Feijun Song

A fuzzy logic controller design methodology for 4D systems with optimal global performance using enhanced cell state space based best estimate directed search method

Best estimate directed search (BEDS) is a generalized automatic nonlinear controller optimization technique. The cell state space based dynamic programming is a simple approach to generating a good estimate of the optimal control table (OCT) even for high order systems, thus can be used by BEDS to generate an initial best estimate control surface resulting in fast convergence rate. Therefore, it would be ideal to integrate OCT and BEDS into a single tool. Furthermore, due to physical memory limit, cell state space of high order systems often has low cell resolution, which may also contribute to the slow convergence of fuzzy logic controller optimization. This paper also proposed a scheme to control the spatial distribution of training data in order to expedite the optimization procedure with low cell resolution. The approaches were tested on a 4D inverted pendulum system and showed great promises. A linear quadratic regulator is also presented for comparison.

A comparison of sliding mode fuzzy controller and fuzzy sliding mode controller

Sliding mode control and fuzzy logic control have been combined together in a variety of ways. One approach taken by many researchers is to use fuzzy logic to smooth the chattering in sliding mode control. Another unusual approach taken by few researchers is to use sliding mode control in a fuzzy logic controller. This paper presents the details of both approaches and compares their respective properties. The paper concludes that the first approach has little technical value, if not totally useless, and the second approach is technically applicable.

Design Robust Nonlinear Controllers for Autonomous Underwater Vehicles with Comparison of Simulated and At-sea Test Data

Successful controller development involves three distinct stages, namely, control law design, code debugging and field test. For Autonomous Underwater Vehicle (AUV) applications, the first two stages require special strategies. Since the dynamics of an AUV is highly nonlinear, and the environment that an AUV operates in is noisy with external disturbance that cannot be neglected, a robust control law must be considered in the first stage. The control law design is even more difficult when optimal criteria are also involved. In the second stage, since the software architecture on an AUV is very complicated, debugging the controllers alone without all the software routines running together often can not reveal subtle faults in the controller code. Thorough debugging needs at-sea test, which is costly. Therefore, a platform that can help designers debug and evaluate controller performance before any at-sea experiment is highly desirable. Recently, a 6 Degree of Freedom (DOF) AUV simulation toolbox was developed for the Ocean Explorer (OEX) series AUVs developed at Florida Atlantic University. The simulation toolbox is an ideal platform for controller in-lab debugging and evaluation. This paper first presents a novel robust controller design methodology, named the Sliding Mode Fuzzy Controller (SMFC). It combines sliding mode control and fuzzy logic control to create a robust, easy on-line tunable controller structure. A formal proof of the robustness of the proposed nonlinear sliding mode control is also given. A pitch and a heading controller have been designed with the presented structure and the controller code was tested on the simulation software package as well as at sea. The simulated and at-sea test data are compared. The whole controller design procedure described in this paper clearly demonstrates the advantage of using the simulation toolbox to debug and test the controller in-lab. Moreover, the pitch and heading controller have been used in the real system for more than 2 years, and have also been successfully ported to other types of vehicles without any major modification on the controller parameters. The similarity of the controller performances on different vehicles further demonstrates the robustness of the proposed Sliding Mode Fuzzy Controller. The main contribution of this paper is to provide useful insights into the design and implementation of the proposed control architecture, and its application in AUV control.

Optimized fuzzy logic controller design for 4D systems using cell state space technique with reduced mapping error

This paper presents an optimized feedforward Takagi-Sugeno type fuzzy logic controller (FLC) design methodology for 4D systems. The method interpolates a cell space based optimal control table to generate optimal trajectories. A FLC is tuned using the sampling data from the optimal trajectories. In this way, the effect of cell mapping error in the FLC tuning is greatly reduced even with very low cell resolution. The optimized feedforward design is further combined with the best estimate directed search, a feedback iterative FLC optimization technique, to expedite the convergence of the optimization procedure. A 4D inverted pendulum case is simulated to justify the methodologies.

Combine Sliding Mode Control and Fuzzy Logic Control for Autonomous Underwater Vehicles

In this chapter, fuzzy sliding mode controllers and sliding mode fuzzy controllers were distinguished, and their respective properties were discussed. A sliding mode fuzzy controller inherits the interpolation property of fuzzy logic control and robustness property of sliding mode control, thereby making it ideal for time optimal robust control. The at-sea experimental data shows that sliding mode fuzzy control can be successfully applied to AUVs, thereby making them another alternative for the robust time optimal control problem. Moreover, since the physical meaning of the rule output function parameters for a sliding mode fuzzy controller is straightforward, the online tuning is made easy. This is exactly why sliding mode fuzzy control is adopted in AUV development at Florida Atlantic University.

How blind can a blind fuzzy logic controller design be? Analysis of cell state space based incremental best estimate directed search algorithm

Reports a discovery that has never been reported before on the global performance of Tskagi-Sugeno (TS) type fuzzy logic controller (FLC) with random rule output function parameters. We found that under certain cell resolutions, the chance that the performance of a random controller is comparable with that of a man made controller is very high. A cell state space based TS type FLC automatic parameter optimization algorithm named incremental best estimate directed search (IBEDS) is presented with a detailed analysis of its capability of designing a FLC totally without any expert knowledge. Initially, IBEDS was suggested to start with an initial training set sampled from the control surface of a FLC with poor performance. Then another random FLC is trained in an iterative procedure by a least mean square (LMS) algorithm. In each iteration, the global and local performance of the trained FLC is evaluated, the training set is then updated based on the evaluation. The initial value of the training set may need expert knowledge. However, with the discovery on random FLCs, IBEDS is found to be able to bootstrap with an empty training set, and still reach an optimal solution within a reasonable number of iterations. The mechanism behind this phenomenon is analyzed in detail with 2D and 4D inverted pendulums. It is shown that with IBEDS, a totally blind FLC design without any expert knowledge can be done efficiently.

Using least mean square learning error to improve Takagi-Sugeno type fuzzy logic controller optimization

An algorithm called Incremental Best Estimate Directed Search (IBEDS) was proposed for Takagi-Sugeno type fuzzy logic controller (FLC) automatic optimization. IBEDS starts with an initial training set that may be empty, an FLC with randomly initialized rule output parameters is trained by least mean square (LMS) learning algorithm in an iterative procedure. In each iteration, the trained FLC is evaluated with cell state space based global and local performance measures, the training set is then updated based on the evaluation under best kept policy, which only keeps the best control commands found so far. In this way, the training set is optimized in every iteration, and the FLC trained by the training set is also optimized progressively. The philosophy behind IBEDS is that the parameters of an FLC do not represent the performance of the controller directly although the goal of the optimization is to find an optimal controller parameter set so that the controller can have optimal global performance. However, the parameter set of an FLC with suboptimal performance may well represent a point in the parameter search space where the optimal one is nearby. Therefore the search algorithm should put more efforts in that area. LMS learning error is discarded in IBEDS as it does not represent the performance of the trained FLC either. This learning error can be reused when the training set is highly optimized and an exact approximation of the training set by an FLC is desired. To further speed up the optimization, in addition to suggesting the reuse of the LMS learning error, this paper also proposes to reuse the FLC parameter set during a search. A 4D inverted pendulum is studied, and the simulation results show that the search speed is improved.

Cell state space based incremental best estimate directed search algorithm for robust fuzzy logic controller optimization with multi-model concept

This paper presents a new version of cell state space based incremental best estimate directed search (IBEDS) algorithm with multi-model concept for robust Takagi-Sugeno type-fuzzy logic controller (FLC) automatic optimization. Typically, IBEDS starts with an initial training set, and a FLC with randomly initialized parameters is trained in an iterative procedure by least mean square algorithm. The optimized FLC may not be robust. This paper proposes a new version of IBEDS that can incorporate robustness information into the training set. First, several models are established to represent model uncertainty, parameter fluctuation, etc., then in each iteration of IBEDS, a trained FLC is evaluated on all models, the control commands with the worst local performance for all models will be used to update the training set. A 2D and a 4D inverted pendulums are studied. It is shown that with multi-model concept and IBEDS, computational design of robust FLC can be done efficiently even for high order systems.

A general cell state space based TS type fuzzy logic controller automatic rule extraction and parameter optimization algorithm

This paper presents a new cell state space based Takagi-Sugeno (TS) type fuzzy logic controller (FLC) automatic rule extraction and parameter optimization algorithm. A discrete optimal control table (OCT) is first generated under a predefined cost function. The rule base antecedents of a FLC can then be extracted from the OCT with fuzzy clustering techniques. The parameters of the rule output functions are optimized by a training data set in a novel iterative procedure through least mean square (LMS) training algorithm. The initial value of the training data set is the OCT. An OCT is generally very noisy, thus may not train a FLC very well. This is especially true for FLCs of high order systems. A new method is developed to exclude the undesirable control commands inside an OCT. In each parameter optimization iteration, the trained FLC is evaluated with cell state space-based global and local performance measures. The training data set is then updated based on the evaluation. In this way, the training set is optimized in every iteration, and the FLC trained by the set is also optimized progressively. Since the new method makes use of every FLC evaluated, a fast convergence speed is expected. A 4D inverted pendulum is studied to justify the algorithm The new approach is compared favorably with a linear quadratic regulator.

A Takagi-Sugeno type fuzzy logic controller with only 3 rules for a 4 dimensional inverted pendulum system

This paper presents a Takagi-Sugeno (TS) type Fuzzy Logic Controller (FLC) with only 3 rules for a 4 dimensional inverted pendulum system. This controller is able to control the system over a larger range of pole angle and cart positions compared with other control schemes. The rule antecedents of this controller are extracted from a cell state space based Optimal Control Table (OCT) by a subtractive clustering method and the rule output function parameters are optimized by an efficient search algorithm called Incremental Best Estimate Directed Search (IBEDS), which is also cell state space based. Simulation results demonstrate the usefulness of this 3 rule controller.