Authors: Martinon, P.; Bonnans, F.; Trelat, E.

Abstract: The scope of this work is trajectory optimization for space launcher problems, using Pontryagin's Minimum Principle and an indirect shooting method. Due to aerodynamic forces (drag), the considered problem may involve singular arcs, i.e. flight phases with a non maximal thrust. The chosen physical model uses tabulated data, which hinders the usual method of computing the singular control. We introduce an alternate, less problem dependent method for computing the singular control. Numerical experiments are carried out for several test problems and a typical Ariane 5 mission.

Keywords: space launcher,optimal control,indirect method,singular arcs

Identifier: 10.3182/20090506-3-SF-4003.00024

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Geletu, Abebe; Klöppel, Michael; Li, Pu; Hoffmann, Armin

Abstract: In this paper, a chance constrained nonlinear dynamic optimization problem is considered, which will be investigated by using a moving horizon scheme. In each horizon, the chance constraints will be written (transformed) in terms of those (input) random variables with known probability distributions by using monotonicity relations. Some definitions and properties related to the required monotonicity properties are introduced. For the application problem considered these monotonicity properties hold automatically true. The chance constraints and their gradients are evaluated by computing multivariate normal integrals using direct numerical integration. Numerical experimentation results will also be reported.

Keywords: chance constrained optimization,dynamic optimization,SQP,MPC,montonic relation,normal distribution,numerical integration

Identifier: 10.3182/20090506-3-SF-4003.00019

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Cardoso, Rodrigo T. N.; Takahashi, Ricardo H. C.; Cruz, Frederico R. B.; Fonseca, Carlos M.

Abstract: This paper proposes a multi-quantile approach for solving open-loop continuous-variable discrete-time stochastic dynamic programming problems in systems with non-standard probability distribution functions. Instead of using the expected value of the objective function for building the optimization criterion, the decision maker performs a choice on the decision variables over the objective function value quantiles. The proposed procedure relies on a Monte Carlo simulation of the unknown process input outcomes, associated with an open-loop multiobjective optimization. The optimal control comes from a trade-off analysis that considers, for instance, the risk associated with each policy versus its yield.

Keywords: stochastic dynamic programming,multiobjective optimization,model predictive control

Identifier: 10.3182/20090506-3-SF-4003.00010

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Chistyakov, Sergei; Nikitin, Fedor

Abstract: The theorem on the existence of the value for positional differential game of fixed duration is presented. A necessary and sufficient condition is formulated in terms of the fixed points of value operators. This theorem supplements the theorem on the existence and uniqueness of solution for a generalized Isaacs-Bellman equation.

Keywords: zero-sum differential game,programmed iteration method,value operators,value of game,positional strategies

Identifier: 10.3182/20090506-3-SF-4003.00038

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Kami, Yasushi; Nobuyama, Eitaku

Abstract: This paper deals with fixed-order controller design problems with output-feedback. It is well known that the control problems are difficult to be solved, because they become non-convex problems described by bilinear matrix inequality(BMI). In this paper, a new exterior-point approach to such BMI problems is proposed. This approach produces a controller sequence from a infeasible region to a feasible one. The advantage of this approach is that nonstabilizing controllers can be used as an initial controller. Numerical examples show the efficiency of our method.

Keywords: optimization based controller synthesis,exterior-point approach,fixed(reduced)-order controller synthesis

Identifier: 10.3182/20090506-3-SF-4003.00039

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Kleimenov, Anatolii F.; Osipov, Sergei I.; Kuvshinov, Dmitry R.

Abstract: The report evolves a method, which uses the formalization and results of positional antagonistic differential games theory, developed by N. N. Krasovskii and his scientific school, for constructing solutions of a class of non-antagonistic differential games. The method transforms non-antagonistic game into so-called non-standard optimal control problem. Numerical solutions for Stackelberg games are constructed by an algorithm developed by S. Osipov. Numerical Nash solution construction algorithm based upon auxiliary bimatrix games sequence is presented. Used computational geometry algorithms include convex hull construction, union and intersection of polygons and a Minkowski sum for polygons. Results of numerical experiment for a material point motion in plane are presented. The point is moved by force formed by two players. Every player has his personal target point. Among the obtained results, there is a Nash solution such that along the corresponding trajectory the position of the game is non-antagonistic, at first, and then becomes globally antagonistic starting from some moment of time.

Keywords: differential games,Stackelberg games,Nash games,trajectories,computing,algorithms

Identifier: 10.3182/20090506-3-SF-4003.00036

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Repin, Sergey I.

Abstract: We present new a posteriori error estimates for approximate solutions of optimal control problems. Our approach is based on so-called functional a posteriori error estimates that were derived in the last decade for many elliptic and parabolic boundary value problems. They provide guaranteed two-sided bounds of approximation errors for any conforming approximation of a problem considered. In the paper, we consider optimal control problems with distributed control functions that enter right-hand sides of elliptic type state equations and apply functional a posteriori estimates to approximate solutions of state equations. This procedure leads to guaranteed two-sided estimates for the cost functional and also allows to obtain guaranteed a posteriori estimates for state and control functions.

Keywords: a posteriori error estimates,elliptic boundary value problems,optimal control problems,guaranteed error bounds

Identifier: 10.3182/20090506-3-SF-4003.00016

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Mota, Alzira; Vaz, A. Ismael F.

Abstract: Semi-infinite programming (SIP) problems arise in several engineering areas such as, for example, robotic trajectory planning, production planning, digital filter design and air pollution control. In spite of being an active research area with many seminal works it lacks available software that could be used by the research community. The only exceptions are the fseminf MATLAB function, available in the Optimization Toolbox, and the NSIPS solver, but neither of them provide an implementation of a method belonging to the well known reduction type class. This paper proposes an implementation of a reduction type algorithm base on a penalty technique and provides a compare between several well known penalty functions. The provided numerical results with a significant number of SIP test problems are reported as performance profiles.

Keywords: semi-infinite programming,reduction type algorithm,particle swarm optimization,Penalty functions

Identifier: 10.3182/20090506-3-SF-4003.00008

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Akerblom, Markku; Hämäläinen, Timo; Pohjolainen, Seppo

Abstract: A simple and easy to use simulator, for linear time invariant exponentially stable infinite-dimensional systems with a self-tuning controller, is presented. The simulator is written in Matlab and allows one to to examine the robust regulation problem with a self-tuning controller described by the authors in an earlier paper.

Keywords: infinite-dimensional systems,adaptive control,robust control and stabilisation

Identifier: 10.3182/20090506-3-SF-4003.00040

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Lozovanu, Dmitrii; Pickl, Stefan

Abstract: In this article we extend classical deterministic control problems towards stochastic networks. A certain class of such stochastic discrete control problems with finite time horizon is introduced. Algorithms for solving the considered class of problems via the theory of Markov processes and dynamic programming are proposed. We apply the time-expanded network method and present complexity results of the constructive algorithm.

Keywords: stochastic discrete system,optimal control,dynamic programming

Identifier: 10.3182/20090506-3-SF-4003.00003

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Westermayer, Christian; Schirrer, Alexander; Hemedi, Mark; Kozek, Martin

Abstract: In a comprehensive control design approach for flexible mechanic structures, such as lightweight vehicles or aircraft, a vital decision is the positioning and design of actuators and sensors for the control tasks. This paper proposes an optimal placement approach that exploits the special structure of flexible mechanical systems and incorporates controllability/observability based measures as well as further knowledge on actuator and sensor properties. It combines the advantages of state of the art positioning criteria such that a balance between low and high frequency modes is assured and at the same time applicability to complex systems in arbitrary system coordinates is guaranteed. These essential properties are illustrated on a clamped beam. The controlled system is studied in terms of the generalized plant description, as it is common in robust control design. Thus it serves as natural extension to the controller design process later on and enables comprehensive control design optimization at an early stage.

Keywords: active control,robust control,optimal actuator placement,optimal sensor placement,modal system representation,vibration damping

Identifier: 10.3182/20090506-3-SF-4003.00021

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Lozovanu, Dmitrii; Pickl, Stefan

Abstract: Time-discrete systems with a finite set of states are considered. Discrete optimal control problems with infinite time horizon for such systems are formulated. We introduce a certain graph structure to model the transitions of the underlying dynamical system. Algorithms for finding the optimal stationary control parameters are presented: Furthermore we determine the optimal mean cost cycles. We elaborate this new intelligent technique in detail. The fractional linear programming representation can be regarded as an example for an intelligent optimization technique.

Keywords: discrete-time system,game-theory,optimization problem

Identifier: 10.3182/20090506-3-SF-4003.00051

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Cardoso, Rodrigo T. N.; Takahashi, Ricardo H. C.; Fonseca, Carlos M.

Abstract: This paper considers an open-loop continuous-variable dynamic programming approach, inspired in the model predictive control technique, which is shown to be computationally attractive, compared with the traditional dynamic programming algorithm, and more flexible than the closed-loop optimal control, working well with arbitrary constraints and objective functions. The extension of the method to the multiobjective case is shown to be straightforward. An example of dynamic cattle herd management policy is considered.

Keywords: dynamic Programming,model predictive control,multiobjective optimization

Identifier: 10.3182/20090506-3-SF-4003.00052

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Aho, M.; Bergman, S.; Hammarström, L.; Yli-Opas, K.; Pelkola, A.; Sourander, M.

Abstract: In this paper the requirements set by the modern petroleum oil and petrochemicals industry on dynamic real-time optimization (DRTO) and advanced process control (APC) applications are discussed. The modern processes in the hydrocarbon industry are large, complex and have challenging dynamics. They also produce a wide variety of products from a spectrum of different feedstocks. Some dynamic real-time optimization approaches used by the industry to tackle the characteristics of the processes as well as results attained are presented in the paper.

Keywords: dynamic real-time optimization,advanced process control,refinery processes

Identifier: 10.3182/20090506-3-SF-4003.00048

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Zaitsev, Vasili A.

Abstract: New necessary and sufficient conditions in the pole assignment problem are obtained for linear systems with incomplete feedback. The concept of consistency is brought in, which is generalization the concept of complete controllability to systems with incomplete feedback. The conditions are obtained under which the property of consistency is equivalent to global controllability of spectrum for systems with incomplete feedback.

Keywords: feedback control,pole assignment,stabilization

Identifier: 10.3182/20090506-3-SF-4003.00063

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Dumitrescu, Bogdan; Sicleru, Bogdan C.; Stefan, Radu

Abstract: The main goal of this paper is to investigate the stability of neutral systems, by using some features of the method introduced by Zhang et al. (2003) for the standard time-delay case. The central idea consists in replacing the delay by some appropriate Padé approximation, obtaining a (sufficient) delay-dependent stability condition for the neutral system. Such a condition can be rewritten as a positivity constraint on a two-variable matrix polynomial, leading to an effective computation of the delay margin by using sum-of-squares representations of multivariable positive matrix polynomials.

Keywords: neutral systems,Padé approximations,positive polynomials,sum-of-squares representations

Identifier: 10.3182/20090506-3-SF-4003.00034

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Lappi, Esa; Bruun, Risto; Jokinen, Kosti

Abstract: When simulating direct fire between units of different sizes in brigade-level combat simulations, there is often a need to automatically determine the ratios of fire directed at different possible targets. We construct a simple and effective rule for dividing fire between different targets, which takes into account the effects of different weapon systems on each other and the need to target not only the most valuable objectives, but also the enemy units which pose an immediate threat. The proposed model will be implemented in Sandis operation analysis tool.

Keywords: simulation,operations research,decision making,military operation analysis

Identifier: 10.3182/20090506-3-SF-4003.00045

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Allevi, Elisabetta; Gnudi, Adriana; Konnov, Igor V.

Abstract: Spatial equilibrium models are utilized for description of behavior and for management of complex systems containing many interacting elements, with taking into account their spatial distribution. We consider such a system of auction markets joined by transmission lines subject to joint balance and capacity flows constraints for a certain time period propose a primal-dual system of variational inequalities whose solutions yield an equilibrium trajectory of this system. A splitting type method is proposed to find a solution.

Keywords: spatial equilibrium model,system of auction markets,variational inequality problem,equilibrium trajectory

Identifier: 10.3182/20090506-3-SF-4003.00044

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Palokangas, Tapio

Abstract: This paper examines an economy with a large number of industries, each producing a different good. Technological change follows a Poisson process where firms improve their productivity through investment in R&D. The less there are firms in the economy or the more they can coordinate their actions, the higher their profits. Labor is used in production or R&D. All workers are unionized and their wages depend on relative union bargaining power. If this power is high enough, then there is involuntary unemployment. Both workers and firms lobby the central planner of the economy which affects firms' and unions' market power. The main findings of the paper can be summarized the follows. Unions' and firms' market power decreases the level of income at each moment of time. On the other hand, the greater the firm's share of value added or the higher union wages, more incentives the firm has to increase the productivity of labor through R&D. In this respect, there can be an optimal amount of unions' and firms' market power. Concerning the regulation of relative union bargaining power, the central planner can increase its welfare either (a) by increasing the level of income or (b) by speeding up economic growth. If (a) is more effective than (b), then the central planner eliminates union power altogether to have full employment. On the other hand, if (b) is more effective than (a), then the central planner supports labor unions to promote cost-escaping R&D.

Keywords: extensive game,maximum principle,stochastic dynamic programming,alternative offers game,common agency

Identifier: 10.3182/20090506-3-SF-4003.00011

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Alvarez, Felipe; Bolte, Jérôme; Bonnans, J. Frédéric; Silva, Francisco J.

Abstract: We consider a control constrained Linear Quadratic Optimal Control Problem and a general interior penalty, including the logarithmic penalty, parameterized by ε> 0. The purpose of this work is to find an error estimate for the difference between the optimal control solution uε of the penalized problem and the optimal solution u0 of the original problem. An application of the Implicit Function Theorem is not possible in this context. Although, we will be able to apply the so called Restoration Theorem to obtain the desired results.

Keywords: control constrained linear quadratic optimal control,control constraints,interior penalty,logarithmic penalty,error bounds

Identifier: 10.3182/20090506-3-SF-4003.00022

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Chentsov, A. G.; Shapar, Ju. V.

Abstract: The terminal game problem of control of the linear system with a discontinuity in coefficients under controlling influences and impulse constraints is considered. In the class of finitely additive measures with the property of the weak absolute continuity with respect to the restriction of the Lebesgue measure to some "sufficient" measurable structure, the generalized game problem of control is constructed.

Keywords: maximin,finitely additive measure,net,generalized control

Identifier: 10.3182/20090506-3-SF-4003.00035

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Laakkonen, Petteri; Pohjolainen, Seppo

Abstract: In this article various definitions and features of transmission zeros for finite-dimensional systems are represented. Then possibilities to generalize these definitions for infinite-dimensional systems are discussed.

Keywords: transfer function,transmission zeros,linear systems,local structures,regulation,finite-dimensional systems,infinite-dimensional systems

Identifier: 10.3182/20090506-3-SF-4003.00023

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Dragone, Davide; Lambertini, Luca; Leitmann, George; Palestini, Arsen

Abstract: We introduce the concept of Hamiltonian potential function for noncooperative openloop differential games and characterise necessary and sufficient conditions for its existence. We also identify a class of games admitting a Hamiltonian potential and illustrate appropriate examples pertaining to oligopoly games where price or quantity competition goes along with non-cooperative investments either in advertising or in R&D, so as to provide a plausible intuitive interpretation of the meaning of the Hamiltonian potential.

Keywords: differential games,game theory,optimal control

Identifier: 10.3182/20090506-3-SF-4003.00002

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Krasovskii, Andrey A.; Tarasyev, Alexander M.

Abstract: The paper deals with analysis of optimal control problems arising in models of economic growth. The Pontryagin maximum principle is applied for analysis of the optimal investment problem. Specifically, the research is based on existence results and necessary conditions of optimality in problems with infinite horizon. Properties of Hamiltonian systems are examined for different regimes of optimal control. The existence and uniqueness result is proved for a steady state of the Hamiltonian system. Analysis of properties of eigenvalues and eigenvectors is completed for the linearized system in a neighborhood of the steady state. Description of behavior of the nonlinear Hamiltonian system is provided on the basis of results of the qualitative theory of differential equations. This analysis allows us to outline proportions of the main economic factors and trends of optimal growth in the model. A numerical algorithm for construction of optimal trajectories of economic growth is elaborated on the basis of constructions of backward procedures and conjugation of an approximation linear dynamics with the nonlinear Hamiltonian dynamics. High order precision estimates are obtained for the proposed algorithm. These estimates establish connection between precision parameters in the phase space and precision parameters for functional indices.

Keywords: nonlinear control systems,numerical algorithms,precision measurements,economic design

Identifier: 10.3182/20090506-3-SF-4003.00013

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009

Authors: Jungers, Marc; Abou-Kandil, Hisham

Abstract: This paper studies Nash strategy for N-players discrete-time linear-quadratic games, in the framework of closed-loop memoryless information structure. Such a strategy being strongly time consistent, an original approach, based on step by step backward in time computation, is provided to facilitate the design of associated controls and value functions. It is shown that this matrix block formulation allows to recover the Coupled Riccati type Equations. An example illustrates this method.

Keywords: game theory,Nash strategy,closed loop information structure,coupled algebraic Riccati type equations

Identifier: 10.3182/20090506-3-SF-4003.00027

Conference: IFAC Workshop on Control Applications of Optimization (2009)

Location: University of Jyväskylä, Finland

Start Date: Wed May 06 2009 - End Date: Fri May 08 2009