Control Of Nonlinear Hybrid Systems Research Articles

Optimal Control of Nonlinear Hybrid Systems Driven by Signed Measures with Variable Intensities and Supports

In this paper we consider a class of nonlinear hybrid systems controlled by discrete signed measures. We develop a new technique to determine the optimal sizes and the optimal time instants for app...

Multiple-model based predictive control of nonlinear hybrid systems based on global optimization using the Bernstein polynomial approach

In this paper, we propose a Bernstein polynomial based global optimization algorithm for the optimal feedback control of nonlinear hybrid systems using a multiple-model approach. Specifically, we solve at every sampling instant a polynomial mixed-integer nonlinear programming problem arising in the model predictive control strategy. The proposed algorithm uses the Bernstein polynomial form in a branch-and-bound framework, with new ingredients such as branching for integer decision variables and fathoming for each subproblem in the branch-and-bound tree. The performance of the proposed algorithm is tested and compared with existing algorithms on a benchmark three-spherical tank system. The test results show the superior performance of the proposed algorithm.

A Computationally Efficient Scheme for Model Predictive Control of Nonlinear Hybrid Systems Using Generalized Outer Approximation

This paper presents an efficient optimization algorithm suitable for online solution of mixed integer nonlinear programs resulting from the model predictive control (MPC) of nonlinear hybrid systems. The system model is based on a recently proposed multiple partially linear (MPL) modeling scheme. The algorithm, based on generalized outer approximation (GOA), uses structural information of the canonical MPL framework as well as analytical expressions for the objective function and constraints of a relatively simple primal problem as well as the master problem. Specifically, the primal problem of GOA reduces to a quadratic program when MPL models are used in MPC. Computational efficiency of the algorithm over the branch and bound strategy is demonstrated using a simulated benchmark three-spherical tank system and a hydraulic process plant.

Predictive Control of Nonlinear Hybrid Systems Using Generalized Outer Approximation

This paper presents an efficient optimization algorithm for mixed integer nonlinear programming (MINLP) problem resulting from multiple partially linearized (MPL) model based control of nonlinear hybrid dynamical system (NHDS). The algorithm uses structural information of the canonical MPL framework and derives comparatively easier quadratic programming (QP) primal problem as well as an MILP master problem for generalized outer approximation (GOA) algorithm, a decomposition based solution strategy for MINLP. Computational efficiency of the algorithm over the branch and bound strategy is demonstrated using a simulated benchmark three-spherical tank system.

A multiple model approach for predictive control of nonlinear hybrid systems

This paper presents modeling and control of nonlinear hybrid systems using multiple linearized models. Each linearized model is a local representation of all locations of the hybrid system. These models are then combined using Bayes theorem to describe the nonlinear hybrid system. The multiple models, which consist of continuous as well as discrete variables, are used for synthesis of a model predictive control (MPC) law. The discrete-time equivalent of the model predicts the hybrid system behavior over the prediction horizon. The MPC formulation takes on a similar form as that used for control of a continuous variable system. Although implementation of the control law requires solution of an online mixed integer nonlinear program, the optimization problem has a fixed structure with certain computational advantages. We demonstrate performance and computational efficiency of the modeling and control scheme using simulations on a benchmark three-spherical tank system and a hydraulic process plant.

Costate prediction based optimal control for non-linear hybrid systems

This paper is derived for solving a non-linear discrete-continuous systems optimal control problem by iterating on a sequence of simplified problems in discrete form. A mixed approach with a discrete cost function and continuous state variable system description is used as the basis of the design, and it is shown how the global problem can be decomposed into local subsystem problems and a coordinator within a hierarchical framework. The correct optimal solution to a real system in which model-reality difference exists can be obtained from the system model by interconnected costate prediction iterative solution. The algorithm efficiency and convergence properties are demonstrated by simulation study.

Model predictive control of nonlinear hybrid systems with discrete inputs employing a hybrid fuzzy model

The paper deals with model predictive control (MPC) of nonlinear hybrid systems with discrete inputs based on reachability analysis. In order to implement a MPC algorithm, a model of the process that we are dealing with is needed. In the paper, a hybrid fuzzy modelling approach is proposed. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for hybrid fuzzy modelling purposes is tackled. An efficient method of identification of the hybrid fuzzy model is also discussed. An algorithm that is–due to its MPC nature–suitable for controlling a wide spectrum of systems (provided that they have discrete inputs only) is presented. The benefits of the algorithm employing a hybrid fuzzy model are verified on a batch reactor example. The results suggest that by suitably determining the cost function, satisfactory control can be attained, even when dealing with complex hybrid–nonlinear–stiff systems such as the batch reactor. Finally, a comparison between MPC employing a hybrid linear model and a hybrid fuzzy model is carried out. It has been established that the latter approach clearly outperforms the approach where a linear model is used.

An Extended Pontryagin Principle for Control Systems whose Control Laws Contain Measures

Previous article Next article An Extended Pontryagin Principle for Control Systems whose Control Laws Contain MeasuresRaymond W. RishelRaymond W. Rishelhttps://doi.org/10.1137/0303016PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. B. Barrar, An analytic proof that Hohman-type transfer is the true minimum two impulse transfer, Astronaut. Acta, 9 (1963), 1–11 Google Scholar[2] H. O. Ladd, Jr. and , B. Friedland, Minimum fuel control of a second order linear process with a constraint on time to run, Trans. ACME Ser. D., 86 (1964), 160–168 CrossrefGoogle Scholar[3] Paul R. Halmos, Measure Theory, D. Van Nostrand Company, Inc., New York, N. Y., 1950xi+304 MR0033869 0040.16802 CrossrefGoogle Scholar[4] D. F. Lawden, Optimal trajectories for space navigation, Butterworths, London, 1963viii+126 MR0199011 0111.19605 Google Scholar[5] E. B. Lee, A sufficient condition in the theory of optimal control, J. Soc. Indust. Appl. Math. Ser. A Control, 1 (1963), 241–245 MR0175693 0151.13105 LinkGoogle Scholar[6] Lucien W. Neustadt, Optimization, a moment problem, and nonlinear programming, J. Soc. Indust. Appl. Math. Ser. A Control, 2 (1964), 33–53 MR0174423 0133.36701 LinkGoogle Scholar[7] L. S. Pontryagin, , V. G. Boltyanskii, , R. V. Gamkrelidze and , E. F. Mishchenko, The mathematical theory of optimal processes, Translated from the Russian by K. N. Trirogoff; edited by L. W. Neustadt, Interscience Publishers John Wiley & Sons, Inc. New York-London, 1962viii+360 MR0166037 0102.32001 Google Scholar[8] W. W. Schmaedeke, Optimal control theory for nonlinear vector differential equations with measure coefficients, Report, U-RD 63 18, Minneapolis-Honeywell, 1963 Google Scholar[9] L. Ting, Optimal orbital transfer by several impulses, Astronaut. 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Warga18 July 2006 | Journal of the Society for Industrial and Applied Mathematics Series A Control, Vol. 3, No. 3AbstractPDF (1122 KB) Volume 3, Issue 2| 1965Journal of the Society for Industrial and Applied Mathematics Series A Control History Submitted:05 October 1964Accepted:21 December 1964Published online:18 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0303016Article page range:pp. 191-205ISSN (print):0887-4603ISSN (online):2168-359XPublisher:Society for Industrial and Applied Mathematics