Adaptive T–S fuzzy controller using reinforcement learning based on Lyapunov stability

In this paper, an adaptive Takagi–Sugeno (T–S) fuzzy controller based on reinforcement learning for controlling the nonlinear dynamical systems is proposed. The parameters of the T–S fuzzy system are learned using the reinforcement learning based on the actor-critic method. This on-line learning algorithm improves the controller performance over the time, which it learns from its own faults through the reinforcement signal from the external environment and tries to reinforce the T–S fuzzy system parameters to converge. The updating parameters are developed using the Lyapunov stability criterion. The proposed controller is faster in learning than the T–S fuzzy that parameters learned using the gradient descent method under the same conditions. Moreover, it is able to handle the load changes and the system uncertainties. The test is carried out based on two mathematical models. In addition, the proposed controller is applied practically for controlling a direct current (DC) shunt machine. The results indicate that the response of the proposed controller has a good performance compared with other controllers.     

Design and analysis of a novel cascade control algorithm for braking-by-wire system based on electromagnetic direct-drive valves

In order to improve the response speed and control precision of the braking system with parameters uncertainty and nonlinear friction, a braking-by-wire system based on the electromagnetic direct-drive valve and a novel cascade control algorithm was proposed in this paper. An electromagnetic linear actuator directly drives the valve spool and rapidly adjusts the pressure of braking wheel cylinders. A dynamic model of electromagnetic direct-drive valve considering improved LuGre dynamic friction is established. A novel cascade control algorithm with an outside loop pressure fuzzy controller and an inside loop electromagnetic direct-drive valve position controller was proposed. An adaptive integral robust inside loop controller is designed by combining friction compensation adaptive control law, linear feedback, and integral robust control. The uncertainty parameters and the friction state are estimated online. The stability of the cascade controller is proved by the Lyapunov method. Then a multi-objective opitimizemization design method of control parameters is proposed, which combines a multi-objective game theory and a technique for order preference by similarity to ideal solution (TOPSIS) based on entropy weight. The results show that the pressurization time of cascade control is less than 0.09 s under the 15 MPa step target signal. The control precision is improved effectively by the cascade controller under the ARTEMIS condition.     

A Direct Method for Model Reduction of Discrete systems

A new method for the model reduction of linear discrete stable systems in Z-transfer functions is presented. First, a set of parameters is defined, whose values uniquely determine the given system. Then an always stable reduced approximant is obtained by neglecting the parameters which do not contribute significantly in the formation of the system's responses. The proposed method slightly modified also preserves, in the reduced model, the rank of the given system. Formulae are provided to select the reduced order.     

A new method for performance evaluation of bit decoding algorithms using statistics of the log likelihood ratio

This paper presents a new method for the performance evaluation of bit decoding algorithms. The method is based on estimating the probability density function (pdf) of the bit log likelihood ratio (LLR) by using an exponential model. It is widely known that the pdf of the bit LLR is close to the normal density. The proposed approach takes advantage of this property to present an efficient algorithm for the pdf estimation. The moment matching method is combined with the maximum entropy principle to estimate the underlying parameters. We present a simple method for computing the probabilities of the point estimates for the estimated parameters, as well as for the bit error rate. The corresponding results are used to compute the number of samples that are required for a given precision of the estimated values. It is demonstrated that this method requires significantly fewer samples as compared to the conventional Monte-Carlo simulation.     

Subspace predictive control with the data-driven event-triggered law for linear time-invariant systems

In this paper, a subspace predictive control (SPC) method with a novel data-driven event-triggered law is proposed for linear time-invariant systems with unknown model parameters. Based on the conventional SPC method, the event-triggered law is introduced to substitute the typical receding horizon optimization, which reduces the data computation load of the traditional SPC method. The key parameters of the event-triggered law are derived by the Q-learning method via system data and the input-to-state stability of the system can be ensured with the designed event-triggered law. The simulation results illustrate the effect and merits of the proposed method with comparisons.     

On-line tuning of PI/Lead compensators for decoupling multivariable processes with specifications on phase and bandwidth

In this paper, an on-line identification and auto-tuning method is proposed for multivariable processes. Systematic identifying procedures and on-line tuning rules are developed for computing parameters of proportional plus integration and Lead compensators. The performance of the compensated systems can be evaluated by wanted bandwidth, phase margins and low-interacting characteristics. No iteration for finding parameters of compensator is needed. Parameters of PI/Lead compensator can be retuned if they are needed. Three numerical examples give the proposed method provides better performance, robustness and less interaction effects than those of other mentioned on-line computing methods.     

改进型Z-N参数整定方法及其硬件实现

针对经典PID参数整定方法复杂的问题,提出了一种改进型的Z-N参数整定方法。该方法提出系统特征参数的硬件解算方法,实现了电机运行过程中PID参数的自整定。在直流无刷电机伺服系统上验证了该算法能够对控制参数的自整定。电机调速过程响应迅速,无超调,运行平稳。     

Improved event-triggered control for networked control systems subject to deception attacks

This paper investigates the event-triggered control problem for networked control systems subject to deception attacks. An improved event-triggered scheme is proposed to reduce transmission rate by using both the information of the relative error and the past released signals. Under the proposed event-triggered scheme, a new switched time-delay system model is proposed for the event-triggered control systems. Based on the new model, the exponential mean-square stability criteria are derived by using the constructed Lyapunov function. Then, a co-design method is developed to obtain both trigger parameters and mode-dependent controller gains. Finally, the proposed scheme is verified by an unmanned aerial vehicle system.     

Numerical estimation of two convective boundary conditions of a two-dimensional rectangular fin

A simultaneous estimation of two convective boundary conditions problem of a two-dimensional rectangular fin is proposed by numerical approach. The aim is to estimate the evolution of the distributions of the unknown heat transfer coefficients from the transient temperature histories taken with several sensors inside a two-dimensional fin. The estimation algorithm of this inverse heat conduction problem is based on the iterative regularization method and on the conjugate gradient method. An optimal choice of the vector of the descent parameters is used in this study and shows an increase in the convergence rate. The effects of some parameters (sensor number, position, measurement errors) on the inverse solutions are discussed.     

Population extremal optimization-based extended distributed model predictive load frequency control of multi-area interconnected power systems

How to design a set of optimal distributed load frequency controllers for a multi-area interconnected power system is an important but still challenging issue in the field of modern electric power systems. This paper presents an adaptive population extremal optimization-based extended distributed model predictive load frequency control method called PEO-EDMPC for a multi-area interconnected power system. The key idea behind the proposed method is formulating the dynamic load frequency control issue of each area power system as an extended distributed discrete-time state-space model based on an extended state vector, obtaining a distributed dynamic extended predictive model, and rolling optimization of real-time control output signal by adopting an adaptive population extremal optimization algorithm, where the fitness is evaluated by the weighted sum of square predicted errors and square future control values. The superiority of the proposed PEO-EDMPC method to a traditional distributed model predictive control method, a population extremal optimization-based distributed proportional-integral control algorithm and a traditional distributed integral control method is demonstrated by the simulation studies on two-area and three-area interconnected power systems in cases of normal, perturbed system parameters and dynamical load disturbances.     

Optimal adaptive reset control with guaranteed transient and steady state tracking error bounds

In this paper, a solution for improvement of transient performance in adaptive control of nonlinear systems is proposed. An optimal adaptive controller based on a reset mechanism and a prescribed performance bound is devised. The suggested controller has the structure of adaptive backstepping controller in which the estimated parameters are reset to an optimal value. The designed controller ensures both the transient bound and the asymptotical convergence of the states. It is shown that the tracking error satisfies the prescribed performance bound all the time, besides the speed of the convergence rate is increased by resetting the estimated parameters. The results have been proved through both the analytical and simulation studies. The proposed method is applied to an Augmented Quarter Car Model as a case study. Simulation results verify the established theoretical consequences that the prescribed performance bound based optimal adaptive reset controller can enhance the transient performance of the adaptive controller.     

Identification of Wiener–Hammerstein models based on variational bayesian approach in the presence of process noise

This paper addresses the identification of Wiener–Hammerstein (WH) models in the presence of process and measurement noises, which has not been well studied yet in the existing works. To achieve an unbiased estimation, the model parameters are obtained by maximizing the likelihood function, which is solved in the expectation-maximization framework. Due to the difficulty of computing the posterior distributions of the latent variables of WH models, variational Bayes (VB) is used here, and a method for approximating the posterior distributions based on Monte Carlo integral is proposed in VB framework. To the best of our knowledge, it is the first time to use VB approach for WH model identification. Two simulation examples demonstrate the effectiveness of the proposed method. Moreover, the proposed method is used for a WH benchmark problem, and the results show that it improves the identification performance.     

Buckling analysis of a beam–column using multilayer perceptron neural network technique

We present the mathematical model and an artificial neural network method for calculating the buckling load of a beam column with different end conditions. A trial solution of the beam column equation is written as a sum of two parts, in which first part satisfies the boundary conditions and the second part represents the feed forward neural network containing adjustable parameters, weights and biases. We prepared the Error function by using the beam column equation and its boundary conditions, which is used in the back propagation method with deflection term to update the network parameters. It is found that the artificial neural network method is capable for calculating deflection of a beam column as a part of the training process. To ascertain the soundness, efficiency and accuracy of the proposed method the results are compared to the Euler critical load.     

Event-triggered control of leader-following and cluster consensus for MAS under directed graph with designable minimum event interval

This paper investigates the event-based consensus problems for linear multi-agent systems under directed network topology. First, a new event-triggered control method is proposed for the leader-following consensus problem of agents under directed graphs. Then this new method is applied to the cluster control problem under special topological conditions. The new event-based control scheme is better than some existing literature in the following aspects. 1) The graph only needs to contain a spanning tree instead of being required to be strongly connected graph or undirected, and the triggering function is state-dependent rather than time-dependent. 2) Some parameters are designable for the trade-off between the event interval and the performance of the controlled system. Besides, the optimization of some parameters is studied to reduce the trigger frequency. All the agents can achieve consensus with an exponential speed when communications among follower agents are intermittent, and Zeno behavior is excluded under the proposed method. 3) When applying this method to the cluster control problem, agents in the same cluster share the same form of triggering function. Cluster consensus can be achieved regardless of intra- and inter-cluster relative coupling strength under the event-triggered control framework.     

An adaptive compensator for a vehicle driven by DC motors

A vehicle system driven by two independent DC motors is presented here, one of which is used for the right wheel and the other is used for the left wheel. An adaptive compensator using Takagi-Sugeno fuzzy systems is proposed to control the vehicle system. The compensator includes an adaptive model identifier and adaptive controller. An online method is used to adjust the parameters of the identifier model to match the behavior model of the vehicle system. Then, the parameters of the identifier model are employed in a standard parallel-distributed compensator to provide asymptotically stable equilibrium for the closed-loop vehicle drive system, in which the velocity and direction angle of the vehicle are controlled. Results demonstrate that the proposed controller structure is robust to load changes and follows different trajectories very well.     

Improved closed loop identification of transfer function model for unstable systems

The method of identifying first order plus time delay transfer function model proposed for unstable systems by Ananth and Chidambaram [Closed loop identification to transfer function model for unstable systems, J. Franklin Inst. 336 (1999) 1055-1061] is modified to avoid the stability problems [Cheres, Parameter estimation of an unstable system with a PID controller in a closed loop configuration, J. Franklin Inst., 2005, accepted for publication] of the method. Two modifications are proposed. In the first modification of the method, the under-determined algebraic equations problem is converted into an optimization problem for calculation of the three parameters of the first order plus time delay (FOPTD) model. A simple method is given for the initial guess values of the model parameters. In the second approach, from the definition of Laplace transform of the output response, a third equation is formulated. The resulted three equations, in terms of the three parameters of the transfer function model, are then numerically solved. Simulation results are given for the second order plus time delay transfer function considered by Cheres 2005 [Parameter estimation of an unstable system with a PID controller in a closed loop configuration, J. Franklin Inst., 2005, accepted for publication]. The responses of the identified models with the same PID controllers are compared with that of the actual system. PID controllers are designed based on the identified models. The closed loop responses of the controllers on the original system are evaluated and compared. The present methods give better control performances.     

Active fault diagnosis for a class of closed-loop systems via parameter estimation

This paper addresses an active fault diagnosis problem for a class of discrete-time closed-loop system with stochastic noise. By introducing the theories of system identification, a novel active fault diagnosis method is developed to detect and isolate the faults. An important advantage of the proposed method is that there is no need to cut off the original input signal, which is necessary in most active fault diagnosis methods. Firstly, due to the features of the faults, we transform the problem of fault diagnosis into a problem of model selection by estimating model parameters. Then, the sufficient condition for active fault diagnosability is analysed, and the property that auxiliary input signal can enhance the fault diagnosability is given. Finally, simulation studies are carried out to demonstrate the effectiveness and applicability of the proposed method.     

Event-triggered consensus of nonlinear multi-agent systems with stochastic switching topology

This paper is concerned with a leader-follower consensus problem for networked Lipschitz nonlinear multi-agent systems. An event-triggered consensus controller is developed with the consideration of discontinuous state feedback. To further enhance the robustness of the proposed controller, modeling uncertainty and switching topology are also considered in the stability analysis. Meanwhile, a time-delay equivalent approach is adopted to deal with the discrete-time control problem. Particularly, a sufficient condition for the stochastic stabilization of the networked multi-agent systems is proposed based on the Lyapunov functional method. Furthermore, an optimization algorithm is developed to derive the parameters of the controller. Finally, numerical simulation is conducted to demonstrate the effectiveness of the proposed control algorithm.     

WSVR-based fuzzy neural network with annealing robust algorithm for system identification

This paper proposes a fuzzy neural network (FNN) based on wavelet support vector regression (WSVR) approach for system identification, in which an annealing robust learning algorithm (ARLA) is adopted to adjust the parameters of the WSVR-based FNN (WSVR-FNN). In the WSVR-FNN, first, the WSVR method with a wavelet kernel function is used to determine the number of fuzzy rules and the initial parameters of FNN. After initialization, the adjustment for the parameters of FNNs is performed by the ARLA. Combining the self-learning ability of neural networks, the compact support of wavelet functions, the adaptive ability of fuzzy logic, and the robust learning capability of ARLA, the proposed FNN has the superiority among the several existed FNNs. To demonstrate the performance of the WSVR-FNN, two nonlinear dynamic plants and a chaotic system taken from the extant literature are considered to illustrate the system identification. From the simulation results, it shows that the proposed WSVR-FNN has the superiority over several presented FNNs even the number of training parameters is considerably small.     

调整特征参量的生态足迹新方法研究——以西安市为例

在传统生态足迹计算方法的基础上,本文提出了最终能源足迹概念.即地球上消耗的能源最终由太阳辐射提供,而能源生态足迹就是消耗能源所需的接收太阳辐射能的建成地面积.相应的,不再使用化石能源地概念.同时,将海洋提供的生态资源,纳入内陆居民人均生态承载力范畴.以西安市1997年～2006年的统计数据为基础,本文分别使用传统方法和上述调整后的方法对10年间西安市的生态足迹进行了计算.传统生态足迹法计算的结果表明西安市人均赤字由1997年的1.07hm~2,逐渐增加至2006年的1.40hm~2,始终处于生态赤字状况.而调整后生态足迹法的计算结果表明,西安市一直处于生态盈余状况,可持续发展状况良好,其人均生态盈余在1997年为0.64hm~2,至2006年为0.45hm~2.本研究调整原方法部分特征参量后,使生态足迹法更具前瞻性,更符合社会发展规律特征,能够更准确地反映区域生态可持续发展状况.