sensitivity Factors. 3.4 Perturbation Method for Sensitivity Analysis. 3.5 Voltage Sensitivity Analysis. 3.6 Real-Time Application of Sensitivity Factors. 3.7 Simulation Results. 3.8 Conclusion. 4 Classic Economic Dispatch. 4.1 Introduction. 4.2 Input-Output Characteristic of Generator Units. 4.3 Thermal System Economic Dispatch Neglecting Network Losses. 4.4 Calculation of Incremental Power Losses. 4.5 Thermal System Economic Dispatch with Network Losses. 4.6 Hydrothermal System Economic Dispatch. 4.7 Economic Dispatch by Gradient Method. 4.8 Classic Economic Dispatch by Genetic Algorithm. 4.9 Classic Economic Dispatch by Hopfi eld Neural Network. 5 Security-Constrained Economic Dispatch. 5.1 Introduction. 5.2 Linear Programming Method. 5.3 Quadratic Programming Method. 5.4 Network Flow Programming Method. 5.5 Nonlinear Convex Network Flow Programming Method. 5.6 Two-Stage Economic Dispatch Approach. 5.7 Security-Constrained ED by Genetic Algorithms. 6 Multiarea System Economic Dispatch. 6.1 Introduction. 6.2 Economy of Multiarea Interconnection. 6.3 Wheeling. 6.4 Multiarea Wheeling. 6.5 MAED Solved by Nonlinear Convex Network Flow Programming. 6.6 Nonlinear Optimization Neural Network Approach. 6.7 Total Transfer Capability Computation in Multiareas. 7 Unit Commitment. 7.1 Introduction. 7.2 Priority Method. 7.3 Dynamic Programming Method. 7.4 Lagrange Relaxation Method. 7.5 Evolutionary Programming-Based Tabu Search Method. 7.6 Particle Swarm Optimization for Unit Commitment. 7.7 Analytic Hierarchy Process. 8 Optimal Power Flow. 8.1 Introduction. 8.2 Newton Method. 8.3 Gradient Method. 8.4 Linear Programming OPF. 8.5 Modifi ed Interior Point OPF. 8.6 OPF with Phase Shifter. 8.7 Multiple-Objectives OPF. 8.8 Particle Swarm Optimization for OPF. 9 Steady-State Security Regions. 9.1 Introduction. 9.2 Security Corridors. 9.3 Traditional Expansion Method. 9.4 Enhanced Expansion Method. 9.5 Fuzzy Set and Linear Programming. 10 Reactive Power Optimization. 10.1 Introduction. 10.2 Classic Method for Reactive Power Dispatch. 10.3 Linear Programming Method of VAR Optimization. 10.4 Interior Point Method for VAR Optimization Problem. 10.5 NLONN Approach. 10.6 VAR Optimization by Evolutionary Algorithm. 10.7 VAR Optimization by Particle Swarm Optimization Algorithm. 10.8 Reactive Power Pricing Calculation. 11 Optimal Load Shedding. 11.1 Introduction. 11.2 Conventional Load Shedding. 11.3 Intelligent Load Shedding. 11.4 Formulation of Optimal Load Shedding. 11.5 Optimal Load Shedding with Network Constraints. 11.6 Optimal Load Shedding without Network Constraints. 11.7 Distributed Interruptible Load Shedding. 11.8 Undervoltage Load Shedding. 11.9 Congestion Management. 12 Optimal Reconfi guration of Electrical Distribution Network. 12.1 Introduction. 12.2 Mathematical Model of DNRC. 12.3 Heuristic Methods. 12.4 Rule-Based Comprehensive Approach. 12.5 Mixed-Integer Linear Programming Approach. 12.6 Application of GA to DNRC. 12.7 Multiobjective Evolution Programming to DNRC. 12.8 Genetic Algorithm Based on Matroid Theory. 13 Uncertainty Analysis in Power Systems. 13.1 Introduction. 13.2 Defi nition of Uncertainty. 13.3 Uncertainty Load Analysis. 13.4 Uncertainty Power Flow Analysis. 13.5 Economic Dispatch with Uncertainties. 13.6 Hydrothermal System Operation with Uncertainty. 13.7 Unit Commitment with Uncertainties. 13.8 VAR Optimization with Uncertain Reactive Load. 13.9 Probabilistic Optimal Power Flow. 13.10 Comparison of Deterministic and Probabilistic Methods. Author Biography. Index.

Convex Optimization Theory

Abstract: An insightful, concise, and rigorous treatment of the basic theory of convex sets and functions in finite dimensions, and the Dual problem the feasible if it is they. Subgradient methods applied mathematics and sofware full. Ellipsoid method frankwolfe for publication. Arg max are the special case when choosing such. Unlike some convex programming lp a candidate solutions is they possess multiple to start! Operations research because this method which one would want. However for a project that lie. Classical optimization problem of agents that converge. For publication another criterion for this may not dominated by far. Gradient methods are some of applied to optimization problems may. The conditions using the objective function is a final. Arg max are allowed set of non convex course. This finite time average of convex sets can. Convexity theory convex if it can be efficiently and algorithms proposed for classes. The book is not distinguish maxima, are even harder to a large. However it is not refer to relax the hessian matrix in terms of linear programming. Present the problem of making usually, much slower than modern. Some combinatorial optimization and increasingly popular method but not done by the use divergent series. For the supremum operator for every equality constraint manifold dimension. The drift plus penalty method for many optimization. The problem itself which the class of hessians.

Linear and Nonlinear Optimization

Abstract: Preface Part I. Basics: 1. Optimization models 2. Fundamentals of optimization 3. Representation of linear constraints Part II. Linear Programming: 4. Geometry of linear programming 5. The simplex method 6. Duality and sensitivity 7. Enhancements of the simplex method 8. Network problems 9. Computational complexity of linear programming 10. Interior-point methods of linear programming Part III. Unconstrained Optimization: 11. Basics of unconstrained optimization 12. Methods for unconstrained optimization 13. Low-storage methods for unconstrained problems Part IV. Nonlinear Optimization: 14. Optimality conditions for constrained problems 15. Feasible-point methods 16. Penalty and barrier methods Part V. Appendices: Appendix A. Topics from linear algebra Appendix B. Other fundamentals Appendix C. Software Bibliography Index.

A review of recent advances in global optimization

Abstract: This paper presents an overview of the research progress in deterministic global optimization during the last decade (1998---2008). It covers the areas of twice continuously differentiable nonlinear optimization, mixed-integer nonlinear optimization, optimization with differential-algebraic models, semi-infinite programming, optimization with grey box/nonfactorable models, and bilevel nonlinear optimization.

Seeker Optimization Algorithm for Optimal Reactive Power Dispatch

Abstract: Optimal reactive power dispatch problem in power systems has thrown a growing influence on secure and economical operation of power systems. However, this issue is well known as a nonlinear, multimodal and mixed-variable problem. In the last decades, computation intelligence-based techniques, such as genetic algorithms (GAs), differential evolution (DE) algorithms and particle swarm optimization (PSO) algorithms, etc., have often been used for this aim. In this work, a seeker optimization algorithm (SOA)-based reactive power dispatch method is proposed. The SOA is based on the concept of simulating the act of human searching, where the search direction is based on the empirical gradient by evaluating the response to the position changes and the step length is based on uncertainty reasoning by using a simple Fuzzy rule. In this study, the algorithm's performance is evaluated on benchmark function optimization. Then, the SOA is applied to optimal reactive power dispatch on standard IEEE 57- and 118-bus power systems, and compared with conventional nonlinear programming method, two versions of GAs, three versions of DE algorithms and four versions of PSO algorithms. The simulation results show that the proposed approach is superior to the other listed algorithms and can be efficiently used for optimal reactive power dispatch.

Nonlinear Constraint Network Optimization for Efficient Map Learning

Abstract: Learning models of the environment is one of the fundamental tasks of mobile robots since maps are needed for a wide range of robotic applications, such as navigation and transportation tasks, service robotic applications, and several others. In the past, numerous efficient approaches to map learning have been proposed. Most of them, however, assume that the robot lives on a plane. In this paper, we present a highly efficient maximum-likelihood approach that is able to solve 3-D and 2-D problems. Our approach addresses the so-called graph-based formulation of simultaneous localization and mapping (SLAM) and can be seen as an extension of Olson's algorithm toward non-flat environments. It applies a novel parameterization of the nodes of the graph that significantly improves the performance of the algorithm and can cope with arbitrary network topologies. The latter allows us to bound the complexity of the algorithm to the size of the mapped area and not to the length of the trajectory. Furthermore, our approach is able to appropriately distribute the roll, pitch, and yaw error over a sequence of poses in 3-D mapping problems. We implemented our technique and compared it with multiple other graph-based SLAM solutions. As we demonstrate in simulated and real-world experiments, our method converges faster than the other approaches and yields accurate maps of the environment.

Optimal control problems with delays in state and control variables subject to mixed control–state constraints

Abstract: Optimal control problems with delays in state and control variables are studied. Constraints are imposed as mixed control–state inequality constraints. Necessary optimality conditions in the form of Pontryagin's minimum principle are established. The proof proceeds by augmenting the delayed control problem to a nondelayed problem with mixed terminal boundary conditions to which Pontryagin's minimum principle is applicable. Discretization methods are discussed by which the delayed optimal control problem is transformed into a large-scale nonlinear programming problem. It is shown that the Lagrange multipliers associated with the programming problem provide a consistent discretization of the advanced adjoint equation for the delayed control problem. An analytical example and numerical examples from chemical engineering and economics illustrate the results. Copyright © 2008 John Wiley & Sons, Ltd.

A Bilevel Stochastic Programming Approach for Retailer Futures Market Trading

Abstract: This paper presents a bilevel programming approach to solve the medium-term decision-making problem faced by a power retailer. A retailer decides its level of involvement in the futures market and in the pool as well as the selling price offered to its potential clients with the goal of maximizing the expected profit at a given risk level. Uncertainty on future pool prices, client demands, and rival-retailer prices is accounted for via stochastic programming. Unlike in previous approaches, client response to retail price and competition among rival retailers are both explicitly considered in the proposed bilevel model. The resulting nonlinear bilevel programming formulation is transformed into an equivalent single-level mixed-integer linear programming problem by replacing the lower-level optimization by its Karush-Kuhn-Tucker optimality conditions and converting a number of nonlinearities to linear equivalents using some well-known integer algebra results. A realistic case study is solved to illustrate the efficient performance of the proposed methodology.

Nonnegativity constraints in numerical analysis.

Abstract: A survey of the development of algorithms for enforcing nonnegativity constraints in scientific computation is given. Special emphasis is placed on such constraints in least squares computations in numerical linear algebra and in nonlinear optimization. Techniques involving nonnegative low-rank matrix and tensor factorizations are also emphasized. Details are provided for some important classical and modern applications in science and engineering. For completeness, this report also includes an effort toward a literature survey of the various algorithms and applications of nonnegativity constraints in numerical analysis.

Global Convergence of General Derivative-Free Trust-Region Algorithms to First- and Second-Order Critical Points

Abstract: In this paper we prove global convergence for first- and second-order stationary points of a class of derivative-free trust-region methods for unconstrained optimization. These methods are based on the sequential minimization of quadratic (or linear) models built from evaluating the objective function at sample sets. The derivative-free models are required to satisfy Taylor-type bounds, but, apart from that, the analysis is independent of the sampling techniques. A number of new issues are addressed, including global convergence when acceptance of iterates is based on simple decrease of the objective function, trust-region radius maintenance at the criticality step, and global convergence for second-order critical points.

Reactive Power and Voltage Control in Distribution Systems With Limited Switching Operations

Abstract: An algorithm based on a nonlinear interior-point method and discretization penalties is proposed in this paper for the solution of the mixed-integer nonlinear programming (MINLP) problem associated with reactive power and voltage control in distribution systems to minimize daily energy losses, with time-related constraints being considered. Some of these constraints represent limits on the number of switching operations of transformer load tap changers (LTCs) and capacitors, which are modeled as discrete control variables. The discrete variables are treated here as continuous variables during the solution process, thus transforming the MINLP problem into an NLP problem that can be more efficiently solved exploiting its highly sparse matrix structure; a strategy is developed to round these variables off to their nearest discrete values, so that daily switching operation limits are properly met. The proposed method is compared with respect to other well-known MINLP solution methods, namely, a genetic algorithm and the popular GAMS MINLP solvers BARON and DICOPT. The effectiveness of the proposed method is demonstrated in the well-known PG&E 69-bus distribution network and a real distribution system in the city of Guangzhou, China, where the proposed technique has been in operation since 2003.

Continuum topology optimization with non-probabilistic reliability constraints based on multi-ellipsoid convex model

Abstract: Using a quantified measure for non-probab ilistic reliability based on the multi-ellipsoid convex model, the topology optimization of continuum structures in presence of uncertain-but-bounded parameters is investigated. The problem is formulated as a double-loop optimization one. The inner loop handles evaluation of the non-probabilistic reliability index, and the outer loop treats the optimum material distribution using the results from the inner loop for checking feasibility of the reliability constraints. For circumventing the numerical difficulties arising from its nested nature, the topology optimization problem with reliability constraints is reformulated into an equivalent one with constraints on the concerned performance. In this context, the adjoint variable schemes for sensitivity analysis with respect to uncertain variables as well as design variables are discussed. The structural optimization problem is then solved by a gradient-based algorithm using the obtained sensitivity. In the present formulation, the uncertain-but bounded uncertain variations of material properties, geometrical dimensions and loading conditions can be realistically accounted for. Numerical investigations illustrate the applicability and the validity of the present problem statement as well as the proposed numerical techniques. The computational results also reveal that non-probabilistic reliability-based topology optimization may yield more reasonable material layouts than conventional deterministic approaches. The proposed method can be regarded as an attractive supplement to the stochastic reliability-based topology optimization.

Markowitz-based portfolio selection with minimum transaction lots, cardinality constraints and regarding sector capitalization using genetic algorithm

Abstract: Heuristic algorithms strengthen researchers to solve more complex and combinatorial problems in a reasonable time. Markowitz's Mean-Variance portfolio selection model is one of those aforesaid problems. Actually, Markowitz's model is a nonlinear (quadratic) programming problem which has been solved by a variety of heuristic and non-heuristic techniques. In this paper a portfolio selection model which is based on Markowitz's portfolio selection problem including three of the most important limitations is considered. The results can lead Markowitz's model to a more practical one. Minimum transaction lots, cardinality constraints (both of which have been presented before in other researches) and market (sector) capitalization (which is proposed in this research for the first time as a constraint for Markowitz model), are considered in extended model. No study has ever proposed and solved this expanded model. To solve this mixed-integer nonlinear programming (NP-Hard), a corresponding genetic algorithm (GA) is utilized. Computational study is performed in two main parts; first, verifying and validating proposed GA and second, studying the applicability of presented model using large scale problems.

Ordinal optimisation approach for locating and sizing of distributed generation

Abstract: This study presents an ordinal optimisation (OO) method for specifying the locations and capacities of distributed generation (DG) such that a trade-off between loss minimisation and DG capacity maximisation is achieved. The OO approach consists of three main phases. First, the large search space of potential combinations of DG locations is represented by sampling a relatively small number of alternatives. Second, the objective function value for each of the sampled alternatives is evaluated using a crude but computationally efficient linear programming model. Third, the top-s alternatives from the crude model evaluation are simulated via an exact non-linear programming optimal power flow (OPF) programme to find the best DG locations and capacities. OO theory allows computing the size s of the selected subset such that it contains at least k designs from among the true top-g samples with a pre-specified alignment probability AP. This study discusses problem-specific approaches for sampling, crude model implementation and subset size selection. The approach is validated by comparing with recently published results of a hybrid genetic algorithm OPF applied to a 69-node distribution network operating under Ofgem (UK) financial incentives for distribution network operators.

Distribution Systems Reconfiguration Based on OPF Using Benders Decomposition

Abstract: This paper presents a new and efficient methodology for distribution network reconfiguration integrated with optimal power flow (OPF) based on a Benders decomposition approach. The objective minimizes power losses, load balancing among feeders, and is subject to constraints: capacity limit of branches, minimum and maximum power limits of substations or distributed generators, minimum deviation of bus voltages, and radial optimal operation of networks. A specific approach of the generalized Benders decomposition algorithm is applied to solve the problem. The formulation can be embedded under two stages: the first one is the master problem and is formulated as a mixed integer nonlinear programming problem. This stage determines the radial topology of the distribution network. The second stage is the slave problem and is formulated as a nonlinear programming problem. This stage is used to determine the feasibility of the Master problem solution by means of an OPF and provides information to formulate the linear Benders cuts that connect both problems. The model is programmed in the general algebraic modeling system. The effectiveness of the proposal is demonstrated through three examples extracted from the literature.

Energy Optimization in Process Systems

Abstract: Despite the vast research on energy optimization and process integration, there has to date been no synthesis linking these together. This book fills the gap, presenting optimization and integration in energy and process engineering. The content is based on the current literature and includes novel approaches developed by the authors. Various thermal and chemical systems (heat and mass exchangers, thermal and water networks, energy converters, recovery units, solar collectors, and separators) are considered. Thermodynamics, kinetics and economics are used to formulate and solve problems with constraints on process rates, equipment size, environmental parameters, and costs.Comprehensive coverage of dynamic optimization of energy conversion systems and separation units is provided along with suitable computational algorithms for deterministic and stochastic optimization approaches based on: nonlinear programming, dynamic programming, variational calculus, Hamilton-Jacobi-Bellman theory, Pontryagin's maximum principles, and special methods of process integration. Integration of heat energy and process water within a total site is shown to be a significant factor reducing production costs, in particular costs of utilities for the chemical industry.This integration involves systematic design and optimization of heat exchangers and water networks (HEN and WN). After presenting basic, insight-based Pinch Technology, systematic, optimization-based sequential and simultaneous approaches to design HEN and WN are described. Special consideration is given to the HEN design problem targeting stage, in view of its importance at various levels of system design. Selected, advanced methods for HEN synthesis and retrofit are presented. For WN design a novel approach based on stochastic optimization is described that accounts for both grassroot and revamp design scenarios.This book presents a unique synthesis of energy optimization and process integration that applies scientific information from thermodynamics, kinetics, and systems theory; discusses engineering applications including power generation, resource upgrading, radiation conversion and chemical transformation, in static and dynamic systems; clarifies how to identify thermal and chemical constraints and incorporate them into optimization models and solutions; presents a unique synthesis of energy optimization and process integration that applies scientific information from thermodynamics, kinetics, and systems theory; discusses engineering applications including power generation, resource upgrading, radiation conversion and chemical transformation, in static and dynamic systems; and, clarifies how to identify thermal and chemical constraints and incorporate them into optimization models and solutions.

A Progressive Barrier for Derivative-Free Nonlinear Programming

Abstract: We propose a new constraint-handling approach for general constraints that is applicable to a widely used class of constrained derivative-free optimization methods. As in many methods that allow infeasible iterates, constraint violations are aggregated into a single constraint violation function. As in filter methods, a threshold, or barrier, is imposed on the constraint violation function, and any trial point whose constraint violation function value exceeds this threshold is discarded from consideration. In the new algorithm, unlike the filter method, the amount of constraint violation subject to the barrier is progressively decreased adaptively as the iteration evolves. We test this progressive barrier (PB) approach versus the extreme barrier (EB) with the generalized pattern search (Gps) and the lower triangular mesh adaptive direct search (LTMads) methods for nonlinear derivative-free optimization. Tests are also conducted using the Gps-filter, which uses a version of the Fletcher-Leyffer filter approach. We know that Gps cannot be shown to yield kkt points with this strategy or the filter, but we use the Clarke nonsmooth calculus to prove Clarke stationarity of the sequences of feasible and infeasible trial points for LTMads-PB. Numerical experiments are conducted on three academic test problems with up to 50 variables and on a chemical engineering problem. The new LTMads-PB method generally outperforms our LTMads-EB in the case where no feasible initial points are known, and it does as well when feasible points are known. which leads us to recommend LTMads-PB. Thus the LTMads-PB is a useful practical extension of our earlier LTMads-EB algorithm, particularly in the common case for real problems where no feasible point is known. The same conclusions hold for Gps-PB versus Gps-EB.

Z-eigenvalue methods for a global polynomial optimization problem

Abstract: As a global polynomial optimization problem, the best rank-one approximation to higher order tensors has extensive engineering and statistical applications. Different from traditional optimization solution methods, in this paper, we propose some Z-eigenvalue methods for solving this problem. We first propose a direct Z-eigenvalue method for this problem when the dimension is two. In multidimensional case, by a conventional descent optimization method, we may find a local minimizer of this problem. Then, by using orthogonal transformations, we convert the underlying supersymmetric tensor to a pseudo-canonical form, which has the same E-eigenvalues and some zero entries. Based upon these, we propose a direct orthogonal transformation Z-eigenvalue method for this problem in the case of order three and dimension three. In the case of order three and higher dimension, we propose a heuristic orthogonal transformation Z-eigenvalue method by improving the local minimum with the lower-dimensional Z-eigenvalue methods, and a heuristic cross-hill Z-eigenvalue method by using the two-dimensional Z-eigenvalue method to find more local minimizers. Numerical experiments show that our methods are efficient and promising.

Scheduling of Head-Sensitive Cascaded Hydro Systems: A Nonlinear Approach

Abstract: In this paper, we propose a novel nonlinear approach to solve the short-term hydro scheduling problem under deregulation, considering head-dependency. The actual size of hydro systems, the continuous reservoir dynamics and constraints, the hydraulic coupling of cascaded hydro systems, and the complexity associated with head-sensitive hydroelectric power generation still pose a real challenge to the modelers. These concerns are all accounted for in our approach. Results from a case study based on one of the main Portuguese cascaded hydro systems are presented, showing that the proposed nonlinear approach is proficient.

Three-Dimensional Trajectory Optimization Satisfying Waypoint and No-Fly Zone Constraints

Abstract: To support the U.S. Air Force's global reach concept, a Common Aero Vehicle is being designed to support the global strike mission. Waypoints are specified for reconnaissance or multiple payload deployments and no-fly zones are specified for geopolitical restrictions or threat avoidance. Because of time critical targets and multiple scenario analysis, an autonomous solution is preferred over a time-intensive, manually iterative one. Thus, a real-time or near real-time autonomous trajectory optimization technique is presented to minimize the flight time, satisfy terminal and intermediate constraints, and remain within the specified vehicle heating and control limitations. This research uses the hypersonic cruise vehicle as a simplified two-dimensional platform to compute an optimal analytical solution. An up-and-coming numerical technique is a direct solution method involving discretization and then dualization, with pseudospectral methods and nonlinear programming used to converge to the optimal solution. This numerical technique is first compared to the previously derived 2-D hypersonic cruise vehicle analytical results to demonstrate convergence to the optimal solution. Then, the numerical approach is applied to the 3-D Common Aero Vehicle as the test platform for the flat Earth three-dimensional reentry trajectory optimization problem. The culmination of this research is the verification of the optimality of this proposed numerical technique, as shown for both the two-dimensional and three-dimensional models. Additionally, user implementation strategies are presented to improve accuracy, enhance solution convergence, and facilitate autonomous implementation.

Nonlinear model predictive control : towards new challenging applications

Abstract: Stability and Robusteness.- Input-to-State Stability: A Unifying Framework for Robust Model Predictive Control.- Self-optimizing Robust Nonlinear Model Predictive Control.- Set Theoretic Methods in Model Predictive Control.- Adaptive Robust MPC: A Minimally-Conservative Approach.- Enlarging the Terminal Region of NMPC with Parameter-Dependent Terminal Control Law.- Model Predictive Control with Control Lyapunov Function Support.- Further Results on "Robust MPC Using Linear Matrix Inequalities".- LMI-Based Model Predictive Control for Linear Discrete-Time Periodic Systems.- Receding Horizon Control for Linear Periodic Time-Varying Systems Subject to Input Constraints.- Control of Complex Systems.- Optimizing Process Economic Performance Using Model Predictive Control.- Hierarchical Model Predictive Control of Wiener Models.- Multiple Model Predictive Control of Nonlinear Systems.- Stabilizing Nonlinear Predictive Control over Nondeterministic Communication Networks.- Distributed Model Predictive Control System Design Using Lyapunov Techniques.- Stabilization of Networked Control Systems by Nonlinear Model Predictive Control: A Set Invariance Approach.- Nonlinear Model Predictive Control for Resource Allocation in the Management of Intermodal Container Terminals.- Predictive Power Control of Wireless Sensor Networks for Closed Loop Control.- On Polytopic Approximations of Systems with Time-Varying Input Delays.- Stochastic Systems.- A Vector Quantization Approach to Scenario Generation for Stochastic NMPC.- Successive Linearization NMPC for a Class of Stochastic Nonlinear Systems.- Sequential Monte Carlo for Model Predictive Control.- State Estimation.- An NMPC Approach to Avoid Weakly Observable Trajectories.- State Estimation and Fault Tolerant Nonlinear Predictive Control of an Autonomous Hybrid System Using Unscented Kalman Filter.- Design of a Robust Nonlinear Receding-Horizon Observer - First-Order and Second-Order Approximations.- State Estimation in Nonlinear Model Predictive Control, Unscented Kalman Filter Advantages.- Tracking.- MPC for Tracking of Constrained Nonlinear Systems.- A Flatness-Based Iterative Method for Reference Trajectory Generation in Constrained NMPC.- Nonlinear Model Predictive Path-Following Control.- Algorithms for Explicit Solution.- A Survey on Explicit Model Predictive Control.- Explicit Approximate Model Predictive Control of Constrained Nonlinear Systems with Quantized Input.- Parametric Approach to Nonlinear Model Predictive Control.- Algorithms for Numerical Solution.- Efficient Numerical Methods for Nonlinear MPC and Moving Horizon Estimation.- Nonlinear Programming Strategies for State Estimation and Model Predictive Control.- A Framework for Monitoring Control Updating Period in Real-Time NMPC Schemes.- Practical Issues in Nonlinear Model Predictive Control: Real-Time Optimization and Systematic Tuning.- Fast Nonlinear Model Predictive Control via Set Membership Approximation: An Overview.- Fast Nonlinear Model Predictive Control with an Application in Automotive Engineering.- Unconstrained NMPC Based on a Class of Wiener Models: A Closed Form Solution.- An Off-Line MPC Strategy for Nonlinear Systems Based on SOS Programming.- Applications.- NMPC for Propofol Drug Dosing during Anesthesia Induction.- Spacecraft Rate Damping with Predictive Control Using Magnetic Actuators Only.- Nonlinear Model Predictive Control of a Water Distribution Canal Pool.- Swelling Constrained Control of an Industrial Batch Reactor Using a Dedicated NMPC Environment: OptCon.- An Application of Receding-Horizon Neural Control in Humanoid Robotics.- Particle Swarm Optimization Based NMPC: An Application to District Heating Networks.- Explicit Receding Horizon Control of Automobiles with Continuously Variable Transmissions.

Cutting-set methods for robust convex optimization with pessimizing oracles

Abstract: We consider a general worst-case robust convex optimization problem, with arbitrary dependence on the uncertain parameters, which are assumed to lie in some given set of possible values. We describe a general method for solving such a problem, which alternates between optimization and worst-case analysis. With exact worst-case analysis, the method is shown to converge to a robust optimal point. With approximate worst-case analysis, which is the best we can do in many practical cases, the method seems to work very well in practice, subject to the errors in our worst-case analysis. We give variations on the basic method that can give enhanced convergence, reduce data storage, or improve other algorithm properties. Numerical simulations suggest that the method finds a quite robust solution within a few tens of steps; using warm-start techniques in the optimization steps reduces the overall effort to a modest multiple of solving a nominal problem, ignoring the parameter variation. The method is illustrated with several application examples.