Multi-objective Synthesis Problem Research Articles

The method of multi objective synthesis of stochastic robust control by multimass electromechanical systems under non-gausian random external disturbances

Aim. Development of the method of multi objective synthesis of stochastic robust control by multimass electromechanical systems to satisfy various requirements for the operation of such systems in various modes under non-gausian random external disturbances. Methodology. The problem of multi objective synthesis of stochastic robust control by multimass electromechanical systems to satisfy various requirements for the operation of such systems in various modes under non-gausian random external disturbances solved based on the choosing of weight matrices in the robust control goal vector.The calculation of the target vector is performed based on the solution of the zero-sum vector antagonistic game. The components of the game payoff vector are variable quality indicators that are applied to the system operation in various modes. The calculation of the components of payoff vector game are performed based on the simulation of the initial system closed by the synthesized stochastic controllers in various operating modes and under various external influences and variations in the parameters of the uncertainty of the initial plant. Results. The results of multi objective synthesis of stochastic robust two-mass electromechanical servo systems modes under non-gausian random external disturbances in which differences requirements for the operation of such systems in various modes were satisfied are given. Based on the results of modeling and experimental studies it is established, that with the help of synthesized robust nonlinear controllers, it is possible to improve of quality indicators of two-mass electromechanical servo system in comparison with the system with standard regulators. Originality. For the first time the method of multi objective synthesis of stochastic robust control by multimass electromechanical systems to satisfy various requirements for the operation of multimass systems in various modes is developed. Practical value. From the point of view of the practical implementation the possibility of solving the problem of multi objective synthesis of stochastic robust control systems to satisfy various requirements for the operation of multimass electromechanical systems in various modes is shown.

The method of multi objective synthesis of nonlinear robust control by multimass electromechanical systems

Aim. Development of the method of multi objective synthesis of nonlinear robust control by multimass electromechanical systems to satisfy various requirements for the operation of multi-mass systems in various modes. Methodology. The problem of multi objective synthesis of nonlinear robust control of multimass electromechanical systems is formulated and the possibility of satisfying various requirements for the operation of such systems in various modes based on the concept of functionally multiple membership of the state vector and the solution of the Hamilton-Jacobi-Isaacs equation is shown. A method for choosing weight matrices with the help the vector of purpose of nonlinear robust control is formed by solving a zero-sum vector antagonistic game has been substantiated and developed. Results. The results multi objective synthesis of nonlinear robust two-mass electromechanical servo systems in which differences requirements for the operation of such systems in various modes were satisfied are given. Based on the results of modeling and experimental studies it is established, that with the help of synthesized robust nonlinear controllers, it is possible to improve of quality indicators of two-mass electromechanical servo system in comparison with the system with standard regulators. Originality. For the first time the method of multi objective synthesis of nonlinear robust control by multimass electromechanical systems to satisfy various requirements for the operation of multimass systems in various modes is developed. Practical value. From the point of view of the practical implementation the possibility of solving the problem of multi objective synthesis of nonlinear robust control systems to satisfy various requirements for the operation of multimass electromechanical systems in various modes is shown.

Interval Markov Decision Processes with Multiple Objectives

Accurate Modelling of a real-world system with probabilistic behaviour is a difficult task. Sensor noise and statistical estimations, among other imprecisions, make the exact probability values impossible to obtain. In this article, we consider Interval Markov decision processes ( IMDP s), which generalise classical MDP s by having interval-valued transition probabilities. They provide a powerful modelling tool for probabilistic systems with an additional variation or uncertainty that prevents the knowledge of the exact transition probabilities. We investigate the problem of robust multi-objective synthesis for IMDP s and Pareto curve analysis of multi-objective queries on IMDP s. We study how to find a robust (randomised) strategy that satisfies multiple objectives involving rewards, reachability, and more general ω-regular properties against all possible resolutions of the transition probability uncertainties, as well as to generate an approximate Pareto curve providing an explicit view of the trade-offs between multiple objectives. We show that the multi-objective synthesis problem is PSPACE -hard and provide a value iteration-based decision algorithm to approximate the Pareto set of achievable points. We finally demonstrate the practical effectiveness of our proposed approaches by applying them on several case studies using a prototype tool.

PARETO OPTIMAL SOLUTION OF MULTIOBJECTIVE SYNTHESIS OF ROBUST CONTROLLERS OF MULTIMASS ELECTROMECHANICAL SYSTEMS BASED ON MULTISWARM STOCHASTIC MULTIAGENT OPTIMIZATION

Purpose. Developed the method for solving the problem of multiobjective synthesis of robust control by multimass electromechanical systems based on the construction of the Pareto optimal solutions using multiswarm stochastic multi-agent optimization of particles swarm, which reduces the time of determining the parameters of robust controls multimass electromechanical systems and satisfy a variety of requirements that apply to the work of such systems in different modes. Methodology. Multiobjective synthesis of robust control of multimass electromechanical systems is reduced to the solution of solving the problem of multiobjective optimization. To correct the above problem solving multiobjective optimization in addition to the vector optimization criteria and constraints must also be aware of the binary preference relations of local solutions against each other. The basis for such a formal approach is to build areas of Pareto-optimal solutions. This approach can significantly narrow down the range of possible solutions of the problem of optimal initial multiobjective optimization and, consequently, reduce the complexity of the person making the decision on the selection of a single version of the optimal solution. Results . The results of the synthesis of multi-criteria electromechanical servo system and a comparison of dynamic characteristics, and it is shown that the use of synthesized robust controllers reduced the error guidance working mechanism and reduced the system sensitivity to changes in the control parameters of the object compared to the existing system with standard controls. Originality. For the first time, based on the construction of the Pareto optimal solutions using a multiswarm stochastic multi-agent optimization particle algorithms improved method for solving formulated multiobjective multiextremal nonlinear programming problem with constraints, to which the problem of multiobjective synthesis of robust controls by multimass electromechanical systems that can significantly reduce the time to solve problems and meet a variety of requirements that apply to the multimass electromechanical systems in different modes. Practical value. Practical recommendations on reasonable selection of the target vector of robust control by multimass electromechanical systems. Results of synthesis of electromechanical servo system shown that the use of synthesized robust controllers reduced the error guidance of working mechanism and reduce the system sensitivity to changes of plant parameters compared to a system with standard controls.

Challenges and opportunities in integration of design and control

Process synthesis and design of plant operation are related topics but current industrial practice solves these problems sequentially. The implication of this sequential strategy may result in design of processing systems which are very hard to control. This paper presents a discussion on drivers for an integrated approach and outlines the challenges in formulation of such a multi-objective synthesis problem. This discussion is viewed in relation to some of the changing trends in the industry. Significant results have been published which in different ways seek to handle the integrated problem. Further, advancements in control algorithms and software have widened the range of feasible operation and control for strongly interconnected production systems. In light of these advances in different areas of the field, recommendations for further research and initiatives for development of an integrated approach are given with focus on how new results on the short term can improve industrial practice.

MULTI-OBJECTIVE SYNTHESIS OF CONFLICT-FREE AIRCRAFT TRAJECTORIES

The problem of multi-objective synthesis of trajectories for aircraft conflict resolution is considered. The optimality criteria that characterize the efficiency of conflict resolution are regularity of flights, economy of flights and maneuvers complexity. Resolution of the potential conflict considered as the sequential multistage decision-making process in discrete time and the maneuvering aircraft considered as the discrete dynamic system. The method of sequential conflict-free space-time trajectories synthesis using multi-objective dynamic programming was developed. The functional equations of bottom-up and top-down multi-objective dynamic programming procedures for determining the set of Pareto-efficient estimations of conflict-flight trajectories are shown. The procedure for selection of the optimal trajectory from the set of Pareto-efficient based on method of criteria convolution is defined.

Multiobjective Synthesis of Antenna Arrays Using a Vector Tabu Search Algorithm

To address fully multiobjective synthesis problems in antenna engineering, a vector tabu search algorithm is proposed to produce a good distribution of the searched Pareto solutions to successfully optimize a completely nonuniform 19-element linear antenna array.

Etat de l'art sur le problème de synthèse multi-objectif H2/H∞, le retour d'état

The goal of this article is to give a clear and comprehensive overview of the numerous studies concerning the multiobjective H 2 /H ∞ synthesis problem for continuous-time linear time-invariant systems. First, the more general problem as well as the possible variations and the associated assumptions are exposed. Then, the known analytical results lead naturally to define the multiobjective fixed-order synthesis problem. In this first part, only the state-feedback case is presented. Even for this simple case, no closed-form solution for the multiobjective synthesis problem can be found except in some particular cases. The approaches developed in the literature attempt therefore to get suboptimal solutions approximating the genuine optimal solution via more or less conservative convex relaxations. All the different frameworks (ranging from entropy maximization and game theory to Lyapunov theory and semidefinite programming) are dealt with. In almost every case, a very simple academic « by hand » numerical example is proposed.

Multi-objective H2/H∞/Impulse-to-Peak Control of a Space Launch Vehicle

A multi-objective synthesis problem involving H 2 , H ∞ and impulse-to-peak performances is investigated. In general, multi-objective control problems are hard problems to solve and do not have exact solutions. Here, an LMI formulation is proposed for the mixed H 2 /impulse-to-peak optimization under an H ∞ constraint for LTI discrete-time systems. This framework is then used to control the attitude of a space launcher. A particular control structure is defined and a multiobjective H 2 / H ∞ /impulse-to-peak synthesis problem is solved to tackle specific specifications. A systematic synthesis procedure including the tuning of design parameters is defined and results from simulations are presented.

Robust Impulse-to-Peak Synthesis: Application to the Control of an Aerospace Launcher

A multiobjective synthesis problem involving H2, Hoo and impulse-to-peak performances is investigated. In general, multiobjective control problems are hard problems to solve and do not have exact solutions. Here, an LMI formulation is proposed for the mixed H2/impulse-to-peak optimization under an Hoo constraint for LTI discrete-time systems. This framework is then used to control the attitude of a space launcher. A particular control structure is defined and a multiobjective H2/H∞/impulse-to-peak synthesis problem is solved to tackle specific specifications.

A mixed norm performance measure for the design of multirate filterbanks

A mixed norm performance measure is presented to design the synthesis filters of a multirate filterbank. The mixed norm performance measure is based on the energy as well as the peak value of the error signal. Mathematically, the performance measure minimizes the l/sub 2/-norm of the error signal subject to the l/sub /spl infin//-norm of the error being bounded by some positive value v (this imposes a bound on the peak value of the error signal). The design problem is shown to be that of a mixed /spl Hscr//sub 2///spl Hscr//sub /spl infin// optimization problem. The theory of linear matrix inequalities (LMIs) offers a tractable solution to such multiobjective synthesis problems. The synthesis filters designed with the new performance measure are compared with those obtained by similar induced norm minimization techniques in terms of degree of reconstruction, order of the synthesis filters, SNR, and aliasing distortion.