Data-driven optimal switching of switched systems

Switched systems are complicated due to the switching among the subsystems. When the subsystem models are unknown, control problems on switched systems turn to be more intractable. In this paper, the optimal switching problems are investigated for continuous-time switched autonomous systems with unknown dynamics and a finite-horizon cost function. Firstly, a novel data-driven optimal scheduling approach is proposed based on the estimated insertion gradients. Secondly, aiming at switched systems with a prescribed switching sequence, a data-driven optimal switching time approach is proposed based on the estimated derivatives of the cost with respect to the switching times. The two approaches take advantages of plenty state data containing necessary information instead of the system models. Furthermore, the errors of the approaches are analysed and bounded. Finally, simulation results of two examples are given to show the validity of the two approaches.     

Optimal control algorithms for switched Boolean network

This paper investigates the time optimal control and optimal infinite-horizon control for a switched Boolean network. First, the switched Boolean network can be converted into a discrete switched system by using the semi-tensor product of matrices. Second, algorithms for time optimal control and optimal infinite-horizon control of the switched Boolean network are presented. Moreover, constrained optimal infinite-horizon control is studied. Finally, illustrative examples are given to show the efficiency of the obtained results.     

一类线性切换系统的鲁棒跟踪控制

文章研究了线性切换系统的鲁棒跟踪控制,并提出可解性的充分条件。设计切换控制规则使得切换线性系统满足加权H∞参考模型,并采用平均驻留时间法和Lyapunov函数来处理稳定性分析和控制器设计。通过使用线性矩阵不等式,控制器设计问题可以得到很好的解决。     

Model reference adaptive control for switched linear systems using switched multiple models control strategy

In this paper, the multiple model strategy is applied to the adaptive control of switched linear systems to improve the transient performance. The solvability of the adaptive stabilization problem of each subsystem is not required. Firstly, the two-layer switching mechanism is designed. The state-dependent switching law with dwell time constraint is designed in the outer-layer switching to guarantee the stability of the switched systems. During the interval of dwell time constraint, the parameter resetting adaptive laws are designed in the inner-layer switching to improve the transient performance. Secondly, the minimum dwell time constraint providing enough time for multiple model adaptive control strategy to work fully and maintaining the stability of the switched systems is found. Finally, the proposed switched multiple model adaptive control strategy guarantees that all the closed-loop system signals remain bounded and the state tracking error converges to zero.     

Data-driven control of consensus tracking for discrete-time multi-agent systems

This paper investigates the consensus tracking problem of leader-follower multi-agent systems. Different from most existing works, dynamics of all the agents are assumed completely unknown, whereas some input-output data about the agents are available. It is well known from the Willems et al. Fundamental Lemma that when inputs of a linear time-invariant (LTI) system are persistently exciting, all possible trajectories of the system can be represented in terms of a finite set of measured input-output data. Building on this idea, the present paper proposes a purely data-driven distributed consensus control policy which allows all the follower agents to track the leader agent’s trajectory. It is shown that for a linear discrete-time multi-agent system, the corresponding controller can be designed to ensure the global synchronization with local data. Even if the data are corrupted by noises, the proposed approach is still applicable under certain conditions. Numerical examples corroborate the practical merits of the theoretical results.     

Sampling and control of switched linear systems

In this paper, we address the sampling and control issues for switched linear systems. Under synchronous switching and piecewise constant control, a continuous-time switched system is naturally related to a discrete-time sampled-data system. We prove that, with almost any sampling rate, the controllable subspace will be preserved for a switched linear system. We also investigate the possibility of achieving controllability using regular switching mechanisms. We show that, to achieve controllability for a switched linear system, it is sufficient to use cyclic and synchronous switching paths and constant control laws.     

Finite-time adaptive control for a class of switched stochastic uncertain nonlinear systems

This paper addresses the problem of global finite-time adaptive control for a class of switched stochastic uncertain nonlinear systems under arbitrary switchings. By applying the delicate introduction of coordinate transformations and adding a power integrator technique, an adaptive controller is constructed to guarantee that the system state is regulated to the origin almost surely in a finite time while maintaining the boundedness of the resulting closed-loop systems in probability. Two examples are given to illustrate the effectiveness of the proposed control scheme.     

A novel event-triggered strategy for networked switched control systems

This paper investigates the problem of event-triggered finite-time control for networked switched control systems with extended dissipative performance. Different from previous event-triggered results of switched systems, we propose a novel event-triggered method that allows more than once system switching over an event-triggered interval. By using a new Lyapunov function method, we discussed the finite-time extended dissipative analysis of the closed-loop networked switched systems. The controller gains and event-triggered parameters are obtained by solving some LMIs. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.     

Non-fragile observer-based sliding mode control for a class of uncertain switched systems

In this work, the problem of non-fragile sliding mode control is investigated for a class of uncertain switched systems with state unavailable. First, a non-fragile sliding mode observer is constructed to estimate the unmeasured state. And then, a state-estimate-based sliding mode controller is designed, in which a weighted sum approach of the input matrices is utilized to obtain a common sliding surface. It is shown that the reachability of the specified sliding surface can be ensured by the present sliding mode controller. Moreover, the exponential stability of the sliding mode dynamics is analyzed by adopting the average dwell time method. Finally, a numerical simulation is given to demonstrate the effectiveness of the results.     

Model-based event-triggered control of switched discrete-time systems

In this paper, we aim to study model-based event-triggered control for a class of uncertain switched discrete-time systems composed of stabilizable and unstabilizable subsystems. A nominal model is introduced at the controller side to form a dynamic controller so that it can provide a kind of approximate estimate of the system state for system input even the overall switched discrete-time system is running in open-loop during any two consecutive event-triggered instants. By using multi-Lyapunov function method and the average dwell time switching strategy, stability conditions given in linear matrix inequality form for the closed-loop switched discrete-time system are derived. The design of control gains is also given. Finally, a numerical example and a physical example are provided to verify the effectiveness and usefulness of the proposed method.     

Adaptive neural asymptotic tracking control for a class of stochastic non-strict-feedback switched systems

The adaptive asymptotic tracking control problem for a class of stochastic non-strict-feedback switched nonlinear systems is addressed in this paper. For the unknown continuous functions, some neural networks are used to approximate them online, and the dynamic surface control (DSC) technique is employed to develop the novel adaptive neural control scheme with the nonlinear filter. The proposed controller ensures that all the closed-loop signals remain semiglobally bounded in probability, at the same time, the output signal asymptotically tracks the desired signal in probability. Finally, a simulation is made to examine the effectiveness of the proposed control scheme.     

Adaptive fuzzy tracking control for switched uncertain strict-feedback nonlinear systems

This paper concerns an adaptive fuzzy tracking control problem for a class of switched uncertain nonlinear systems in strict-feedback form via the modified backstepping technique. The unknown nonlinear functions are approximated by the generalized fuzzy hyperbolic model (GFHM). It is shown that if the designed parameters in the controller and adaptive laws are appropriately selected, then all closed-loop signals are bounded and the stability of the system can be kept under average dwell time methods. In the end, simulation studies are presented to illustrate the effectiveness of the proposed method.     

Data-driven fault monitoring for spacecraft control moment gyro with slice residual attention network

This paper studies the fault monitoring problem of a spacecraft control moment gyro (CMG) in complex environments based on the data-driven method. First, the wavelet denoising method and short-time Fourier transform (STFT) are utilized to preprocess the signal measured by an industrial personal computer (IPC) to obtain the frequency spectrum of each failure mode. Then, a slice residual attention network (SRAN) based on the ResNeXt model, attention mechanism, and random slice idea is proposed, which can fully capture the edge features of images while satisfying the learning efficiency. Furthermore, a set of comparative experiments are carried out to validate the ability of the proposed method, and the performance of SRAN is further verified under different datasets. Finally, based on the confusion matrix and t-SNE dimension reduction technique, the monitoring ability of SRAN for various faults is analyzed. Experimental results show that SRAN processes good fault monitoring capability and ideal robustness and can identify different fault degrees under the real-time fault monitoring scenario.     

Distributed event-triggered sliding mode control of switched systems

This paper investigates the problem of distributed event-triggered sliding mode control (SMC) for switched systems with limited communication capacity. Moreover, the system output and switching signals are both considered to be sampled by distributed digital sensors, which may cause control delay and asynchronous switching. First of all, a novel distributed event-triggering scheme for switched systems is proposed to reduce bandwidth requirements. Then, a state observer is designed to estimate the system state via sampled system output with transmission delay. Based on the observed system state, a switched SMC law and corresponding switching law are designed to guarantee the exponential stability of the closed-loop system with H_∞ performance. Finally, an application example is given to illustrate the effectiveness of the proposed method.     

Observer-based quantized control for discrete-time switched systems with infinitely distributed delay

This paper studies the globally almost surely exponential stabilization of discrete-time switched systems (DSSs) with infinitely distributed delay. On account of the limitation of communication resources in the actual environment, a novel class of observer-based quantized control scheme is designed that incorporates the quantization of three kinds of signals: the measurement output, the state of observer, and the measurement output of observer. By employing S-procedure and some matrix inequality techniques, an algorithm is given to design the controller parameters. To reduce the conservativeness of the obtained results, new multiple Lyapunov–Krasovskii functionals (LKFs) with negative terms are proposed to deal with the infinitely distributed delay and mode-dependent average dwell time (MDADT) switching based on transition probability (TP) is introduced to study the stabilization of DSSs with both stable and unstable modes. It is worth highlighting that the improved stabilization conditions for DSSs can release the restriction on the length of dwell time (DT) of stable and unstable subsystems. Finally, a simulation example is presented to demonstrate the validity of the proposed method.     

Finite-time guaranteed cost control for uncertain delayed switched nonlinear stochastic systems

This paper studies the finite-time guaranteed cost control problem for switched nonlinear stochastic systems with parameter uncertainties and time-varying delays. By choosing a model-dependent and delay-dependent Lyapunov-Krasovskii functional, applying the average dwell time approach and the Gronwall inequality, some novel sufficient conditions are derived to ensure that the switched nonlinear stochastic closed-loop system is finite-time stochastically stable and an upper bound is given on the performance index. The obtained nonlinear matrix is transformed into a linear matrix form, and then the feedback controller gains of the switched nonlinear stochastic systems with time-varying delay are obtained. Finally, two simulation examples are designed to verify the effectiveness of the suggested approach.     

Hybrid control strategy for positive switched delay systems with unstable modes

In this paper, the problem of hybrid control strategy (HCS) for time-varying delay positive switched linear systems (PSLS) with unstable modes is studied. Firstly, the HCS, which includes minimum switching strategy and discretized state feedback controller, is applied to PSLS with time-varying delay for the first time. Secondly, by using the discretized multiple linear copositive Lyapunov-Krasovskii functional, a sufficient condition of globally uniformly asymptotically stable (GUAS) under the HCS is given. Finally, the HCS is extended to discrete-time positive switched time delay systems, and a delay independent stabilization condition is obtained in the discrete system. The effectiveness of the HCS is verified by two simulation examples.     

Adaptive fault-tolerant control with prescribed performance for switched nonlinear pure-feedback systems

In this paper, the problem of adaptive fuzzy fault-tolerant control is investigated for a class of switched uncertain pure-feedback nonlinear systems under arbitrary switching. The considered actuator failures are modeled as both lock-in-place and loss of effectiveness. By utilizing mean value theorem, the considered pure-feedback systems are transformed into a class of switched nonlinear strict-feedback systems. Under the framework of backstepping design technique and common Lyapunov function (CLF), an adaptive fuzzy fault-tolerant control (FTC) method with predefined performance bounds is developed. It is proved that under the proposed controller, all the signals of the close-loop systems are bounded and the state tracking error for each step remains within the prescribed performance bound (PPB) regardless of actuator faults and the system switchings. In addition, the tracking errors and magnitudes of control inputs can be reduced by adjusting the PPB parameters of errors in the first and last steps. The simulation results are provided to show the effectiveness of the proposed control scheme.     

Data-driven optimal tracking control for discrete-time systems with delays using adaptive dynamic programming

In this paper, the data-driven adaptive dynamic programming (ADP) algorithm is proposed to deal with the optimal tracking problem for the general discrete-time (DT) systems with delays for the first time. The model-free ADP algorithm is presented by using only the system’s input, output and the reference trajectory of the finite steps of historical data. First, the augmented state equation is constructed based on the time-delay system and the reference system. Second, a novel data-driven state equation is derived by virtue of the history data composed of input, output and reference trajectory, which is considered as a state estimator.Then, a novel data-driven Bellman equation for the linear quadratic tracking (LQT) problem with delays is deduced. Finally, the data-driven ADP algorithm is designed to solve the LQT problem with delays and does not require any system dynamics. The simulation result demonstrates the validity of the proposed data-driven ADP algorithm in this paper for the LQT problem with delays.