Seiichi Kawata

Genetic algorithms for optimal feedback control design

Abstract This paper presents a technique for optimal feedback control design which combines a relatively recent artificial intelligence (AI) method, the genetic algorithm (GA), and the more traditional methods of control system design, achieved via a new problem formulation. The performance function of a control system is generally formulated as a linear combination of xTQx and uTRu, where Q is the state weighting matrix and R is the control weighting matrix. These matrices are difficult to ascertain in real-world cases. The approach outlined here formulates the optimal feedback control design as a multiple-criteria problem, thereby avoiding use of the weighting matrices. It is shown that using the proposed problem formulation, a non-linear state feedback can also be implemented, which expands the search space for the design. A numerical example is computed to show the efficacy of such a method.

A teaching method using a self-organizing map for reinforcement learning

We described a new preteaching method for re-inforcement learning using a self-organizing map (SOM). The purpose is to increase the learning rate using a small amount of teaching data generated by a human expert. In our proposed method, the SOM is used to generate the initial teaching data for the reinforcement learning agent from a small amount of teaching data. The reinforcement learning function of the agent is initialized by using the teaching data generated by the SOM in order to increase the probability of selecting the optimal actions it estimates. Because the agent can get high rewards from the start of reinforcement learning, it is expected that the learning rate will increase. The results of a mobile robot simulation showed that the learning rate had increased even though the human expert had showed only a small amount of teaching data.

AI in Control System Design Using a New Paradigm for Design Representation

A new design representation paradigm different from traditional control system design is proposed. This representation of the control system design problem necessitates an Artificial Intelligence (AI) based search strategy to arrive at solutions. The search is performed by a multicriteria Genetic Algorithm (GA) to achieve Pareto optimal design solutions. The new design representation paradigm is used to implement both linear and non-linear state feedback. We also demonstrate with experimental results how non-linear state feedback expands the search space for the design. As an illustrative example an application of this new representation paradigm to control system design is presented.

A Multicriteria Approach to Control System Design with Genetic Algorithm

Abstract Design of optimal control system by use of a multicriteria genetic algorithm (GA) is presented. A new problem formulation and a new GA solution technique using the Pareto set concept is developed. The performance index of a linear control system is usually the time integral of the sum of quadratic forms x T Qx and u T Ru , where the choice of the weighting matrices Q and R are almost always heuristic in nature. Thus a re-formulation of the optimal control system design as a multicriteria optimization task is developed here which avoids use of Q and R . Design of the optimal control system is considered as a feedback search procedure where a new design solution is assigned a fitness value for the GA by a reference to the previously obtained Pareto optimal solution set. A numerical control design example and simulation results are presented.

Local coefficients of Walsh functions and their applications to model reference adaptive control

In the existing method of Walsh functions (WF), a major disadvantage is that the process signals need to be recorded prior to obtaining their Walsh spectral expansions. This paper proposes a novel method of local coefficients of WF to overcome this shortcoming. An approximate algorithm of local coefficients is developed. Several properties of local coefficients and error analysis of the method are also investigated. By introducing a new delay operational matrix, recursive integral equations based on the local coefficients of WF are formulated. Using the new method to deal with process signals, it is shown that an integral equation can be directly solved in recursion with process data by WF. This method has successfully been used to update controller parameters for model reference adaptive control of a first-order system.

The linear-quadratic-Gaussian control design using an improved product formula of Walsh functions

By using the Walsh functions an approximate solution is obtained for the linear-quadratic-Gaussian control design problem. An improved formula of Walsh functions is derived for giving a simple expression of products of two or more arbitrary matrix time functions. It is shown that the Riccati matrix equation can directly be solved with the improved formula. Calculation results are presented to illustrate the validity and applicability of this method.

Modelling and Sliding Mode Temperature Control of a Semi-Batch Polymerization Reactor Implemented at the Mixer

Abstract A detailed mathematical model of a semi-batch polymerization reactor is derived by considering the basic equations of reaction rate, mass and energy balances. Kinetic parameters and reactor operating conditions are obtained from experiments. Dynamic responses of reactor temperature, concentrations of monomer and polymer confirmed the justification of this model by comparing with experimental results. However, since this model is nonlinear and still has several unknown parameters, the sliding-mode control strategy is considered at the mixer. It is shown from computer simulation that this control system has excellent dynamic responses and robustness to parameter variations. Then, it is confirmed in the production reactor that this control strategy shows the effective responses and robustness.

Evolutionary Multicriteria Optimization for Improved Design of Optimal Control Systems

Design of optimal control systems has been traditionally based on minimization of a quadratic performance measure, which typically is an integral of a weighted linear combination of x T Qx and u T Ru. Choice of the linear weighting matrices Q and R based on heuristics and experiments are required to ascertain a satisfactory optimal value. In this paper we present a mathematical reformulation of the optimal control problem and restructure it with multiple performance indices instead of a single performance index. We thus reformulate the control system design as a multicriteria optimization problem. By reference to a Pareto set we assign a fitness values. We also show that this reformulation allows us to construct a nonlinear function of the state which we use as a feedback for the control. By use of this non-linear state feedback we demonstrate that the time response of the system, as it stabilizes, is considerably improved. Computer simulations and comparisons of linear and nonlinear state feedback convincingly demonstrates the effectiveness of such an approach.

Some Emergences of Mobiligence in the Pursuit Game

In this paper, we have proposed a realization of the mobiligence by constructing a pursuit game. The pursuit game has been used as a benchmark problem of a multi-agent system by many researchers. A “purpose-oriented Q-nets” is used for constructing the intelligence for mobile agents in this study. In the Q-nets, one evaluation function is to capture the prey and the other is to evaluate how the agents go back to the nest to charge energy. This configuration is designed to realize the self sufficiency of the hunter agents. The numerical experiments using Khepera Simulator well verifies that our proposed system shows some emergent behaviors of “mobiligence”.

Evaluation of errors in reduced order modeling

The purpose of the paper is to make a comparison between the equation errors and the output errors which are used as criteria for measuring modeling errors in system identification. In many practical situations real systems have high system orders which are often unknown, and reduced order models are used for estimating the parameters of the systems. In such a case there inevitably exists a modeling error due to the reduction of orders. The modeling error is usually evaluated by the equation error and the output error. The paper analyzes a relationship between these two errors in the case of an ARX model, and consequently derives that the variance of the output error is no less than that of the equation error. It also examines how the systems characteristics affect these two errors. For this purpose, it attempts to describe the estimated model parameters by the system parameters. The result shows that when the system poles are near the unit circle, which means a marginal stability of the system, the variance of the output error takes the maximum value.