A Game-Theoretic Approach For Multi-Loop Control System Design

A new approach is developed in the present thesis, to tune PI-Controllers in a Multi-loop Control System, regarding to certain control loop properties, constraints and requirements. Several control loops in a Multi-loop Control System interact to a greater or lesser extend, depending on the control loop structure. This behavior could yield to a degradation of one loop requirement due to an optimization of a second control loop in tuning it’s controllers according to another requirement. This is a conflict situation, which could not be avoided, but improved. A consideration of one or more requirements in a Multi-loop Control System is known as a multi-objective optimization problem. To solve such a kind of Multi-objective problem, a new approach is developed that supports finding a fair trade-off from the point of view of all requirements, criteria and each control loop of a Multi-loop Control System. The developed approach uses tools from game theory, which could be applied meaningfully, to describe and solve conflict situations as described within several control loop requirements and criteria. Assistant steps of the approach are that the conflict situation, respectively the Multi-objective optimization problem is structured and described as a game, first. The belonging requirements as well as constraints are formalized mathematically in the next step. Finally, game theory provides several solution concepts to calculate a fair trade-off, which is the solution to the game. In the wide research field of game theory, the structure of information plays a decisive role. This fact leads to a second application in the control theory of the developed approach. Using different information structures of a game, respectively a Multi-loop Control System, leads to a change of the players’ strategy sets. This has a bearing on the final solution of the game. Through this game-theoretic point of view, multiple Multi-loop Control System structures could be analyzed and compared for one and the same control theoretic problem

Index Information Algorithm with Local Tuning for Solving Multidimensional Global Optimization Problems with Multiextremal Constraints

Multidimensional optimization problems where the objective function and the constraints are multiextremal non-differentiable Lipschitz functions (with unknown Lipschitz constants) and the feasible region is a finite collection of robust nonconvex subregions are considered. Both the objective function and the constraints may be partially defined. To solve such problems an algorithm is proposed, that uses Peano space-filling curves and the index scheme to reduce the original problem to a H\"{o}lder one-dimensional one. Local tuning on the behaviour of the objective function and constraints is used during the work of the global optimization procedure in order to accelerate the search. The method neither uses penalty coefficients nor additional variables. Convergence conditions are established. Numerical experiments confirm the good performance of the technique.Comment: 29 pages, 5 figure

Analytical results for the multi-objective design of model-predictive control

In model-predictive control (MPC), achieving the best closed-loop performance under a given computational resource is the underlying design consideration. This paper analyzes the MPC design problem with control performance and required computational resource as competing design objectives. The proposed multi-objective design of MPC (MOD-MPC) approach extends current methods that treat control performance and the computational resource separately -- often with the latter as a fixed constraint -- which requires the implementation hardware to be known a priori. The proposed approach focuses on the tuning of structural MPC parameters, namely sampling time and prediction horizon length, to produce a set of optimal choices available to the practitioner. The posed design problem is then analyzed to reveal key properties, including smoothness of the design objectives and parameter bounds, and establish certain validated guarantees. Founded on these properties, necessary and sufficient conditions for an effective and efficient solver are presented, leading to a specialized multi-objective optimizer for the MOD-MPC being proposed. Finally, two real-world control problems are used to illustrate the results of the design approach and importance of the developed conditions for an effective solver of the MOD-MPC problem

Multi agent collaborative search based on Tchebycheff decomposition

This paper presents a novel formulation of Multi Agent Collaborative Search, for multi-objective optimization, based on Tchebycheff decomposition. A population of agents combines heuristics that aim at exploring the search space both globally (social moves) and in a neighborhood of each agent (individualistic moves). In this novel formulation the selection process is based on a combination of Tchebycheff scalarization and Pareto dominance. Furthermore, while in the previous implementation, social actions were applied to the whole population of agents and individualistic actions only to an elite sub-population, in this novel formulation this mechanism is inverted. The novel agent-based algorithm is tested at first on a standard benchmark of difficult problems and then on two specific problems in space trajectory design. Its performance is compared against a number of state-of-the-art multi objective optimization algorithms. The results demonstrate that this novel agent-based search has better performance with respect to its predecessor in a number of cases and converges better than the other state-of-the-art algorithms with a better spreading of the solutions