Proposed Switching Law 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.

A combined cyclic stabilizing switching law for continuous time positive switched systems

AbstractBased on a linear copositive Lyapunov function (LF), a combined cyclic stabilizing switching law with one stage being classified into four cases is proposed for continuous time positive switched systems composed of two unstable subsystems. Under the combined cyclic stabilizing switching law, the positive switched system is asymptotically stable and robust against certain class of perturbations. Finally, simulation verifies the effectiveness of the proposed switching law.

Periodic Time-Triggered Hybrid Control for DC–DC Converter Based on Switched Affine System Model

The introduction of the switched affine system opens new perspectives for the control design of dc–dc converters. In order to overcome the drawbacks of the continuous-time switching control methods, several sampled-data-based switching control approaches have been proposed in the literature. However, in these works, the solution of control parameters involves a nonlinear optimization problem. In addition, the designed switching laws are nonlinear functions about the system state, which require higher computational resources. In this article, a periodic time-triggered hybrid control is proposed based on a new design framework. All the design conditions are in linear matrix inequality formulations, which can be conveniently solved by common semidefinite programming software. Moreover, the proposed switching law is a linear function about the state, reducing the online computing burden. Finally, a unified view of the classical continuous-time switching scheme and the proposed method is established. Simulation and experiment tests on a buck–boost converter demonstrate the good performance of the proposed control strategy.

Semi-time-dependent stabilization for a class of continuous-time impulsive switched linear systems

In this paper, the stability and stabilization problems of a class of impulsive switched linear systems with mode-dependent persistent dwell-time (MPDT) switching are investigated in continuous-time domain. The proposed switching law is more general, which not only covers the widely probed dwell-time (DT) and average dwell-time (ADT) as special cases but also extends the persistent dwell time (PDT) in the literature. By invoking novel modal partition time-dependent multiple Lyapunov-like functions, the stability criteria for the systems under MPDT switching in nonlinear settings are established as a first attempt, upon which the desired mode-dependent and semi-time-dependent (STD) stabilizing controllers for continuous-time impulsive switched linear systems are designed. It is demonstrated that the control performance is improved as both the length of admissible MPDT and the number of time partition segment are added. Finally, a numerical example is provided to illustrate the potential of the obtained theoretical results.

New stability criteria of switched systems with unstable modes under a weighted ADT scheme

ABSTRACT Two concepts of the weighted average dwell time (WADT) and the fast weighted average dwell time (FWADT) are introduced for continuous-time switched systems. The stability problems for a switched system with WADT and FWADT are investigated under a class of ergodic switching signals. The relationship between the ADT/mode-dependent ADT schemes and the WADT scheme is also discussed, which shows that the classic schemes are included in the new one under some conditions. The proposed switching law based on the (F)WADT scheme is more flexible and has a larger feasible region than the existing results. Finally, two numerical examples with some comparisons among several schemes are included to illustrate the validity and superiority of the developed techniques.

Synchronization of different order fractional-order chaotic systems using modify adaptive sliding mode control

This paper proposes a modified adaptive sliding-mode control technique and investigates the reduced-order and increased-order synchronization between two different fractional-order chaotic systems using the master and slave system synchronization arrangement. The parameters of the master and slave systems are different and uncertain. These systems exhibit different chaotic behavior and topological properties. The dynamic behavior of the proposed synchronization schemes is more complex and unpredictable. These attributes of the proposed synchronization schemes enhance the security of the information signal in digital communication systems. The proposed switching law ensures the convergence of the error vectors to the switching surface and the feedback control signals guarantee the fast convergence of the error vectors to the origin. Lyapunov stability theory proves the asymptotic stability of the closed-loop. The paper also designs suitable parameters update laws the estimate the unknown parameters. Computer-based simulation results verify the theoretical findings.

A generalized mode-dependent average dwell time approach to stability analysis of positive switched systems with two subsystems

The stability problem for positive switched systems with two subsystems is investigated with an improved mode-dependent average dwell time (MDADT) scheme. By utilizing system positivity and the new scheme, the stability conditions of the considered system are addressed. The proposed switching law is more applicable in practice than the average dwell time (ADT) and MDADT schemes with certain conditions, and those existing methods can be regarded as some special cases of the theoretical findings in the paper. Then, the new stability criteria are extended to non-autonomous systems. Finally, two simulation examples with some comparisons to the classical results are given to illustrate the advantages of our obtained results.

Integrated Spacing Policy Considering Micro- and Macroscopic Characteristics

An appropriate spacing policy improves traffic flow and traffic efficiency while reducing commuting time and energy consumption. In this paper, the integrated spacing policy that combines the benefits of the constant time headway (CTH) and safety distance (SD) spacing policies is proposed in an attempt to improve traffic flow and efficiency. Firstly, the performance of the CTH and SD spacing policies is analyzed from the perspective of the microscopic characteristics of human-vehicle and the macroscopic characteristics of traffic flow. The switching law between CTH and SD spacing policies and the integrated spacing policy are then proposed to increase traffic efficiency according to the traffic conditions, and the critical speed for the proposed integrated spacing policy is derived. Using the proposed switching law, the integrated spacing policy utilizes the safety redundancy difference between the CTH and SD spacing policies in a flexible manner. Simulation tests demonstrate that the proposed integrated spacing policy increases traffic flow and that the traffic flow maintains string stability in a wider range of traffic flow density.

Passivity and passification for switched T-S fuzzy systems with sampled-data implementation

This article investigates the issues of passivity analysis and feedback passification for a class of switched Takagi–Sugeno (T–S) fuzzy systems with the sampled-data-dependent switching strategy and controllers. Different from the previous switching laws, the proposed switching law only requires the values of system state at the discrete sampling instants. More incisively, a dwell time constraint for all subsystems is produced, which reduces the switching frequency and avoids the occurrence of chattering phenomenon or Zeno behavior. Then, sufficient conditions for the existence of the sampled-data-dependent switching strategy and controllers are formulated, under which the switched T–S fuzzy systems is strictly passive without requiring the strict passivity of any subsystem. In addition, the storage function is only decreasing with respect to its value at the sampling times, which in turn implies that the storage function can be nonmonotonous. Finally, a numeral example and a room air regulating system are employed to demonstrate the effectiveness and applicability of the presented theoretical results.

Semi‐active vibration reduction based on a variable structure controlled serial‐stiffness‐switch‐system

AbstractA concept for semi‐active vibration control with a serial‐stiffness‐switch‐system based on vibration energy harvesting was previously presented. This contribution investigates a variable structure control‐based switching law to reduce the settling time of the system response under a nonzero velocity initial condition. The proposed switching law is able to fasten the transformation of initial vibration energy of the system into potential energy stored equally in its two springs. It is characterized, simulated, and proven to be more effective than the old switching law.

External stability of switching control systems

This paper investigates external stability (defined by the normal L2 norm) of switching control systems. It proposes definitions of the maximum, minimum dwell time for switching systems and then derives an important relation between the number of switchings and the maximum, minimum dwell time. Applying this relation, it establishes criteria on external stability of switching control systems consisting of Hurwitz stable subsystems. Furthermore, a switching law is proposed, and is proven to be realizable. Given this proposed switching law and applying the previous derived relation, the switching control systems comprised of both Hurwitz stable and Hurwitz unstable subsystems are proved to be externally stable.

H∞ control for linear switched systems with time‐varying delay and dead‐zone inputs via an adaptive memory controller

SummaryThis paper deals with the problem of robust H∞ control for linear switched systems with time‐varying delay and dead‐zone inputs. First, a new state‐dependent switching law is proposed for the switched system with stable and unstable subsystems. Based on the proposed switching law and using the scaled small gain theorem, a more general stability criterion for the switched delay systems is established. Second, an adaptive memory controller is proposed for the switched system with dead‐zone inputs. With the help of a two‐term approximation of the time‐varying delay, the proposed memory controller only depends on the bounds of the time‐varying delay. Sufficient conditions on the existence of the desired controller are formulated in terms of linear matrix inequalities. Three examples are provided to illustrate the effectiveness of the proposed methods. Copyright © 2016 John Wiley & Sons, Ltd.

Mixed Skyhook and Power-Driven-Damper: A New Low-Jerk Semi-Active Suspension Control Based on Power Flow Analysis

In practice, semi-active suspensions provide better tradeoffs between performances and costs than passive or active damping. Many different semi-active control algorithms have been developed, including skyhook (SH), acceleration-driven-damper (ADD), power-driven-damper (PDD), mixed SH and ADD (SH-ADD), and others. Among them, it has been shown that the SH-ADD is quasi-optimal in reducing the sprung mass vibration. In this paper, we analyze the abilities of vehicular suspension components, the shock absorber and the spring, from the perspective of energy transfer between the sprung mass and the unsprung mass, and propose a new sprung mass control algorithm named mixed SH and PDD (SH-PDD). The proposed algorithm defines a switching law that is capable of mixing SH and PDD, and simultaneously carries their advantages to achieve a better suspension performance. As a result, the proposed SH-PDD is effective in reducing the sprung mass vibration across the whole frequency spectrum, similar to SH-ADD and much better than SH, PDD, and ADD, while eliminating the control chattering and high-jerk behaviors as occurred in SH-ADD. The superior characteristics of the SH-PDD are verified in numerical analysis as well as experiments. In addition, the proposed switching law is extended to mix other semi-active control algorithms such as the mixed hard damping and soft damping, and the mixed SH and clipped-optimal linear quadratic regulator (LQR).

Robust H∞ switching control techniques for switched nonlinear systems with application to urban traffic control

SummaryThis paper presents robust switching control strategies for switched nonlinear systems with constraints on the control inputs. A quantization technique is used to relax the constraint on continuous control inputs and the L2‐gain analysis and H∞ control design problem for switched nonlinear systems are presented. Next, as an alternative method, the switched nonlinear system is approximated by a switched affine system that has autonomous and controlled switching behavior. A robust switching control law is proposed to stabilize the switched affine system. The design procedure involves solving an optimization problem that is nonconvex in a single scalar variable only. Furthermore, we provide the sufficient conditions under which the proposed switching law is able to stabilize the original switched nonlinear system. Finally, the proposed methods are utilized for control of urban traffic networks modeled on a high level. The traffic control objective is translated into a stability and disturbance attenuation problem for the urban network represented by a switched nonlinear system. The switching control approaches are able to reduce congestion in the network and to attenuate the effects of uncertain trip demands. Because the design of the switching laws is performed offline, real‐time traffic control is possible with the proposed methods. Copyright © 2015 John Wiley & Sons, Ltd.

Practical stability of switched uncertain nonlinear systems using state-dependent switching laws

In this paper, it is proven that a state dependent switching law designed for integrator switched systems can be used to stabilize complex switched uncertain nonlinear systems as well as a class of impulsive systems, provided that the upper bound of the uncertainty terms satisfy a relationship with the nominal system parameters estimation of the nominal system parameters. In order to establish such a result, firstly, a switching law is proposed to ε-practically stabilize an uncertain integrator switched system; secondly, the proposed switching law is used to prove that the trajectories of a general class of uncertain nonlinear systems are ε-practical stable and connections to switched nonlinear impulsive systems are revealed. Numerical simulations allow us to illustrate the proposed stability results and an example in a power electronics device is used to show the applicability of the proposed state-dependent switching control strategy.

Fault detection for discrete-time switched systems with sensor stuck faults and servo inputs

This paper addresses the fault detection problem of switched systems with servo inputs and sensor stuck faults. The attention is focused on designing a switching law and its associated fault detection filters (FDFs). The proposed switching law uses only the current states of FDFs, which guarantees the residuals are sensitive to the servo inputs with known frequency ranges in faulty cases and robust against them in fault-free case. Thus, the arbitrarily small sensor stuck faults, including outage faults can be detected in finite-frequency domain. The levels of sensitivity and robustness are measured in terms of the finite-frequency H− index and l2-gain. Finally, the switching law and FDFs are obtained by the solution of a convex optimization problem.

Simultaneous Fault Detection and Control for Discrete-Time Switched Systems

This paper studies the simultaneous fault detection and robust control problem for discrete-time switched systems. A switching law and output feedback-based controller/detectors are designed to meet control and detection objectives. In state-dependent switching framework, the proposed switching law uses only the partial measurable states of the closed-loop switched system, which is easy to design and realize. Under the switching law, some regions in which each subsystem is activated are first constructed. Sufficient conditions are then provided such that the sensitivity to faults and robustness to unknown inputs are guaranteed in these regions, and not necessarily everywhere. Thus, the closed-loop system is with the detection and robust performances even if all subsystems are without them, which reduces the performance requirements for each subsystem in time-dependent switching framework. A solution of the considered problem is obtained via linear matrix inequalities. Finally, an example is given to show the effectiveness of the proposed method.

Robust control and fault detection for continuous‐time switched systems subject to a dwell time constraint

SummaryThis paper is concerned with the simultaneous robust control and fault detection problem for continuous‐time switched systems subject to a dwell time constraint. To meet the control and detection objectives under the constraint, the controller/detectors matching different time intervals are first constructed in an output feedback framework. A state‐dependent switching law that obeys the dwell time constraint is then designed such that the closed‐loop switched system is asymptotically stable and also with the robust and detection performance. Further, the proposed switching law is dependent only on the partial measurable states of the closed‐loop system, which is applicable when the states of system mode are fully unavailable. Thus, our result extends the existing ones in state‐dependent switching and state‐feedback frameworks. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.

Weighted H ∞ performance analysis of switched linear systems with mode-dependent average dwell time

This article is concerned with the disturbance attenuation properties of a class of switched linear systems by using a mode-dependent average dwell time (MDADT) approach. The proposed switching law is less strict than the average dwell time (ADT) switching in that each mode in the underlying system has its own ADT. By using the MDADT approach, a sufficient condition is obtained to guarantee the exponential stability with a weighted H ∞ performance for the underlying systems. A numerical example is given to show the validity and potential of the developed results on improving the disturbance attenuation performance.

Stability and Stabilization of Switched Linear Systems With Mode-Dependent Average Dwell Time

In this paper, the stability and stabilization problems for a class of switched linear systems with mode-dependent average dwell time (MDADT) are investigated in both continuous-time and discrete-time contexts. The proposed switching law is more applicable in practice than the average dwell time (ADT) switching in which each mode in the underlying system has its own ADT. The stability criteria for switched systems with MDADT in nonlinear setting are firstly derived, by which the conditions for stability and stabilization for linear systems are also presented. A numerical example is given to show the validity and potential of the developed techniques.