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

Abstract: We investigate the possibility of using public firms to abate polluting emissions in a Cournot oligopoly where production takes place at constant returns to scale and entails a negative environmental externality. We model the problem as a differential game and investigate (i) the open-loop Nash equilibrium of the Cournot game among profit-seeking firms, showing that such equilibrium is strongly time consistent because firms neglect the externality; (ii) the feedback solution of social planning equilibrium where the industry output is entirely controlled by a benevolent planner aiming at the maximisation of social welfare; and (iii) a mixed setup where at least one firm is public (i.e., controlled by the social planner), while the others remain profit-seeking agents. Our analysis shows the conditions whereby having one public firm as a regulatory instrument suffices to drive the industry to the same levels of output, externality and ultimately also social welfare as under social planning. Intuitively, this is due to constant returns, under which the regulator needs no more than a single firm to compensate for the output distortion due to strategic interaction among Cournot firms.

Keywords: economic design,economic systems,optimal control

Identifier: 10.3182/20090506-3-SF-4003.00014

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: Östman, Fredrik; Pettersson, Frank; Toivonen, Hannu T.

Abstract: When designing a regulator for a specific system, a set of different objectives needs to be evaluated. This is usually done by manual tuning of parameters and evaluation of the step response. In recent years gradient-based multiobjective constraint optimization methods have been successfully applied on this problem while, in this report, a multiobjective genetic algorithm approach is applied. By defining a set of cost-functions in the frequency-domain for different frequency intervals, PID regulator settings for two bench-mark models are identified and successfully evaluated.

Keywords: regulator design,multiobjective optimizations,genetic algorithms

Identifier: 10.3182/20090506-3-SF-4003.00020

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: Ortner, P.; Gruenbacher, E.; Del Re, L.

Abstract: In this paper we discuss the problem of trajectory tracking of non control affine nonlinear systems. The main idea is to approximate the non control affine system by a special class of nonlinear systems, the so called extended Hammerstein systems (EHS). The control affine dynamic part of the EHS is computed such that an optimal control problem and therefore the robustifying feedback part of the tracking controller is already solved in the transformation process. Therefore no positive definite solution of the HJE needs to be computed since it gets a design parameter. The resulting system is then controlled by a trajectory tracking algorithm which ensures robustness against input disturbances and system uncertainties as well. A simulation example shows the efficiency of the proposed method.

Keywords: nonlinear control,nonlinear tracking,non control affine systems

Identifier: 10.3182/20090506-3-SF-4003.00004

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: Airimitoaie, Tudor-Bogdan; Popescu, Dumitru; Dimon, Catalin; Stamatescu, Grigore

Abstract: A new methodology for the design of control systems for real time applications is presented. It is proposed to have a first stage of assisted design of nominal systems with simulation based verification of the achieved performances. The control algorithm will then be improved by robustification to reproduce as good as possible the performances obtained in simulation on the real time process. Finally, a supervisor is implemented to optimize the thermo-energetic process and to compute the best choice for the reference signals.

Keywords: robustness,control system design,optimization,robust control,real time

Identifier: 10.3182/20090506-3-SF-4003.00006

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: Vanbiervliet, Joris; Michiels, Wim; Vandewalle, Stefan

Abstract: In this paper we propose two smooth optimization methods, one that can stabilize a system, and the other that can perform a stabilization as well as solve the optimal H2-norm design problem. For both methods, we make use of the smoothed spectral abscissa, a stabilization measure which originates from the inversion of an H2-norm type function, and that behaves as a smooth approximation of the spectral abscissa. In this way, we can set up an optimization framework in which a stabilizing point can efficiently be found. Taking advantage of its computation via Lyapunov equations, we derive computationally attractive formulae for the first-order and second-order derivatives of this smooth objective, which allows for the use of standard gradient- or Hessian-based optimization techniques. A second optimization framework, also involving the smoothed spectral abscissa, can be designed to deal with the H2-norm synthesis. This method has the advantage that it is not necessary to find a stable point for the system on beforehand, as the stabilization is done simultaneously with the actual minimization of the H2-norm. We apply the discussed methods to the class of systems with low-order, or fixed-order, feedback laws, where the number of controller parameters is smaller than the dimension of the plant.

Keywords: stabilization,optimal H2 controller design

Identifier: 10.3182/20090506-3-SF-4003.00005

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: Nikulin, Yury; Mäkelä, Marko M.

Abstract: A multicriteria boolean programming problem with linear cost functions in which initial coefficients of the cost functions are subject to perturbations is considered. For any optimal alternative, with respect to parameterized principle of optimality "from Condorcet to Pareto", an appropriate measure of the quality is introduced. This measure corresponds to the so-called stability function defined earlier for optimal solutions of a generic multicriteria combinatorial optimization problem with Pareto and lexicographic optimality principles. Various properties of such function are studied and maximum norm of perturbations for which an optimal solution preserves its optimality is calculated.

Keywords: condorcet optimality,Pareto set,stability,quality measure,parameterization,multicriteria optimization

Identifier: 10.3182/20090506-3-SF-4003.00060

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: Mazalov, Vladimir V.; Rettieva, Anna N.

Abstract: In this article a discrete-time game model related with the bioresource management problem (fish catching) is considered. The center (referee) shares a reservoir between the competitors. The players (countries) which harvest the fish stock are the participants of this game. We assume that there is a migratory exchange between the regions of reservoir. We derive the Nash and cooperative equilibrium for infinite planning horizon.We investigate the cooperative incentive equilibrium in the case when the center punishes players for a deviation from cooperative equilibrium. The numerical modelling and the results comparison are given.

Keywords: dynamic game,discrete-time game,fishery problems,incentive equilibrium

Identifier: 10.3182/20090506-3-SF-4003.00031

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: Subbotina, N.; Kolpakova, E.

Abstract: A generalization of the method of characteristics for Bellman equation is applied to solving optimal control problems with terminal cost functional. A new numerical method is suggested for constructing optimal open-loop controls. The method is based on the backward procedure of integrating the characteristic system ODE's. This method is tested in mechanical examples. Estimates of accuracy and results of simulations are exposed.

Keywords: Bellman equation,characteristic system,optimal open-loop controls

Identifier: 10.3182/20090506-3-SF-4003.00058

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: Diveev, Askhat I.; Sofronova, Elena A.

Abstract: The problem of synthesis of optimal control system is considered. It is proved that generally it is necessary to search for control as function of not only coordinates of space of conditions, but of velocities of changes of these coordinates. To solve the problem of synthesis it is offered to use the network operator that allows to present mathematical expression of functional dependence in the form of the directed graph. Properties of the network operator are given. For the search of optimal functional dependence on the set of network operators the genetic algorithm is used. The practical example of the solution of a problem of synthesis is given.

Keywords: optimal control synthesis,nonlinear control systems,network operator,genetic programming,principle of basic solution

Identifier: 10.3182/20090506-3-SF-4003.00043

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: Sinha, Ankur; Deb, Kalyanmoy

Abstract: A number of studies can be found in the context of bilevel single objective optimization problems, but not many exist, which tackle the bilevel multi-objective problems. Deb and Sinha (October, 2008) proposed a bilevel multi-objective optimization algorithm based on evolutionary multi-objective optimization (EMO) principles and discussed the issues involved in solving such a problem. In this paper we suggest an improved version of the previous algorithm which leads to high number of savings in function evaluations. Simulation results have been presented for two test problems and a comparison with the previous version has been done. The paper also discusses the complexity of bilevel problems and challenges involved in handling such problems. The existence of these problems in many practical problem solving tasks like optimal control, process optimization, game-playing strategy development, transportation problems, and others make it an important area which still needs to be considered by researchers. A two level optimization task involved in solving such problems makes the problem difficult and poses a number of challenges in getting close to the pareto front which has been addressed in the paper.

Keywords: multi-objective optimization and control,optimal control,optimization methods,applications in engineering,economics and management

Identifier: 10.3182/20090506-3-SF-4003.00062

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: Sandou, G.; Duc, G.

Abstract: Efficient dedicated methods have been developed for H∞.controller synthesis. However, such methods compute a full order controller which has often to be reduced to be implemented. Solving the reduced order H∞ problem is a hard task, as the corresponding optimization problem is non convex, due to rank constraints. In this paper, a particle swarm optimization method is used to solve such a problem. Experimental tests have been performed for a pendulum in the cart, showing much than satisfactory results. The computed controller is compared with a classical Hankel reduction of the full order H∞ controller, exhibiting a lower H∞ norm and a more robust behavior against measurement noise.

Keywords: robust control,H∞ optimization,reduced-order controllers,particle swarm optimization

Identifier: 10.3182/20090506-3-SF-4003.00009

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: Lukoyanov, Nikolay Yu.

Abstract: Control under disturbances or counteraction is considered for dynamical systems with both discrete and distributed delays. The problem is posed within the game-theoretic approach of N.N. Krasovskii and A.I. Subbotin in the class of strategies with memory. An appropriate functional Hamilton-Jacobi-Bellman-Isaacs equation with co-invariant derivatives is associated with the control problem. It is shown that the functional of optimal guaranteed result (the value functional) is a viscosity-type solution of this equation. The uniqueness of such a viscosity solution is proved.

Keywords: control theory,differential games,dynamic programming,delay,Hamilton-Jacobi equations,viscosity solutions

Identifier: 10.3182/20090506-3-SF-4003.00055

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: None

Abstract:

Keywords:

Identifier: 10.3182/20090506-3-SF-4003.90001

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