Switched Affine Systems Research Articles

H ∞ bumpless transfer control for switched affine systems with its application to turbofan engine model

Switched affine systems (SASs) are a special class of switched systems. The existing works about SASs predominantly focuses on steady-state performance. There exist limited attention given to transient performance, particularly the transient performance induced by switchings. The inappropriate switchings can induce severe signal jumps, degrade the steady-state performance of the system, and even lead to instability. The bumpless transfer control (BTC) represents an effective strategy for mitigating signal jumps. However, the existing BTC methods are primarily designed for general switched systems, and these approaches are often not applicable to SASs. This article is focussed on the issue of H ∞ BTC for SASs under unmodeled disturbances. Firstly, an affine term (AT) related to H ∞ bumpless transfer (BT) performance definition is introduced for the SAS to characterise the alleviation level of the bumps in the control input signal at switching points. Secondly, a criterion is established to enable the solvability of the H ∞ BTC problem for the SAS. Thirdly, an H ∞ BT controller and a switching signal are co-designed to drive the SAS to satisfy the H ∞ BT performance which may not be shared by the subsystems. Finally, a turbofan engine model example is implemented to illustrate the availability and rationality of the suggested H ∞ BTC scheme.

Finite-Time Stability Analysis and Stabilization of Switched Affine Systems via an Event-Triggered Strategy.

This article investigates the finite-time control problem of the switched affine systems via an event-triggered strategy. It is well known that the existence of affine terms brings great difficulties in analysis of the finite-time property of such systems. Furthermore, the design of the globally feasible event-triggered mechanism (ETM) under a finite-time control framework is challenging. Thus, a two-step hybrid control scheme is proposed in this article. The first step focuses on the event-triggered finite-time control for practical stability, while the second step aims to achieve finite-time stabilization. Particularly, in step one, by constructing the intersection between the affine term's threshold and feasible state region of the established ETM, it is verified that the Zeno behavior can be excluded. Thereafter, an affine state-dependent switching law and sufficient conditions are provided for achieving practical stability. Meanwhile, an estimation for the practical settling time to enter the bounded set is provided. In step two, the criteria for finite-time stabilization of the considered systems are further presented, and an overall settling-time upper bound is derived. Finally, a numerical example is illustrated to demonstrate the effectiveness of our proposed method.

Data-Driven Control Design for Power Converters Approximated as Switched Affine Systems and Experimental Validation

Data-Driven Control Design for Power Converters Approximated as Switched Affine Systems and Experimental Validation

Stabilization of aperiodic sampled-data switched affine systems to hybrid limit cycles

This paper deals with the stabilization of aperiodic sampled-data switched affine systems to a predetermined hybrid limit cycle using a hybrid dynamical system representation and a control Lyapunov function approach. Some preliminaries on the hybrid dynamical system formalism provide the framework for modeling switched affine systems followed by definitions on hybrid limit cycles and related notions. The main result, based on simple Linear Matrix Inequalities (LMI), guarantees that the solutions to the closed-loop system converge to a hybrid limit cycle defined by the states, functioning modes with their corresponding dwell times. The theoretical results are evaluated on academic examples and demonstrate the potential and the originality of the method over the recent literature.

H∞ Anti-Disturbance Switching Control for Switched Affine Systems With Its Application to Turbofan Engine Model

H_∞ Anti-Disturbance Switching Control for Switched Affine Systems With Its Application to Turbofan Engine Model

Dynamic output feedback based fault tolerant control for continuous-time switched affine systems via reduced-order observer

In this study, the issue on dynamic output feedback fault-tolerant controller design is addressed for a class of continuous-time switched affine systems in the presence of actuator faults. The existence of affine terms gives rise to the lack of a common equilibrium point and further makes it more difficult to propose the desired output-feedback-based fault-tolerant control scheme. Firstly, the actuator fault estimation is achieved through a reduced-order observer design approach. Then, a kind of dynamic output feedback controller is constructed to perform the fault tolerance goal by utilizing fault estimation information. Moreover, the mode-dependent average dwell time switching constraint is borrowed to avoid the chattering owing to the high-frequency switching. The sufficient conditions with less conservative are derived to guarantee the practical exponential stability of closed-loop system with a prescribed L∞ gain. Finally, both the effectiveness and validity of the designed fault-tolerant control strategy are illustrated via a case study of a buck-boost DC-DC converter.

Corrections to “On the global practical stabilization of discrete-time switched affine systems: application to switching power converters” [Scientia Iranica (2021) 28(3), 1621-1642] and [Scientia Iranica (2021) 28(3), 1606-1620

Corrections to “On the global practical stabilization of discrete-time switched affine systems: application to switching power converters” [Scientia Iranica (2021) 28(3), 1621-1642] and [Scientia Iranica (2021) 28(3), 1606-1620

Trajectory tracking with integral action of switched periodic affine systems

This paper deals with integral control of a class of switched affine systems characterised by time-varying differential equations that, along with the discontinuities caused by the switching, also depend periodically on an exogenous parameter, which is an affine function of time. The goal is to design a state-dependent switching function with integral action that ensures global asymptotic tracking of a trajectory of interest. The integral action is responsible for providing robustness to the system against uncertainties and load variations, whenever the discrepancy between the model and the real system is sufficiently bounded. Due to the integrator, all the convex combinations of the dynamic matrices are non-Hurwitz. In this case, the main difficulty is to guarantee that the time derivative of the Lyapunov function is strictly negative definite, which is done by means of LMIs and conditions on the affine terms. To the best of our knowledge, this is the first Lyapunov-based switching rule with integral action able to ensure global asymptotic tracking of a pre-specified profile. When applied to AC circuits the advantage is to design the switching rule based on the original system, without resorting to averaged models. The theory is illustrated by the control of a three-phase AC-DC converter.

Lyapunov-Based Policy Synthesis for Multi-Objective Interval MDPs

In this paper, we provide an analysis of the convergence characteristics of the dynamic programming value iteration method based on stability-theoretical results of discrete-time switched affine systems. For interval Markov decision processes subject to multiple objective functions, we reformulate the value iteration algorithm as a switched affine system with additive uncertainties. Building on this change of perspective, we adopt a Lyapunov-based strategy for designing a control policy by finding a switching law that stabilizes the system towards an invariant set of attraction centered at a desired target value. The results provide insights into the convergence of the value iteration algorithm and the feasibility of desired target values. The results are demonstrated on two case studies.

Predictive Control Design for Discrete Switched Affine Systems Subject to a Constant Input Delay

Predictive Control Design for Discrete Switched Affine Systems Subject to a Constant Input Delay

Robust Sampled-Observer-Based Switching Law for Uncertain Switched Affine Systems Subject to Sensor Faults With an Application to a Bidirectional Buck-Boost DC-DC Converter

Robust Sampled-Observer-Based Switching Law for Uncertain Switched Affine Systems Subject to Sensor Faults With an Application to a Bidirectional Buck-Boost DC-DC Converter

Local stabilization of networked linear systems with decentralized switching controllers

In this paper, we consider the decentralized control design problem for a particular case of networked switched affine systems. The considered network consists of interconnected (identical) linear systems with the controlled input switching among a finite set of values. We address a challenging case where the network can be only locally stabilized. Scalable Lyapunov based conditions are proposed for designing such decentralized controllers. The derived conditions (theoretical and linear matrix inequalities) do not depend on the number of subsystems. Ellipsoidal estimates of the domain of attraction are given.

Fault estimation of continuous‐time switched affine systems with actuator faults under dwell time constraint

SummaryThis paper investigates the problem of fault estimation for a class of continuous‐time switched affine systems with actuator faults. In most of the existing results of switched affine systems based on the min‐switching approach, the candidate Lyapunov function is usually common, such that it is conservative to derive the practical stability conditions. To overcome this restriction, a class of switched Lyapunov function is introduced to increase more degrees of freedom of the designed min‐switching strategy and to ensure the stability of error systems. At the same time, the proposed dwell‐time dependent switching strategy can avoid the frequent switchings commonly existing in the min‐switching mechanism. Then, a new intermediate estimator is designed to estimate the state and fault simultaneously, and the intermediate estimator based fault estimation is performed under the proposed mixed switching law. Moreover, the gains of fault estimator are explicitly calculated via resolving the conditions of linear matrix inequalities. Finally, two examples including a flyback DC‐DC power converter are illustrated to verify the effectiveness and advantage of proposed fault estimation approach.

Stability of Switched Affine Systems: Arbitrary and Dwell-Time Switching

Stability of Switched Affine Systems: Arbitrary and Dwell-Time Switching

Event-triggered finite-time stabilization of nonlinear switched affine systems under mode-dependent and state-dependent switchings

This paper investigates the event-triggered finite-time stabilization (FTS) problem of nonlinear switched affine systems (NSASs) under mode-dependent and state-dependent switching signals, respectively. Firstly, an event-triggered control (ETC) strategy for NSASs with mode-dependent average dwell time constraint is proposed. Note that the presence of affine terms gives rise to difficulties in the exclusion of Zeno behavior for the widely-adopted triggering mechanism consisting of current state and error information. Therefore, a novel triggering mechanism including affine term threshold is proposed to exclude Zeno behavior. Secondly, an event-triggered impulsive control strategy for NSASs under autonomous state-dependent switching is studied. Some Lyapunov-based criteria and a state-dependent switching law for FTS are presented. Moreover, the established event-based control strategies are applied to FTS of boost converter to illustrate the effectiveness of the proposed results.

Control of Switched Affine Systems with Bounded Sampling Time Rate on the Switching Function: Application to Buck DC-DC Converter

The paper addresses the problem of designing a stabilizing control for switched affine and its experimental verification based on Linear Matrix Inequalities (LMIs). The main contribution is on the determination of a switching function that exploits the potential of LMI control approaches and which assures global stability and minimizes a guaranteed quadratic cost. Slack variables are introduced to reduce the design conservatism and new sufficient LMI conditions for the synthesis of the controllers are presented. Thus, it is showed that the performance of the control system is superior with a smaller guaranteed cost upper bound of that afforded by recent results. In addition, a theorem with sufficient conditions for the control of switched affine systems that allows a way to garantee a bounded sample time rate on the switching function is proposed. The implementation of the switching function taking into account a bounded sampling time is analysed and discussed with particular interest. Finally, the theoretical results are applied to Buck DC-DC converter. Several simulations show the usefulness of the methodology and experimental results obtained from a prototype validate this approach.

A Novel Approach to H2 and H∞, Filter Design for Discrete-time Switched Affine Systems

A Novel Approach to H2 and H∞, Filter Design for Discrete-time Switched Affine Systems

Linear matrix inequality relaxations and its application to data‐driven control design for switched affine systems

AbstractThe problem of data‐driven control is addressed here in the context of switched affine systems. This class of nonlinear systems is of particular importance when controlling many types of applications in electronic, biology, medicine and so forth. Still in the view of practical applications, providing an accurate model for this class of systems can be a hard task, and it might be more relevant to work on data issued from some trajectories obtained from experiments and to deploy a new branch of tools to stabilize the systems that are compatible with the processed data. Following the recent concept of data‐driven control design, this paper first presents a generic equivalence lemma that shows a matrix constraint based on data, instead of the system parameter. Then, following the concept of robust hybrid limit cycles for uncertain switched affine systems, robust model‐based and then data‐driven control laws are designed based on a Lyapunov approach. The proposed results are then illustrated and evaluated on an academic example.

Multimode diagnosis for switched affine systems with noisy measurement

We study a diagnosis scheme to reliably detect the active mode of discrete-time, switched affine systems in the presence of measurement noise and asynchronous switching. The proposed scheme consists of two parts: (i) the construction of a bank of filters, and (ii) the introduction of a residual/threshold-based diagnosis rule. We develop an exact finite optimization-based framework to numerically solve an optimal bank of filters in which the contribution of measurement noise to the residual is minimized. The design problem is safely approximated through linear matrix inequalities and thus becomes tractable. We further propose a thresholding policy along with probabilistic false-alarm guarantees to estimate the active system mode in real-time. In comparison with the existing results, the guarantees improve from a polynomial dependency in the probability of false alarm to a logarithmic form. This improvement is achieved under the additional assumption of sub-Gaussianity, which is expected in many applications. The performance of the proposed approach is validated through a numerical example and an application of the building radiant system.

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.