Prescribed performance based data-driven adaptive sliding mode control for discrete-time nonlinear systems

This paper is concerned with an adaptive Sliding Mode Control (SMC) for non-linear discrete-time systems with mismatched uncertainty. The proposed adaptive SMC is composed of the equivalent and the switching controls, and it is constructed on the basis of the information from the proposed estimator to take the estimates for the state and uncertainty. It is assumed that some of the state variables can be measured and the uncertainty in the discrete-time systems is parameterised linearly in the unknown constant terms. The estimates for the state and the uncertainty are taken by applying the proposed weighted least squares method. It is verified based on the Lyapunov scheme according to which the estimation errors converge to zero as time increases, and the trajectory of the system response is stable as the sliding surface is suitably selected. The effectiveness of the proposed adaptive SMC is illustrated by the simulation experiment in a simple numerical example.

This paper is concerned with the event-triggered $H_{\infty }$ control problem for discrete-time nonlinear networked control systems with unreliable communication links. First, an event-triggered scheme is proposed to determine whether the sampled data should be released into the network or not. Second, when the released data is transmitted in the network, a Bernoulli process is employed to model the phenomenon of data losses. Third, considering the instants at which the sampled data is not released or data losses occur, a new random process is first developed to model the input data sequence of the controller under the effect of the buffer. Consequently, a novel method is presented to address the stability analysis and control synthesis problems based on the polynomial fuzzy model approach. Finally, some simulation results are given to illustrate the effectiveness of the proposed method.

The problem of dynamic output feedback equivalence of nonlinear observable discrete-time control systems with outputs has been studied by Pawluszewics-Bartosiewics. In this paper we use those results to achieve equivalence of a nonlinear system to a linear one. In this way we obtain an algebraic criterion of dynamic output linearization for discrete-time systems. We recall the concept of anticipating output equivalence, where transformations of outputs and controls depend on future values, and the concept of dynamic output equivalence, depending on past and present controls and outputs values. In order to give the criterion of linearisation of a discrete-time control system we have to use the difference output algebra and the difference output universe associated with the given system.

Discrete-time neural network output feedback control of nonlinear discrete-time systems in non-strict form

摘要: 确定学习运用自适应控制和动力学系统的概念与方法, 研究未知动态环境下的知识获取、表达、存储和利用等问题. 针对产生周期或回归轨迹的连续 非线性动态系统, 确定学习可以对其未知系统动态进行局部准确建模, 其基本要 素包括: 1)使用径向基函数(Radial basis function, RBF)神经网络; 2)对于周期(或回归)状态轨迹 满足部分持续激励条件; 3)在周期(或回归)轨迹的邻域内实现对非线性系统动态的局部准确神经网络逼近(局部准确建模); 4)所学的知识以时不变且空间分布的方式表达、以常值神经网络权值的方式存储, 并可在动态环境下用于动态模式的快速识别或者闭环神经网络控制. 本文针对离散动态系统, 扩展了确定学习理论, 提出一个根据时态数据序列对离散动态系统进行建模与控制的框架. 首先, 运用确定学习原理和离散系统的自适应辨识方法, 实现对产生时态数据的离散非线性系统的未知动态进行局部准确的神经网络建模, 并利用此建模结果对时态数据序列进行时不变表达. 其次, 提出时态数据序列的基于动力学的相似性定义, 以及对离散动态系统产生的时态数据序列(亦可称为动态模式)进行快速识别方法. 最后, 针对离散非线性控制系统, 实现了基于时态数据序列对控制系统动态的闭环辨识(局部准确建模). 所学关于闭环动态的知识可用于基于模式的智能控制. 本文表明确定学习可以为时态数据挖掘的研究提供新的途径, 并为基于数据的建模与控制等问题提供新的研究思路. 关键词: 确定学习 / 时态数据序列 / 离散动态系统 / 基于数据的建模 / 部分持续激励条件 / 时态数据挖掘 / 动态模式识别 / 基于模式的控制

Robust Failure Detection and Isolation in Non-Linear Control Systems

Neural-network-based accelerated safe Q-learning for optimal control of discrete-time nonlinear systems with state constraints.

In this paper, the output feedback based finite-horizon near optimal regulation of nonlinear affine discrete-time systems with unknown system dynamics is considered by using neural networks (NNs) to approximate Hamilton-Jacobi-Bellman (HJB) equation solution. First, a NN-based Luenberger observer is proposed to reconstruct both the system states and the control coefficient matrix. Next, reinforcement learning methodology with actor-critic structure is utilized to approximate the time-varying solution, referred to as the value function, of the HJB equation by using a NN. To properly satisfy the terminal constraint, a new error term is defined and incorporated in the NN update law so that the terminal constraint error is also minimized over time. The NN with constant weights and time-dependent activation function is employed to approximate the time-varying value function which is subsequently utilized to generate the finite-horizon near optimal control policy due to NN reconstruction errors. The proposed scheme functions in a forward-in-time manner without offline training phase. Lyapunov analysis is used to investigate the stability of the overall closed-loop system. Simulation results are given to show the effectiveness and feasibility of the proposed method.

The problem of finite-time reliable guaranteed cost fuzzy control for discrete-time nonlinear systems with actuator faults is investigated in this article. We first provide a novel and explicit interpretation for finite-time reliable guaranteed cost fuzzy control. Second, a suitable reliable controller is designed such that the provided performance criterion is satisfied for the normal and possible actuator fault cases. Moreover, the switched Lyapunov function approach is utilised for relaxing the conservatism of these obtained conditions and the related optimisation problem is also offered to minimise the guaranteed cost performance bound. Finally, an illustrative example is given to show the validity of the proposed scheme.

This paper investigates the formation control problem of heterogeneous discrete-time nonlinear multi-agent systems with structural uncertainties. The control objective is to make the outputs of agents reach a desired formation while tracking a leader. The formation control problem of heterogeneous discrete-time multi-agent systems is first converted into a robust output regulation problem, and then, a distributed formation control scheme based on output regulation framework is proposed. A $p$ -copy internal model is synthesized into the distributed formation control law such that the overall closed-loop system can be robust to structural uncertainties. It is shown that the heterogeneous discrete-time nonlinear multi-agent system can reach the desired formation regardless of small parameter permutations of agents under the proposed control law. Finally, simulation and experiment studies are provided to demonstrate the effectiveness of the proposed control law.

For discrete-time nonlinear systems, this research is concerned with optimal control problems (OCPs) with constrained cost, and a novel value iteration with constrained cost (VICC) method is developed to solve the optimal control law with the constrained cost functions. The VICC method is initialized through a value function constructed by a feasible control law. It is proven that the iterative value function is nonincreasing and converges to the solution of the Bellman equation with constrained cost. The feasibility of the iterative control law is proven. The method to find the initial feasible control law is given. Implementation using neural networks (NNs) is introduced, and the convergence is proven by considering the approximation error. Finally, the property of the present VICC method is shown by two simulation examples.

In this paper, a learning-based predictive control (LPC) scheme is proposed for adaptive optimal control of discrete-time nonlinear systems under stochastic disturbances. The proposed LPC scheme is different from conventional model predictive control (MPC), which uses open-loop optimization or simplified closed-loop optimal control techniques in each horizon. In LPC, the control task in each horizon is formulated as a closed-loop nonlinear optimal control problem and a finite-horizon iterative reinforcement learning (RL) algorithm is developed to obtain the closed-loop optimal/suboptimal solutions. Therefore, in LPC, RL and adaptive dynamic programming (ADP) are used as a new class of closed-loop learning-based optimization techniques for nonlinear predictive control with stochastic disturbances. Moreover, LPC also decomposes the infinite-horizon optimal control problem in previous RL and ADP methods into a series of finite horizon problems, so that the computational costs are reduced and the learning efficiency can be improved. Convergence of the finite-horizon iterative RL algorithm in each prediction horizon and the Lyapunov stability of the closed-loop control system are proved. Moreover, by using successive policy updates between adjoint time horizons, LPC also has lower computational costs than conventional MPC which has independent optimization procedures between two different prediction horizons. Simulation results illustrate that compared with conventional nonlinear MPC as well as ADP, the proposed LPC scheme can obtain a better performance both in terms of policy optimality and computational efficiency.

A novel tracking control algorithm based on sliding mode prediction is proposed for a class of discrete-time nonlinear uncertain systems in this paper. By constructing a sliding mode prediction model at first, the future, present and history information of the system can be used to improve the performance of sliding mode control. Because of sliding mode reference trajectory, the reachability of sliding mode is achieved, and the reaching mode can be determined by designers in advance. Due to feedback correction and receding horizon optimization, the influence of uncertainty can be compensated in time and control law is obtained subsequently. Theoretical analysis proves the closed-loop system possesses robustness to matched or unmatched uncertainty, without requiring the known bound of uncertainty. Simulation results illustrate the validity of the presented algorithm.

In this article, a novel multistep look-ahead policy iteration with isoperimetric constraints (MLPIIC) method is developed to solve infinite horizon optimal control problems (OCPs) with isoperimetric constraints for discrete-time nonlinear systems. In order to overcome the difficulty that Bellman’s principle of optimality does not hold directly in OCPs with isoperimetric constraints, a method to approximate OCPs with isoperimetric constraints by OCPs with new constraints is developed. For the MLPIIC method initialized with an admissible control law, the convergence and optimality of the iterative value function and the feasibility of the iterative control law are proven. Utilizing the function approximator, the implementation of the MLPIIC method is described. Finally, simulation results are provided.

Localized BF-Type Networks for Identification and Adaptive Control of Discrete-Time Nonlinear Systems