Papers by Adam Korytowski
Applicationes Mathematicae, 1977
Time optimal control of pendulum-cart system
We consider the synthesis of time optimal control which steers a pendulum hinged to a cart to a g... more We consider the synthesis of time optimal control which steers a pendulum hinged to a cart to a given state (e.g., the upright position), starting from arbitrary initial conditions. The control of the pendulum can system has attracted attention of many authors because of its relatively simple structure and at the same time, nontrivial nonlinearity. Various heuristic approaches combined with 1q stabilization in the vicinity of the target state were used to swing the pendulum up to the upright position and to keep it there. However, time-optimality was not achieved. We construct the time optimal control using a sequence of fixed horizon problems in which the norms of terminal states are minimized. The problems with fixed horizons are solved numerically by means of gradient optimization, with gradients determined from the solution of adjoint equations. Due to embedding the synthesis algorithms in the Matlab - Simulink environment, it is possible to track and visualize the control process as well as the results of simulation experiments.
Consistent Control Procedures in the Monotone Structural Evolution. Part 2: Examples and Computational Aspects
Springer eBooks, 2010
The consistent control procedures for state-constrained and interior arcs are implemented in the ... more The consistent control procedures for state-constrained and interior arcs are implemented in the MSE, and their performance demonstrated on numerical examples. For state constrained problems with index 1, a two-phase technique is proposed which ensures the exact fulfillment of the state constraint. To enhance efficiency of the method of prototype adjoints applied to consistent representation of interior control arcs, a new ‘freezing’ technique is used.
In this paper the method for optimal control of a fermentation process is presented, that is base... more In this paper the method for optimal control of a fermentation process is presented, that is based on an approach for optimal control-Neuro-dynamic programming. For this aim the approximation neural network is developed and the decision of the optimization problem is improved by an iteration mode founded on the Bellman equation. With this approach computing time and procedure are decreased and quality of the biomass at the end of the process is increased.
Applicationes Mathematicae, 1988
Optimal algorithms for seeking the minimum
Mathematica Applicanda, Dec 1, 1977
The definition of the optimality of an algorithm is modified so that the optimal algorithm satisf... more The definition of the optimality of an algorithm is modified so that the optimal algorithm satisfies Bellman's principle. The search for a minimum using this technique is compared with J. Kiefer's algorithm
On convergence of the Monotone Structural Evolution
Control and Cybernetics, 2016
Postan 3 - Extended Postoptimal Analysis Package for Minos
This paper is one of the series of 11 Working Papers presenting the software for interactive deci... more This paper is one of the series of 11 Working Papers presenting the software for interactive decision support and software tools for developing decision support systems. These products constitute the outcome of the contracted study agreement between the System and Decision Sciences Program at IIASA and several Polish scientific institutions. The theoretical part of these results is presented in the IIASA Working Paper WP-88-071 entitled "Theory, Software and Testing Examples in Decision Support Systems" which contains the theoretical and methodological backgrounds of the software systems developed within the project. This paper presents the POSTAN 3 package. This package constitutes the tool for postoptimal analysis for linear and linear-fractional programming problems. POSTAN consists of a number of FORTRAN routines which are incorporated into MINOS, the well known linear and nonlinear programming code developed at the Stanford University. The postoptimal analysis is perf...
This paper presents a new software package which has been developed in collaboration with IIASA T... more This paper presents a new software package which has been developed in collaboration with IIASA The new package, POSTAN, is designed for postoptimal analysis of linear programming problems, and is embedded in the well-known linear and nonlinear programming code MINOS. POSTAN is composed of a number of FORTRAN subroutines which may be called by adding some new keywords to the original list of MINOS specifications. The main function of POSTAN is to determine the ranges in which certain parameters may be changed without affecting the optimal solution and/or the optimal basis. In this paper the authors outline the general form of the linear programming problems studied, describe the six new subroutines in some detail, and illustrate this description with a printout obtained in the solution of a sample problem. The mathematical theory behind the software package is given in an Appendix.
Teoria sterowania. Materialy pomocnicze do 'cwicze'n laboratoryjnych
Games, 2021
An elementary approach to a class of optimal control problems with pathwise state constraint is p... more An elementary approach to a class of optimal control problems with pathwise state constraint is proposed. Based on spike variations of control, it yields simple proofs and constructive necessary conditions, including some new characterizations of optimal control. Two examples are discussed.
Advances in Mathematical Modeling, Optimization and Optimal Control
Springer Optimization and Its Applications, 2016
This book contains extended, in-depth presentations of the plenary talks from the 16th French-Ger... more This book contains extended, in-depth presentations of the plenary talks from the 16th French-German-Polish Conference on Optimization, held in Krakow, Poland in 2013. Each chapter in this book exhibits a comprehensive look at new theoretical and/or application-oriented results in mathematical modeling, optimization, and optimal control. Students and researchers involved in image processing, partial differential inclusions, shape optimization, or optimal control theory and its applications to medical and rehabilitation technology, will find this book valuable. The first chapter by Martin Burger provides an overview of recent developments related to Bregman distances, which is an important tool in inverse problems and image processing. The chapter by Piotr Kalita studies the operator version of a first order in time partial differential inclusion and its time discretization. In the chapter by Gunter Leugering, Jan Sokolowski and Antoni Żochowski, nonsmooth shape optimization problems for variational inequalities are considered. The next chapter, by Katja Mombaur is devoted to applications of optimal control and inverse optimal control in the field of medical and rehabilitation technology, in particular in human movement analysis, therapy and improvement by means of medical devices. The final chapter, by Nikolai Osmolovskii and Helmut Maurer provides a survey on no-gap second order optimality conditions in the calculus of variations and optimal control, and a discussion of their further development
Abstract. A mathematical model of the 3D crane with three control inputs is given. The time-optim... more Abstract. A mathematical model of the 3D crane with three control inputs is given. The time-optimal control problem is solved with the use of the variable control parameterization method. The implementation in a real laboratory model is presented.
Integral Performance Criteria for Time-Delay Systems with Applications
The paper presents a new, relatively simple proof of Pontryagin’s maximum principle for the canon... more The paper presents a new, relatively simple proof of Pontryagin’s maximum principle for the canonical problem of optimal control, with equality and inequality constraints imposed on the trajectory endpoints. The proof combines together two ideas, which appeared separately in the earlier works: application of the Karush-John conditions for finite-dimensional problems, and using packages of needle variations.
Mathematischen Kolloquium im Rahmen des Internationalen Doktorandenkollegs " Identifikation, Optimierung und Steuerung f¨
The Monotone Structural Evolution is a direct computational method of optimal control for ODE sys... more The Monotone Structural Evolution is a direct computational method of optimal control for ODE systems. Its distinctive feature is that the decision space undergoes evolution in a series of structural changes alternating with gradient optimization. This process reduces the discrepancy from the Maximum Principle conditions to a desired accuracy. The cost decreases monotonously. In typical cases and suciently equipped, the MSE detects optimal control structures and yields exact approximations of optimal solutions by adjusting a bounded number of parameters.
Variable Control Parameterization for Time-Optimal Problems 1 1This work was supported by Polish State Committee of Scientific Research under Grant 8 TI1A 018 18
IFAC Proceedings Volumes
ABSTRACT A gradient matching method for computing bang-bang time-optimal controls is described. A... more ABSTRACT A gradient matching method for computing bang-bang time-optimal controls is described. A horizon-depending auxiliary functional, parameterized by the horizon weighting factor, is minimized for an appropriately chosen sequence of the parameter values. Every iteration of quasi-Newton search for optimal switching times and horizon is preceded by a possible generation of new switchings and followed by a reduction of coinciding ones. The generations result from an analysis of the gradient of the auxiliary functional w.r.t. control. The algorithm normally converges to a local minimum in control space, and the auxiliary functional decreases monotonously during each stage of optimization with constant weighting parameter. An example of time-optimal control of a pendulum-cart system is solved.
Non-Existence of Adjoints on Singular Optimal Solutions with the Control in a State-Feedback Form
ABSTRACT
Analysis of a Class of Fermentation Models by Optimal Control Methods
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Papers by Adam Korytowski