Discrete-time Switching Research Articles

Data-driven controller design of discrete-time switched systems using virtual clock approach.

This paper presents a novel data-driven controller design methodology for discrete-time switching systems, emphasizing reduced conservativeness. This approach leverages both lifting and virtual clock approaches to achieve this goal. The paper thoroughly examines different application scenarios, including noise-free state measurable, noise-free state unmeasurable, and the consideration of noise. A compromise between conservativeness and applicability is also explored to relax usage restrictions. Importantly, the proposed controller design method is non-conservative in the noise-free case under specific conditions. Simulation results demonstrate that, in the presence of noise, the H∞ performance of the controllers significantly surpasses that of gain controllers based on traditional methods. Corresponding numerical and practical examples are added to all the methods presented to illustrate their validity.

Switching funnel transformation function-based discrete-time sliding-mode control for servo systems with time-varying external disturbances

This paper proposes a switching funnel transformation function-based discrete-time sliding-mode control with lower cost to prevent the issue of control failure caused by time-varying external disturbances leading to tracking errors exceeding the performance boundary. This scheme employs an offline spectral regularization-based neural network with good generalization capability to approximate the unknown nonlinear dynamics and modeling errors in the system, resulting in a more accurate discrete-time system model. Based on the discrete-time system model with time-varying external disturbances, a novel discrete-time switching funnel transformation function-based sliding surface is proposed to solve the problem when the tracking error exceeds performance boundaries. The discrete-time funnel boundaries are switched through a predefined event-triggered mechanism, ensuring that the tracking error remains within the performance boundaries at all times, thereby avoiding control failure. Furthermore, a time-varying sliding mode variable reaching rate is proposed to reduce control cost. Finally, theoretical analysis demonstrates that the tracking error remains within a smaller funnel region compared to the predefined one, and the sliding-mode variable ultimately stays within a bounded sliding-mode boundary. Experimental results on SCARA verify the effectiveness of the proposed method.

On containment control for discrete-time switching networks of delayed first-order systems

This paper delves into the domain of dynamic containment control, with specific focus on discrete-time perturbed and delayed systems characterised by first-order dynamics. Central to containment control is the aspiration to guide agents towards desired spatial formations while mitigating the effects of disturbances, ensuring cohesive behaviour. In this respect, we propose a containment protocol that ensures input-to-state stability with respect to the convex hull generated by the leader trajectories while guaranteeing robustness with respect to both fixed and distributed communication delays acting on the state measurements exchanged between the network nodes. Numerical simulations on a team of interconnected drones show the effectiveness of the proposed approach.

Stability analysis and stabilization of discrete-time switched nonlinear systems with mode-dependent average dwell time under nested actuator saturation

In this paper, the stability analysis and stabilization of a class of mode-dependent mean residence time-based discrete-time switching nonlinear systems are addressed. More specifically, under the mode-dependent average dwell time (MDADT) switching mode, combined with the practical problem, the nonlinear factor of nested actuator saturation (NAS) is introduced. Firstly, in order to ensure the system stability, based on the parameter-dependent discontinuous switching Lyapunov function and several basic lemmas, a state feedback controller is designed that makes the closed-loop system (CLS) achieve local exponential stability (LES) by solving the optimal problem in terms of linear matrix inequalities (LMIs). Secondly, the system considers the maximum attraction domain that can be achieved by the NAS system under the conditions. The simulation results show the effectiveness of the proposed design method. At the same time, the efficiency of the proposed method is verified via a water tank example.

Controller switching with the anti-bump adapter

Switching on a new or retuned controller while keeping the control loop engaged tends to generate transient “bumps” in the commands and plant outputs. For a linear time-invariant (LTI) controller in state–space form, these bumps can be mitigated or even suppressed by resetting the controller state to an appropriate non-zero value adapted to the pre-switching trajectories of the feedback loop signals. This paper proposes a simple way to compute this adapted controller state by minimizing the difference between the commands actually applied immediately before switching and the virtual command trajectory which the new controller would have generated if it had been activated in parallel. This adapted state can be recursively computed as the output of an LTI system in standard state–space form, the anti-bump adapter. Computing the anti-bump adapter involves only standard matrix algebra and control concepts (e.g., observability and controllability matrices/Gramians). Calculations are very simple and can be translated into compact computer code. This bump suppression procedure is applicable to any discrete-time or continuous-time LTI SISO or MIMO controller, without any assumption on or knowledge of either the previously active controller or the plant. Illustrative applications to continuous-time and discrete-time switching problems and a Matlab® code for computing the anti-bump adapter are presented.

Improved results of asynchronous mixed [formula omitted] and passive control for discrete-time linear switched system with mode-dependent average dwell time

This paper primarily discusses the hybrid H∞ and passive control problems of asynchronous discrete-time switching systems based on mode-dependent average dwell time. In the process of analysis, we divide the running time of the subsystem into two cases: matching and not matching the controller. Firstly, we employ the method of mode-dependent average dwell time to model the system and derive a suitable switching signal, ensuring the system is global uniform asymptotic stability. Meanwhile, the weighted hybrid H∞ and passivity are achieved. Then, according to the different performance parameters of each subsystem, the appropriate controller is designed using the form of linear matrix inequalities to improve the stability of the system. Finally, the effectiveness of the proposed method is demonstrated by a numerical example and a population ecosystem.

Data-Driven Distributed Information-Weighted Consensus Filtering in Discrete-Time Sensor Networks With Switching Topologies.

This article proposes a data-driven distributed filtering method based on the consensus protocol and information-weighted strategy for discrete-time sensor networks with switching topologies. By introducing a data-driven method, a linear-like state equation is designed by utilizing only the input and output (I/O) data without a controlled object model. In the identification step, data-driven adaptive optimization recursive identification (DD-AORI) is exploited to identify the recurrence of time-varying parameters. It is proved that for discrete-time switching networks, estimation errors of all nodes are ultimately bounded when data-driven distributed information-weighted consensus filtering (DD-DICF) is executed. The algorithm combines with the received neighbors and direct or indirect observations for the target node to produce modified gains, resulting in a novel state estimator containing an information interaction mechanism. Subsequently, convergence analysis is performed on the basis of the Lyapunov equation to guarantee the boundedness of DD-DICF estimate error. Simulations verify the performance of the DD-DICF against the theoretical results as well as in comparison with some existing filtering algorithms.

A Sigma-Delta Modulator with Single-Pole Double-Throw Analog Switch

In this paper, a high precision and high energy efficiency discrete-time switching capacitive 3-order Sigma-Delta modulator (SDM) is proposed. The SDM is applied to portable electroencephalograms (EEG) because of its little energy and good performance. The energy efficiency levels of the current mainstream modulator systems are analyzed and compared, and the CIFF modulator architecture which is most conducive to realizing high energy efficiency is selected. The single-loop CIFF structure is selected to give consideration to the accuracy and stability of the circuit. The circuit is implemented in a hierarchical structure, and a single-pole double-throw (SPDT) analog switch is adopted to overcome the difficulty of opening conventional CMOS analog switches at low supply voltages and the increase in threshold voltage Vth of NMOS devices due to the base bias effect. The proposed discrete-time Sigma delta ADC modulator is designed with SMIC 0.18um CMOS technology and achieves an SNDR of 101.6dB under a 1.8V power supply voltage and a signal bandwidth of 2kHz. The power consumption is 520uW and the significant bit (ENOB) is 16.58 bits.

Analysis of the Relation Between L<sub>2</sub> Gain and Dwell Time in Discrete Time Switching System

This paper focuses on the design of <i>l</i>₂ gain controller for discrete time switching systems with dwell time (DT) switching. So far, the quantitative relationship between <i>l</i>₂ gain stability and dwell time is one of the unsolved problems in the field of switching systems. Different from previous studies, a novel dwell time dependent Lyapunov function (DTDLF) is proposed in this paper for the first time to obtain a less conservative stability criterion. The innovation of this Lyapunov function lies in that it is no longer built by the traditional two-step controller design method, but combines the two design tasks of controller and switching law into one framework, in which solving linear matrix inequalities (LMIs) involves only one step. Compared with the two-step design scheme, this method greatly simplifies the design process. Based on the resident time dependent Lyapunov function and the resident time switching strategy, a dwell time dependent (DTD) H_∞ controller is designed such that the system is globally uniformly asymptotically stable (GUAS) and has a guaranteed H_∞ performance index. Finally, a numerical example is given to verify the validity of the proposed design method. The simulation results show that the proposed design method can guarantee a shorter resident time limit and a smaller error result.

Discrete-Time Switching Systems as Difference Inclusions: Deducing Converse Lyapunov Results for the Former From Those for the Latter

Nonlinear discrete-time switching systems under mode-dependent switching and dwell-time constraints are modeled by difference inclusions. Novel proofs of converse Lyapunov results are obtained for the switching systems as consequences of a converse Lyapunov result for a difference inclusion.

Stability Analysis for Digital Redesign of Discrete-Time Switched Systems Using H∞ Linear Matrix Inequality

In this paper, the stability problem for the digital redesign of discrete-time switched systems using H∞ linear matrix inequality (LMI) is investigated. We propose the switching time approach for digital redesign between controller work and failure, and this switching time will limit the system output within the system capacity. When the controller fails, the overall system will be unstable. Therefore, if the digital redesign controller is not restored in a certain period of time, the system output will exceed the system capacity. To solve this problem, we propose a switching law to determine the switching time between the stable mode (controller work) and the unstable (controller failure) mode; this will limit the overall system states in the unstable mode. In addition, the digital redesign controller has the advantage of faster tracking. After we propose a discrete-time switching system with stable and unstable modes, we use H∞ linear matrix inequality (LMI) and Lyapunov functions to prove the stability in detail. Finally, the numerical example illustrates the feasibility of the proposed approach.

Reduced Model-Based Fault Detector and Controller Design for Discrete-Time Switching Fuzzy Systems

The reduced model-based coordinated design of fault detectors and controllers for discrete-time switching fuzzy systems is examined. First, the mean-square exponential stabilization of switching Takagi–Sugeno fuzzy systems is performed using the average dwell time method under an arbitrary switching law. Next, using segmented Lyapunov function techniques, a dynamic full- and reduced-order fault detector and controller is designed to ensure that the overall dynamic residual system is mean-square exponentially stable with a balanced <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> performance level <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\xi, \beta)$</tex-math></inline-formula> . The solvability conditions for the fault detector and controller are derived using a linearization method, and the relevant parameters can be determined using the mathematical linear matrix solver toolbox. Two examples including a switching Chua’s circuit system are presented to demonstrate the effectiveness of the proposed fault detector and controller.

Attractors and limit cycles of discrete-time switching affine systems: Nominal and uncertain cases

This paper deals with the robust stabilization of uncertain discrete-time switched affine systems using a control Lyapunov approach and a min-switching state-feedback control law. After presenting some preliminaries on limit cycles, a constructive stabilization theorem, expressed as linear matrix inequalities, guarantees that the solutions to the nominal closed-loop system converge to a limit cycle. This method is extended to the case of uncertain systems, for which the notion of limit cycle needs to be adapted. The theoretical results are evaluated on academic examples and demonstrate the potential of the method over the recent literature.

Double discrete‐time‐switch protocol for SWIPT at the energy harvesting relays: Protocol design and optimization

Here, the energy harvesting (EH) relaying node which needs to complete the simultaneous wireless information and power transfer (SWIPT) is considered. The EH relaying node uses the EH technique to get the energy supply and uses the directional transmission to improve the performance of SWIPT. The double discrete-time-switch (D-DTS) based energy harvesting–power transfer–information transmission (EH–PT–IT) protocol is designed. One of the discrete-time-switch (DTS) controls the receiver of the EH relaying node and the other controls the transmitter. The performance is analysed by considering the average information rate and the average transferred power. The expressions of the average information rate and the average transferred power are derived analytically. The balanced maximization is considered, and the optimal parameters are obtained analytically. The simulations are presented to verify the analytical results and compare the performance. Comparing with previous works, the SWIPT performance using D-DTS protocol in this work is better.

Discrete-time switching control in random walks

In this paper we study a discrete-time switching control problem when the dynamic of the system evolves as a random walk. The payoff function is a discounted-type total cost whose discount factor may depend on the state and/or the action variables. This flexibility includes cases when the controller can stop the dynamics of the system whether is optimal to do it. To provide optimality results, we use the well-known dynamic programming method that leads to the study of certain functional equations. Under suitable conditions, we prove the existence of solutions to these equations, and we also show that the optimal value of the control problem becomes a minimal solution of these equations. Finally, we illustrate our results through an example about the control of epidemic processes.

Stability analysis of nonlinear impulsive switched positive systems

Abstract In this paper, the global asymptotic stability (GAS) of continuous-time and discrete-time nonlinear impulsive switched positive systems (NISPS) are studied. For continuous-time and discrete-time NISPS, switching signals and impulse signals coexist. For both of these systems, using the multiple max-separable Lyapunov function method and average dwell-time (ADT) method, some sufficient conditions on GAS are given. Based on these, the GAS criteria are also given for continuous-time and discrete-time linear impulsive switched positive systems (LISPS). From our criteria, the stability of the systems can be judged directly from the characteristics of the system functions, switching signals and impulse signals of the systems. Finally, simulation examples verify the validity of the results.

Модифицированная прогнозирующая система управления повышающего DC-DC-преобразователя

Nowadays, predictive control systems are becoming more and more popular, which significantly reduce the cost of setting up converters. However, DC-DC converter control problem persists. In this work, a modified model of the predictive control system (MPCS) for step-up DC-DC converters is presented. For its implementation, a nonlinear model of a converter with discrete time switching was derived, which describe a continuous conduction mode of operation. The synthesis of the controller was achieved by formulating the objective function that should be minimized considering the dynamic model of the converter. The proposed predictive control strategy, used as a voltage control system, allows keeping the output voltage at the reference level. The modified system for calculating the objective function makes it possible to significantly reduce the required computing power and expand the prediction horizon. The results of modeling have been presented that demonstrate the advantages of the proposed control method: a fast transient response and a high degree of robustness.

Multi-objective generalized predictive control for switching systems under unknown switching sequences

This paper describes a new generalized predictive control to track and stabilize a class of discrete time switching system. The focus is specifically centered on classes of switching systems characterized by unstable modes, undetermined switching signal, anon-minimumphase, and variable dead-times. To overcome this type of issue, an effective predictive control law is established by solving a dynamic multi-objective optimization function. Control problems are formulated in order to stabilize and regulate the system response around the targeted reference. The theoretical background of the proposed method is inspired by the standard generalized predictive control (GPC), in such a way that all desirable features are retained as possible. As a result, the obtained controller is more efficient in terms of stability and tracking. In fact within the framework of this research, the control problem has been formulated by taking into account behaviors of subsystems as well as the switching phase. The optimization of the problem is established in such a way that the obtained control law will be adapted to system dynamics, regardless of the mode. A number of simulation tests are established to evaluate the performance of the developed method. Four benchmark examples were considered for the simulation tests. Simulation results have shown the potential of the developed strategy to control and stabilize switching systems under unknown switching sequences. For further evaluation, the closed-loop performance of the developed strategy has been compared to that obtained with the Multi-Criteria Predictive Control (MOMPC) method. Comparison results have highlighted the effectiveness of the proposed method in terms of stability and tracking than MOMPC method.

Formula omitted]th Moment Exponential Stability of Switched Discrete-Time Stochastic Systems: A Multiple Lyapunov Functions Method

This paper studies the pth moment exponential stability of switched discrete-time stochastic systems with stable and unstable subsystems. By using multiple Lyapunov functions and mode-dependent average dwell time, we provide a sufficient condition for the pth moment exponential stability with fast convergence rate for deterministic switched discrete-time stochastic systems with stable and unstable subsystems. Obviously, our result has a weaker conservatism than those previous results where the effect of random factor was ignored. In addition, the criteria for stability and instability of discrete-time stochastic systems without switching are provided. Finally, the correctness of the results is verified by two numerical examples. To the best of our knowledge, it is the first time that the stability of discrete time switching system with random disturbance has been discussed.

Passivity and Reduced-order Feedback Passification of Discrete-Time Switched Systems with Mode-Dependent Persistent Dwell Time

Passivity and Reduced-order Feedback Passification of Discrete-Time Switched Systems with Mode-Dependent Persistent Dwell Time