Continuous Action Generation of Q‐Learning in Multi‐Agent Cooperation

Conventional Q‐learning requires pre‐defined quantized state space and action space. It is not practical for real robot applications since discrete and finite numbers of action sets cannot precisely identify the variances in the different positions on the same state element on which the robot is located. In this paper, a Q‐Learning composed continuous action generator, called the fuzzy cerebellar model articulation controller (FCMAC) method, is presented to solve the problem. The FCMAC displays continuous action generation by linear combination of the weighting distribution of the state space where the optimal policy of each state is derived from Q‐learning. This provides better resolution of the weighting distribution for the state space where the robot is located. The algorithm not only solves the single‐agent problem but also solves the multi‐agent problem by extension. An experiment is implemented in a task where two robots are taking action independently and both are connected with a straight bar. Their goal is to cooperate with each other to pass through a gate in the middle of a grid environment.     

Sliding Mode Control for Swing‐Up and Stabilization of the Cart‐Pole Underactuated System

This paper uses sliding mode control to accomplish the objectives of swing‐up and stabilization of the cart‐pole underactuated system. The features of underactuated systems prohibit direct application of conventional sliding mode control for fully‐actuated systems. In this paper, we design a novel sliding mode control for the cart‐pole underactuated system so that the control goals can be achieved. In addition, by simply changing the parameters of the sliding surface, we use only one sliding mode control scheme to swing up and to stabilize the cart‐pole system. Using the sliding mode dynamics and the internal dynamics, we show that the proposed sliding mode control can swing up the cart‐pole system from the stable equilibrium and can stabilize the system to the unstable equilibrium. Our simulation results on a cart‐pole system demonstrate the feasibility of the proposed sliding mode control. The proposed control schemes, the stability analysis, and the numerical simulation provide a useful guideline for designing the sliding mode control for the cart‐pole underactuated system.     

Adaptive Control of the Electro‐Hydraulic Servo‐System with External Disturbances

The paper deals with the structure of the adaptive control electro‐hydraulic servo‐system (EHSS) with external load disturbances, practical verification of the identification, and control algorithms. The electro‐hydraulic servo system composed of a servo‐cylinder controlled with a servo‐valve is discussed. It is a strongly nonlinear object with parameters changing over time. Adaptive adjuster parameters were determined by means of current identification resulting in the parametric model. Identification was conducted on the basis of measurement of the controlling size and regulated size objects. The identified model of the object was applied to carry out the on‐line synthesis of the proportional–integral–derivative (PID) controller. The selected problems connected with obtaining the algorithm of adaptive control are presented. The computer program for implementing the algorithm with numerical simulation and identification of the control physical model object were calculated. The aim of the research was to examine the effectiveness of the adaptive control method in an electro‐hydraulic servo system, both theoretically and experimentally.     

Consensus of Fractional‐Order Uncertain Multi‐Agent Systems Based on Output Feedback

This paper is devoted to the consensus protocol design for a set of agents with fractional‐order uncertainty dynamics where the fractional order α satisfies 0 < α < 2. For multi‐agent systems (MASs) with fixed undirected topology, a distributed static output feedback protocol is proposed with an undetermined system matrix. Based on model transformation and fractional‐order stability theory, sufficient conditions are derived to ensure the consensus of MASs in terms of linear matrix inequalities (LMIs). Finally, a simulation example is employed to validate the effectiveness of the proposed consensus protocol.     

On Detectability and Observability of Discrete‐Time Stochastic Markov Jump Systems with State‐Dependent Noise

This paper mainly studies the notions of detectability and observability for discrete‐time stochastic Markov jump systems with state‐dependent noise. Two concepts, called “W‐detectability” and “W‐observability,” for such systems are introduced, and are shown to coincide with the other concepts on detectability and observability reported recently in literature. Moreover, some criteria and interesting properties for both W‐detectability and W‐observability are obtained.     

Robust Absolute Stability Analysis of Multiple Time‐Delay Lur'e Systems With Parametric Uncertainties

The problem of robust absolute stability for time‐delay Lur'e systems with parametric uncertainties is investigated in this paper. The nonlinear part of the Lur'e system is assumed to be both time‐invariant and time‐varying. The structure of uncertainty is a general case that includes norm‐bounded uncertainty. Based on the Lyapunov–Krasovskii stability theory, some delay‐dependent sufficient conditions for the robust absolute stability of the Lur'e system will be derived and expressed in the form of linear matrix inequalities (LMIs). These conditions reduce the conservativeness in computing the upper bound of the maximum allowed delay in many cases. Numerical examples are given to show that the proposed stability criteria are less conservative than those reported in the established literatures.     

Explicit Solution for a Class of Discrete‐Time Algebraic Riccati Equations

In the present paper we obtain an explicit closed‐form solution for the discrete‐time algebraic Riccati equation (DTARE) with vanishing state weight, whenever the unstable eigenvalues are distinct. We discuss links to current algorithmic solutions and observe that the AREs in such a class solve on one hand the infimal signal‐to‐noise ratio (SNR) problem, whilst on the other hand, in their dual form they solve a Kalman filter problem. We then extend the main result to an example case of the optimal linear quadratic regulator gain. We relax some of the assumptions behind the main result and conclude with possible future directions for the present work.     

Variable Structure Control with Chattering Reduction of a Generalized T‐S Model

In this paper, a fuzzy logic controller (FLC) based variable structure control (VSC) is presented. The main objective is to obtain an improved performance of highly non‐linear unstable systems. New functions for chattering reduction and error convergence without sacrificing invariant properties are proposed. The main feature of the proposed method is that the switching function is added as an additional fuzzy variable and will be introduced in the premise part of the fuzzy rules; together with the state variables. In this work, a tuning of the well known weighting parameters approach is proposed to optimize local and global approximation and modelling capability of the Takagi‐Sugeno (T‐S) fuzzy model to improve the choice of the performance index and minimize it. The main problem encountered is that the T‐S identification method can not be applied when the membership functions are overlapped by pairs. This in turn restricts the application of the T‐S method because this type of membership function has been widely used in control applications. The approach developed here can be considered as a generalized version of the T‐S method. An inverted pendulum mounted on a cart is chosen to evaluate the robustness, effectiveness, accuracy and remarkable performance of the proposed estimation approach in comparison with the original T‐S model. Simulation results indicate the potential, simplicity and generality of the estimation method and the robustness of the chattering reduction algorithm. In this paper, we prove that the proposed estimation algorithm converge the very fast, thereby making it very practical to use. The application of the proposed FLC‐VSC shows that both alleviation of chattering and robust performance are achieved.     

Robust Fault‐Tolerant Control of Launch Vehicle Via GPI Observer and Integral Sliding Mode Control

A robust fault‐tolerant attitude control scheme is proposed for a launch vehicle (LV) in the presence of unknown external disturbances, mismodeling dynamics, actuator faults, and actuator's constraints. The input‐output representation is employed to describe the rotational dynamics of LV rendering three independently decoupled second order single‐input‐single‐output (SISO) systems. In the differential algebraic framework, general proportional integral (GPI) observers are used for the estimations of the states and of the generalized disturbances, which include internal perturbations, external disturbances, and unknown actuator failures. In order to avoid the defects of the conventional sliding surface, a new nonlinear integral sliding manifold is introduced for the robust fault‐tolerant sliding mode controller design. The stability of the GPI observer and that of the closed‐loop system are guaranteed by Lyapunov's indirect and direct methods, respectively. The convincing numerical simulation results demonstrate the proposed control scheme is with high attitude tracking performance in the presence of various disturbances, actuator faults, and actuator constraints.