As learning enabled cyber physical systems become more prolific, modeling for the purposes of verification and validation (V&V) becomes a primary barrier. A key challenge is to model cyber physical systems at the appropriate level of abstraction while maintaining a clear and understandable linkage between the human designer and the system under design. Fuzzy logic is a framework to synthesize linguistic, natural language requirements into machine learning models. It has been shown that fuzzy logic is a suitable method to learn the behavior of a nonlinear system when a model is not present. The implementation of a constrained fuzzy inference system presented in this paper is a specific class of machine learning architecture that provides a mechanism to relate a system model to human specified requirements. It is not at all dissimilar to more popular neural network architectures. The goal of this paper is to introduce a framework for constrained learning that enables both fast approximation of real valued systems while simultaneously enabling the modeling and analysis of safety properties. This paper focuses on a foundational constrained intelligent learning framework. The framework describes an alternative and constrained machine learning architecture capable of producing highly efficient structures that are also amenable to verification. This paper will focus on the efficiency of the computational structure while future papers will demonstrate the verifiability.

As of late, hierarchical Fuzzy Inference Systems (hFIS) have received considerable attention because of their ability to control complex decision-making procedures. Although the performance of hFISs appears to be extremely effective in complex scenarios, there is a question about the differences between the hierarchical and single FISs (sFIS) and the relationship between the two. In this work, a transformation is derived which converts a Mamdani type hFIS into its equivalent sFIS representation. This is accomplished by equating their output membership functions. The equivalency between the outputs of the two representations is proven using a Satisfiability Modulo Theories (SMT) solver approach. Furthermore, we provide a detailed development procedure and results are presented which demonstrate the ease of implementation of the transformation as well as a wide applicability to meaningful large-scale problems.

This paper presents a controller integrity monitoring method for a class of second-order nonlinear uncertain systems incorporating neural network-based adaptive control algorithms. The adaptive neural network model is employed to ensure robust tracking performance in the presence of certain modeling uncertainty under consideration during the offline controller design process. Based on Lyapunov stability analysis, an online controller integrity monitoring scheme is developed to detect the occurrence of controller software/algorithm faults and unanticipated physical component faults, which may lead to unstable learning behaviors and malfunctions of the adaptive controller. Adaptive thresholds for detecting controller malfunctions are derived, ensuring the robustness with respect to modeling uncertainty and neural network approximation error. Additionally, the detectability conditions are investigated, characterizing the class of detectable software faults and unanticipated physical faults. An upper bound on the fault detection time is also established. Simulation results are shown to illustrate the effectiveness of the proposed method.

This paper presents a method to dynamically transform a one-input, one-output fuzzy inference system into a hybrid system. Hybrid systems are used to model and evaluate the discrete and continuous behavior of a physical systems. The method can easily be extended to two or more dimensions; mapping intelligent systems to a formal and verifiable model.

This paper describes a multi-layered fuzzy control algorithm to control an autonomous mobile robot capable of reaching a pre-defined destination without any human intervention. This control algorithm is divided into three different layers to control the robot in different environments. The first layer, orientation layer, helps the robot align itself in the direction of the destination. The second layer, PD layer, helps the robot navigation through passageways. The third layer, obstacle avoidance, keeps the robot away from any obstacles in its path. This multi-layered navigational algorithm is implemented on an autonomous mobile robot built on a modular platform consisting of three modules: the sensor module, the motor driver module, and the supervisor module. The experimental results show that the autonomous mobile robot moves efficiently through different passageways, avoiding all the obstacles in its path.

A multi-stage fuzzy logic model is systematically reduced to obtain a significantly smaller rulebase. The multi-stage structure is obtained by unfolding a single-stage, n-dimension fuzzy logic model into multiple, two-dimension stages. The interconnection between stages is not defuzzified. Rule reduction is performed by comparing output membership functions in the final two-dimension rulebase, weighted by the amount of use each rule receives, called the sum of truth, from the previous stage. The method is demonstrated on a Mackey Glass series and on a two-link robot, both with encouraging results.

Inverse dynamics is a commonly used technique in the control of dynamic systems. A fuzzy inverse dynamics controller (feedforward control) for a Pneumatic Muscle system is designed using two methods: Weighted Average and the Least Squared Error. Both methods use data collected from the system. The inverse model obtained using the two methods are tested for its trajectory tracking capabilities and the results are compared. Simulation results show that the feedforward controller obtained using Least Squared Error method has better trajectory tracking capabilities than the weighted average scheme.

A genetic algorithm is used to optimize the membership functions and rule bases of a multi-stage fuzzy PID controller with a fuzzy switch. The multistage controller uses the fuzzy switch to blend a proportional-plus-derivative fuzzy logic controller with an integral fuzzy logic input. The multi-stage structure operates on fuzzy values by passing the consequence of a prior stage onto the next stage as fact. The genetic algorithm is used to optimize the large number of variables across a range of inputs and operating states. A sample run of the genetic algorithm produces a controller with better rise time, overshoot and settling time than both a classical PID controller and a multi-stage fuzzy PID controller tuned by an intuitive method. The genetic algorithm designed controller is compared to the intuitive controller.

Many industrial applications use pneumatic cylinders to position loads using a rectilinear motion. Classical industrial control techniques allow pneumatic cylinders to position loads to a high degree of accuracy. However, these techniques do not allow for trajectory tracking control because they cannot compensate for the nonlinear nature of the compressed air flow and of the internal friction present in the cylinders. Multilayer neural networks (MNN) can be used to compensate for the nonlinear nature of these dynamic systems. For this study, a MNN was designed to be an inverse model of the cylinder and was used in conjunction with a PID feedback controller for the cylinder motion. An off-line adaptive MNN provides initial training to the controller resulting in the ability to track the desired trajectory. Once the controller has been designed, an online adaptive MNN is used for continued learning as the system dynamics change over time.

The control of flexible arms with friction in the joints is studied. A method to identify the dynamics of a flexible arm from its frequency response (which is strongly distorted by Coulomb's friction) is proposed. A robust control scheme that minimizes the effects of this friction is presented. The scheme consists of two nested feedback loops: an inner loop to control the motor position and an outer loop to control the tip position. It is shown that a proper design of the inner loop eliminates the effects of friction while controlling the tip position and significantly simplifies the design of the outer loop. The proposed scheme is applied to a class of lightweight flexible arms, and the experiments show that the control scheme results in a simple controller. As a result, the computations are minimized and, thus, high sampling rates may be used.>

The design of feedforward controllers to control the tip position of single-link flexible arms is developed. The objective is to drive the tip position along a commanded trajectory without any oscillations at the tip. The method is based on the well-known dynamics model inversion technique. Since the controllers are implemented on a computer, the dynamic inversion of the single-link flexible arms is studied from a discrete point of view. A general method to obtain a feedforward controller is developed, even in the case when the system transfer function is of nonminimum phase. The method is general in the sense that it removes oscillation in the arm with any number of vibration modes. It is shown that the input preshaping scheme developed by N.C. Singer and W.P. Seering (1990) is a special case of this method. The design technique is illustrated with numerical examples, and a comparison with the input preshaping method is carried out.>

Tip-position control of a flexible arm with friction in the joints is carried out. The control scheme is based on two nested feedback loops, an inner loop to control the position of the motor and an outer loop that controls the tip position of the flexible arm. The inner loop is controlled by a high-gain controller to remove the effects of friction. A control law partitioning scheme that partitions the control law into a model-based portion and a servo portion is used for the control of the outer loop. To make the arm follow the desired trajectory without any delay, a feedforward term is added to the control law. The control scheme is experimentally evaluated on two very lightweight flexible arms.>

A method for controlling single-link, lightweight, flexible manipulators is proposed. The objective of this method is to control the tip position of the flexible manipulator in the presence of joint friction and changes in the payload. Both linear and nonlinear friction are overcome using a very robust control scheme that is based on two nested feedback loops: an inner loop to control the position of the motor and an outer loop to control the tip position. Changes in the load are compensated by decoupling the dynamics of the system and then applying a very simple adaptive control for the tip position. This results in a quite simple control law that requires minimal computing effort and thus can be used for real-time control of flexible arms.>