Minimum Dwell Time Constraint Research Articles

Stabilization of discrete-time switched systems with constraints by dynamic logic-based switching feedback

A switching feedback has more flexibility in stabilizing systems compared to a feedback being continuous in state. In practice, a system controlled by a state-triggered switching law exhibits more robustness than by a time-triggered one. However, designing an admissible switching law in the static feedback form is difficult or even impossible when the switching sequence is subjected to certain constraints, such as the minimum dwell-time constraints. This study proposes a class of switching feedbacks with dynamic switching logic for discrete-time switched systems with constrained switching. First, a logic dynamic generator (LDG) is constructed to generate all admissible switching sequences. By combining the switched system with the LDG, the original switched system is transformed into a switched system without constraint on switching. Then, the logic and the continuous states are merged by using the theories of the semi-tensor product (STP) of matrices and the vector-representation of logic. Using this technique, the problem considered is then transformed into a problem of designing a state-triggered switching feedback for a merged switched system without constraints, and then to a problem of solving a set of bilinear matrix inequalities. Examples show that the proposed switching law with dynamic logic can stabilize certain switched systems that cannot be stabilized by existing switching laws in the static feedback form.

Periodically intermittent H∞ control for discrete‐time switched interval type‐2 fuzzy systems with dwell time constraints: A switching‐path‐dependent Lyapunov function approach

AbstractThis article studies the periodically intermittent control problem of discrete‐time switched interval type‐2 fuzzy systems (DSIT2FSs) with dwell time constraints. A novel switching‐path‐dependent Lyapunov functions (SPDLFs) approach, which utilizes the switching path information over multiple controller operation periods, is proposed. First, the ‐mode DSIT2FS with periodic intermittent control inputs is regarded as a switched system with controller‐busy modes and controller‐free modes. Then, by constructing a class of non‐increasing SPDLFs, sufficient conditions on the existence of intermittent interval type‐2 (IT2) fuzzy controllers are obtained for DSIT2FS with minimum dwell time constraints. The controller gains can be gotten by solving a set of strict linear matrix inequalities. It is shown that the designed IT2 fuzzy controllers work intermittently but still can guarantee stability and performance of the close‐loop systems. Finally, two numerical examples are provided to illustrate the effectiveness and advantages of the results.

An efficient MPC algorithm for switched systems with minimum dwell time constraints

This paper presents an efficient suboptimal model predictive control (MPC) algorithm for nonlinear switched systems subject to minimum dwell time constraints (MTC). While MTC are required for most physical systems due to stability, power and mechanical restrictions, MPC optimization problems with MTC are challenging to solve. To efficiently solve such problems, the on-line MPC optimization problem is decomposed into a sequence of simpler problems, which include two nonlinear programs (NLP) and a rounding step, as typically done in mixed-integer optimal control (MIOC). Unlike the classical approach that embeds MTC in a mixed-integer linear program (MILP) with combinatorial constraints in the rounding step, our proposal is to embed the MTC in one of the NLPs using move blocking. Such a formulation can speedup on-line computations by employing recent move blocking algorithms for NLP problems and by using a simple sum-up-rounding (SUR) method for the rounding step. An explicit upper bound of the integer approximation error for the rounding step is given. In addition, a combined shrinking and receding horizon strategy is developed to satisfy closed-loop MTC. Recursive feasibility is proven using a l-step control invariant (l-CI) set, where l is the minimum dwell time step length. An algorithm to compute l-CI sets for switched linear systems off-line is also presented. Numerical studies show significant speed-up and comparable control performance of the proposed MPC algorithm against the classical approach, though at the cost of significant solution quality degradation especially when the MTC are large.

Resilient [formula omitted] control for uncertain turbofan linear switched systems with hybrid switching mechanism and disturbance observer

In this paper, a composite resilient anti-disturbance H∞ control scheme is presented for the turbofan linear switched systems with uncertainties and external disturbances via the disturbance observer-based control (DOBC) approach. Since the single-point linearization model cannot be used to accurately describe the engine characteristics of the whole envelope, the multi-model switching method is adopted to preferably describe the working characteristics of the turbofan. A hybrid switching scheme based on state-dependent switching and minimum dwell time constraint is developed to ensure the stability of closed-loop systems and satisfy the dwell-time requirement of turbofan systems. Then, a robust resilient controller is built by combining the DOBC approach and resilient control technique. Based on the multiple Lyapunov functions method, some easy-to-test results are given to guarantee that the closed-loop switched systems are asymptotically stable with H∞ property. Finally, the effectiveness of the proposed method is verified through some simulations and comparisons.

Sampled-Data Control for Asynchronously Switched Linear Systems Without MDT Constraints

In this paper, the sampled-data control problem is studied for asynchronously switched linear systems (SLSs) without minimum dwell time (MDT) constraints. The asynchronous phenomenon exists due to that the information of system mode can be acquired only at the sampling instant. First, a sufficient condition of global asymptotic stability (GAS) is presented for sampled-date switched control systems with a novel class of switching signals, which allows the switching number to be a non-affine function of time, and does not involve any point-wise bound on the switching number. Moreover, unlike the existing literature concerned with sampled-data control problem of switched systems, the MDT constraints are removed. We allow that no sampling happens between two adjacent switching instants, which makes the results more applicable to practice. Then, a sufficient condition checking the existence of sampled-data controllers is presented in terms of linear matrix inequalities (LMIs). Finally, it is shown by a boost converter circuit system that the designed sampled-data controller and switching signals can stabilize the system cooperatively.

Computationally Tractable Stability Criteria for Exogenously Switched Model Predictive Control

Although state-based switching is well-studied in the context of model predictive control (MPC), the theory for exogenous switches is less advanced. External switching affects many systems and is of growing importance due to the increasing use of networked control systems where abrupt changes in communication lines induce switched dynamics. In search of practical means to implement MPC for switched systems, this letter examines techniques to ensure their stability. Several existing methods are summarized and a novel approach is suggested to reduce computational costs while unifying the process for both average and minimum dwell time constraints. Two numerical examples contrast current and previous works.

A Switching-Based Adaptive Dynamic Programming Method to Optimal Traffic Signaling

The work presented in this paper concerns a switching-based control formulation for multi-intersection and multiphase traffic light systems. A macroscopic traffic flow modeling approach is first presented, which is instrumental to the development of a model-based and switching-based optimization method for traffic signal operation, in the framework of adaptive dynamic programming (ADP). The main advantage of the switching-based formulation is its capability to determine both “when”’ to switch and “which” mode to switch on without the need to use the cycle-based average flow approximation typical of state-of-the-art formulations. In addition, the framework can handle different cycle times across intersections without the need for synchronization constraints and, moreover, minimum dwell-time constraints can be directly enforced to comply with minimum green/red times in each phase. The simulation experiments on a multi-intersection and multiphase traffic light systems are presented to show the effectiveness of the method.

Mixed-integer optimal control under minimum dwell time constraints

Tailored Mixed-Integer Optimal Control policies for real-world applications usually have to avoid very short successive changes of the active integer control. Minimum dwell time (MDT) constraints express this requirement and can be included into the combinatorial integral approximation decomposition, which solves mixed-integer optimal control problems (MIOCPs) to epsilon -optimality by solving one continuous nonlinear program and one mixed-integer linear program (MILP). Within this work, we analyze the integrality gap of MIOCPs under MDT constraints by providing tight upper bounds on the MILP subproblem. We suggest different rounding schemes for constructing MDT feasible control solutions, e.g., we propose a modification of Sum Up Rounding. A numerical study supplements the theoretical results and compares objective values of integer feasible and relaxed solutions.

Finite-Time H∞ Estimator Design for Switched Discrete-Time Delayed Neural Networks With Event-Triggered Strategy.

This article is concerned with the event-triggered finite-time H∞ estimator design for a class of discrete-time switched neural networks (SNNs) with mixed time delays and packet dropouts. To further reduce the data transmission, both the measured information of system outputs and switching signal of the SNNs are only allowed to be accessible for the constructed estimator at the certain triggering time instants. Under this consideration, the simultaneous presence of the switching and triggering actions also leads to the asynchronism between the indices of the SNNs and the designed estimator. Unlike the existing event-triggered strategies for the general switched linear systems, the proposed event-triggered mechanism not only allows the occurrence of multiple switches in one triggering interval but also removes the minimum dwell-time constraint on the switched signal. In light of the piecewise Lyapunov-Krasovskii functional theory, sufficient conditions are developed for the estimation error system to be stochastically finite-time bounded with a finite-time specified H∞ performance. Finally, the effectiveness and applicability of the theoretical results are verified by a switched Hopfield neural network.

Nonconservative Lifted Convex Conditions for Stability of Discrete-Time Switched Systems Under Minimum Dwell-Time Constraint

In this note, a novel conception called virtual clock, which is defined by an artificial timer over a finite cycle, is introduced for stability analysis of discrete-time switched linear systems under minimum dwell-time constraint. Two necessary and sufficient conditions associated with a virtual clock with a sufficient length are proposed to ensure the global uniform asymptotic stability of discrete-time switched linear systems. For the two nonconservative stability criteria, the lifted version maintains the convexity in system matrices. Based on the lifted convex conditions, the extensions to $\ell _2$ -gain computation and $\mathcal {H}_\infty$ control problems are presented in the sequel. In particular, a novel virtual-clock-dependent controller is designed, which outperforms the traditional mode-dependent and common gain controllers. Several numerical examples are provided to illustrate our theoretic results.

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.

Hybrid Control of Single-Inductor Multiple-Output Converters

In this paper, a new control strategy for single-inductor multiple-output (SIMO) converters is proposed. The strategy is based on the hybrid control scheme. Switched linear equations of the converter are used in the design procedure. As a result, the cross regulation is suppressed inherently. A minimum dwell-time constraint is considered to suppress the switching loss and electromagnetic interference. The proposed scheme can control both minimum phase and nonminimum phase SIMO converters. It will be shown that the system is robust to input voltage and load variations. In order to compare the results, a recent pulsewidth-modulation-based control system is considered. Performance of the system is evaluated by a number of simulations and experiments.

An Algorithm for the Calculation of the Dwell Time Constraint for Switched ℋ∞ Filters

Abstract This paper presents a numerical algorithm for determining the minimum dwell time constraint for switched linear ℋ∞ fault detection filters. When applying switched systems, ensuring the stability is a crucial target, which can be guaranteed, when we switch slowly enough between the subsystems, more precisely when the intervals between two consecutive switching instants, called dwell time, are large enough. The problem formulation is based on multiple Lyapunov functions and is expressed through a special form of linear matrix inequalities (LMIs), which include a nonlinear term of the dwell time. This represents a multivariable, time dependent optimization problem. As a result, the task cannot be treated as a simple feasibility problem involving a LMI solver as it is widely used in applications of the linear control. To solve these special LMIs, we propose a numerical algorithm, called 𝒯 d -iteration, which combines the procedure of interval halving with an LMI solver. The algorithm implemented in MATLAB shows its applicability as well as suggest further benefits for the switched linear control and filter synthesis.

Stabilization of linear impulsive systems under dwell-time constraints: Interval observer-based framework

The problem of interval observer design is studied for a class of linear impulsive systems. Ranged and minimum dwell-time constraints are considered under detectability assumption. The first contribution of this paper lies in designing interval observers for linear impulsive systems under ranged and minimum dwell-time constraints, and investigating positivity of the estimation error dynamics in addition to stability. Several observers are designed oriented on different conditions of positivity and stability for estimation error dynamics. The boundedness of the estimation error (input-to-state stability property) and the observer stability conditions are stated as infinite-dimensional linear programming problems. Next, an output stabilizing feedback design problem is discussed, where the stability is checked using linear matrix inequalities (LMIs). Efficiency of the proposed approach is demonstrated by computer simulations for a commercial electric vehicle equipped with a low power range extender fuel cell, a bouncing ball, an academic linear impulsive system and for Fault Detection and Isolation (FDI) and Fault-Tolerant Control (FTC) of a power split device with clutch for heavy-duty military vehicles.

Simple interval observers for linear impulsive systems with applications to sampled-data and switched systems

Abstract Sufficient conditions for the design of a simple class of interval observers for linear impulsive systems subject to minimum and range dwell-time constraints are obtained and formulated in terms of infinite-dimensional linear programs. The proposed approach is fully constructive in the sense that suitable observer gains can be extracted from the solution of the optimization problems and is flexible enough to be extended to include performance constraints and tackle parametric uncertainties. In order to be solvable, the infinite-dimensional linear programs are relaxed using a method based on sum of squares which is known to be asymptotically exact in the present case. Three examples are given for illustration: the first one pertains on the interval observation of an impulsive system under a minimum dwell-time constraint, the second one is about the interval observation of an aperiodic sampled-data system and the last one is about the interval observation of a linear switched system.

Optimal switching with minimum dwell time constraint

The problem of optimal switching between different subsystems/configurations with minimum dwell time constraints is investigated in this study and a feedback solution, using the framework of approximate dynamic programming, is proposed. The method calls for a tuning stage in which parameters of a function approximator are tuned. Online control will then be conducted with a computational load as low as evaluating a few scalar-valued functions. Finite-horizon and infinite-horizon cost functions are investigated and convergence and stability are analyzed considering the presence of approximation errors. Moreover, the case of applying a full or partial constraint on the mode sequence, as well as having a mode-dependent minimum dwell time are investigated. Finally, performance of the scheme in handling different challenges is numerically evaluated through different examples.

Synchronous switching observer for nonlinear switched systems with minimum dwell time constraint

This paper deals with the issue of state observability for a class of nonlinear switched systems under minimum dwell time (MDT) switching. First, multiple full-order switched observers are designed to estimate the states of nonlinear switched system under MDT switching, and the observer gains are derived from the feasible solutions of linear matrix inequality. Meanwhile, the condition where the minimum dwell time should satisfy is provided such that the observer error dynamic is exponentially asymptotically stable. Second, under the assumption, the output matrices of nonlinear switched system are with some special forms which can also be dealt by orthogonal procedure if they are not satisfied, multiple reduced-order switched observers are proposed by coordinate transformation approach such that the state estimation purpose is reached for original nonlinear switched systems. Third, the MDT condition that the switching signal should meet with is given such that both full-order and reduced-order switched observers can be simultaneously designed. Finally, the effectiveness of the proposed approaches is illustrated by a numerical example and longitudinal switched dynamics of an F-18 aircraft.

Chattering free control of continuous‐time switched linear systems

Chattering is an undesirable phenomenon characterised by infinitely fast switching which may cause equipment damage in real systems. To avoid its occurrence, this study proposes a chattering-free switching strategy for continuous-time switched linear systems ensuring global asymptotical stability and a guaranteed cost level associated to the rms gain of a class of input to output signals. The switching function is designed considering a minimum dwell-time constraint in order to avoid chattering and a maximum one to ensure robustness with respect to sampling jitters and implementation imperfections as, for instance, delays in the switching process. The conditions are based on Riccati–Metzler inequalities which take into account an equivalent discrete-time switched linear system obtained from the continuous-time one guided by a sampled switching rule without any kind of approximation. As a new result, for a subclass of Metzler matrices, necessary and sufficient conditions for the existence of a solution for the Riccati–Metzler inequalities are provided. Theoretical aspects are illustrated by some academical examples.

Convex lifted conditions for robust [formula omitted]-stability analysis and [formula omitted]-stabilization of linear discrete-time switched systems with minimum dwell-time constraint

Stability analysis of discrete-time switched systems under minimum dwell-time is studied using a new type of LMI conditions. These conditions are convex in the matrices of the system and shown to be equivalent to the nonconvex conditions proposed in Geromel and Colaneri (2006b). The convexification of the conditions is performed by a lifting process which introduces a moderate number of additional decision variables. The convexity of the conditions can be exploited to extend the results to uncertain systems, control design and ℓ2-gain computation without introducing additional conservatism. Several examples are presented to show the effectiveness of the approach.