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This paper studies the consensus tracking problem of uncertain Lagrangian systems. In contrast to the existing results where the command signals are sufficiently smooth, we consider a class of nonsmooth command signals generated by a switched command generator, which might be more realistic from the perspective of practical applications. The main technical innovations of this paper are threefold. First, to enable a rigorous problem formulation, some piecewise decaying function sets are defined to precisely describe the steady-state behaviors of the tracking errors. Second, to ensure the stability of the switched nonlinear closed-loop system, a system-based scaling method with the establishment of several lemmas is developed to determine the minimal dwell time of the switching signal. Third, a quantitative analysis is performed to acquire the ultimate bound for the steady-state tracking errors. The proposed control approach is evaluated by a simulation example. [ABSTRACT FROM AUTHOR]

This paper presents iterative sequential action control (iSAC), a receding horizon approach for control of nonlinear systems. The iSAC method has a closed-form open-loop solution, which is iteratively updated between time steps by introducing constant control values applied for short duration. Application of a contractive constraint on the cost is shown to lead to closed-loop asymptotic stability under mild assumptions. The effect of asymptotically decaying disturbances on system trajectories is also examined. To demonstrate the applicability of iSAC, we employ a variety of systems and conditions, including a 13-dimensional quaternion-based quadrotor and NASA's Transition Region and Coronal Explorer (TRACE) spacecraft. Each system is tested in different scenarios, ranging from feasible and infeasible trajectory tracking to setpoint stabilization, with or without the presence of external disturbances. Finally, limitations of this paper are discussed. [ABSTRACT FROM AUTHOR]

This paper addresses the event-triggered dynamic output feedback control for switched linear systems with frequent asynchronism. Different from existing work, which limits at most once switching during an interevent interval, we adopt the average dwell time approach without limiting the minimum dwell time of each subsystem, and thus frequent switching is allowed to happen in an interevent interval. Since the difficulty in acquiring the full information of system states, the dynamic output feedback controller is taken into account to stabilize the switched system. By employing a controller-mode-dependent Lyapunov functional, stability criterion is proposed for the resulting closed-loop system, based on which the dynamic output feedback controller together with the mode-dependent event-triggered mechanism is codesigned. Besides, the existence of the lower bound on interevent intervals is attentively discussed, which gets rid of the Zeno behavior. Finally, the effectiveness of the proposed method is illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we propose a state-dependent switching controller for multiple-input multiple-output (MIMO) bilinear systems with constant delays in both the state and the input. The control input is assumed to be restricted to take only a finite number of values. The stability analysis of the closed loop is based on a Lyapunov–Krasovskii functional, and the design is reduced to solve a system of linear matrix inequalities. The controller can be designed by considering (state) delay-dependent or delay-independent conditions. [ABSTRACT FROM AUTHOR]

The joint spectral radius (JSR) of a set of matrices characterizes the maximal asymptotic growth rate of an infinite product of matrices of the set. This quantity appears in a number of applications including the stability of switched and hybrid systems. A popular method used for the stability analysis of these systems searches for a Lyapunov function with convex optimization tools. We analyze the accuracy of this method for constrained switched systems, a class of systems that has attracted increasing attention recently. We provide a new guarantee for the upper bound provided by the sum of squares implementation of the method. This guarantee relies on the $p$ -radius of the system and the entropy of the language of allowed switching sequences. We end this paper with a method to reduce the computation of the JSR of low-rank matrices to the computation of the constrained JSR of matrices of small dimension. [ABSTRACT FROM AUTHOR]

In this paper, we consider the l\infty gain characterizations of linear switched systems (LSS) and present various relevant results on their exact computation and optimization. Depending on the role of the switching sequence, we study two broad cases: first, when the switching sequence attempts to maximize, and second, when it attempts to minimize the l\infty gain. The first, named as worst-case throughout the paper, can be related to robustness of the system to uncontrolled switching; the second relates to situations when the switching can be part to the overall decision making. Although, in general, the exact computation of l\infty gains is difficult, we provide specific classes, the input-output switching systems, for which it is shown that linear programming can be used to obtain the worst-case l\infty gain. This is a sufficiently rich class of systems as any stable LSS can be approximated by one. Certain applications to robust control design are provided where we show that a switched compensation independently of the plant has no advantage over a linear time invariant (LTI) compensation, and further, if the plant is strictly causal, even a switched compensation which has a matched switching with the plant does not provide a better performance over an LTI compensation. Also, we present a new necessary and sufficient condition to check the stability of LSS in form of a model matching problem. On the other hand, if one is interested in minimizing the l\infty gain over the switching sequences, we show that, for finite impulse response (FIR) switching systems the minimizing switching sequence can be chosen to be periodic. For input-only or output-only switching an exact, readily computable, characterization of the minimal l\infty gain is provided, and it is shown that the minimizing switching sequence is constant, which, as also shown, is not true for input-output switching. [ABSTRACT FROM AUTHOR]

Controlled distinguishability of two dynamical systems is the property of the systems that guarantees the existence of a control input generating different outputs of the systems regardless of their initial state vectors. These inputs are referred in the literature as discerning control inputs. In this paper, a necessary and sufficient condition for controlled distinguishability of continuous-time bilinear systems is established. It generalizes the classic one provided in the literature for the class of linear systems and a method for designing discerning inputs of bilinear systems that stabilize the systems is also proposed. [ABSTRACT FROM AUTHOR]

It is proved in this paper that the existence of suitable multiple Lyapunov functions is a necessary and sufficient condition for a discrete-time nonlinear switching system, with given switches digraph, to be globally asymptotically stable. The same result is provided for the input-to-state stability. The less is the number of edges in the switches digraph, the less is the number of inequalities that are involved in the provided necessary and sufficient Lyapunov conditions. [ABSTRACT FROM AUTHOR]

This paper addresses the stability problem for linear continuous-time Markovian switching singular systems. Considering the inherent state jump behavior at the switching instants, a necessary and sufficient condition of exponential stability in the mean square sense for the Markovian switching singular system is established in terms of linear matrix inequalities by means of a stochastic Lyapunov approach. Based on the obtained stability result, sufficient conditions of exponential stability in the mean square sense for the Markovian switching singular system with uncertain and partly unknown transition probability are presented. Numerical examples are presented to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper introduces a model for freeway traffic dynamics under stochastic capacity-reducing incidents, and provides insights for freeway incident management by analyzing long-time (stability) properties of the proposed model. Incidents on a multicell freeway are modeled by reduction in capacity at the affected freeway sections, which occur and clear according to a Markov chain. We develop conditions under which the traffic queue induced by stochastic incidents is bounded. A necessary condition is that the demand must not exceed the time-average capacity adjusted for spillback. A sufficient condition, in the form of a set of bilinear inequalities, is also established by constructing a Lyapunov function and applying the classical Foster–Lyapunov drift condition. Both conditions can be easily verified for realistic instances of the stochastic incident model. Our analysis relies on the construction of a globally attracting invariant set, and exploits the properties of the traffic flow dynamics. We use our results to analyze the impact of stochastic capacity fluctuation (frequency, intensity, and spatial correlation) on the throughput of a freeway segment. [ABSTRACT FROM AUTHOR]

This paper addresses the cooperative output regulation problem of linear multi-agent systems under switching communication topologies. A distributed event-triggered control scheme is proposed so that the cooperative output regulation problem is solved with only intermittent communication. The communication topology is not required to be connected at every time instant under the jointly connected assumption. With the proposed triggering mechanism, each agent only transmits the information to its neighbors at its own triggering times or the switching times. By introducing a fixed timer, Zeno behavior is strictly excluded for each agent. The effectiveness of the proposed control scheme is demonstrated by an example. [ABSTRACT FROM AUTHOR]

This paper generalizes the LaSalle–Yoshizawa Theorem to switched nonsmooth systems. The Filippov and Krasovskii regularizations of a switched system are shown to be contained within the convex hull of the Filippov and Krasovskii regularizations of the subsystems, respectively. A common candidate Lyapunov function that has a negative semidefinite generalized time derivative along the trajectories of the subsystems is shown to be sufficient to establish LaSalle–Yoshizawa-like results for the switched system. Of independent interest, are the results on approximate continuity and Filippov regularization of set-valued maps, reduction of differential inclusions using Lipschitz continuous regular functions, and comparative remarks on different generalizations of the time derivative along the trajectories of a nonsmooth system. [ABSTRACT FROM AUTHOR]

We study feedback control for a discrete-time integrator with unitary delay in the presence of quantization both in the control action and in the measurement of the controlled variable. In some applications the quantization effects can be neglected, but when high precision is needed, they have to be explicitly accounted for in control design. In this paper, we propose a switched control solution for minimizing the effect of quantization of both the control and controlled variables for the considered system, that is quite common in the computing systems domain, for example, in thread scheduling, clock synchronization, and resource allocation. We show that the switched solution outperforms the one without switching, designed by neglecting quantization, and analyze necessary and sufficient conditions for the controlled system to exhibit periodic solutions in the presence of an additive constant disturbance affecting the control input. Simulation results provide evidence of the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

Event-triggered control is an effective control strategy, capable of reducing the amount of communications and retaining a satisfactory closed-loop performance. In this paper, we aim at proposing an event-triggered sampling mechanism and studying observer-based output feedback control for switched linear neutral systems with mixed time-varying delays. Different from the conventional event-triggered control strategies, our proposed one transmits not only the state but also the switching information to the controller, which is advantageous in applications where the measured outputs and the switching information have to be transmitted over a communication network. Moreover, asynchronous switchings may be caused between the subsystems and their matched subcontrollers under the proposed sampling mechanism, which increases difficulties in analyzing stability. We develop a sufficient condition, under which the proposed control scheme guarantees globally the exponential stability of the closed-loop system meanwhile taking into account asynchronous switchings. Finally, an illustrative example is given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper introduces the notion of common zeroing-output systems (CZOS) to analyze the stability of switched systems. The concept of CZOS allows one to verify weak zero-state detectability. It characterizes a common behavior of any individual subsystem when the output signal for each subsystem is “approaching” zero. Heuristically speaking, it removes the effect of switching behavior, and thus enables one to analyze stability properties in systems with complex switching signals. With the help of CZOS, the Krasovskii–LaSalle theorem can be extended to switched nonlinear time-varying systems with both arbitrary switching and more general restricted switching cases. For switched nonlinear time-invariant systems, the needed detectability condition is further simplified, leading to several new stability results. Particularly, when a switched linear time-invariant system is considered, it is possible to generate a recursive method, which combines a Krasovskii–LaSalle result and a nested Matrosov result, to find a CZOS if it exists. The power of the proposed CZOS is demonstrated by consensus problems in literature to obtain a stronger convergence result with weaker conditions. [ABSTRACT FROM AUTHOR]

This paper investigates the state observer design of a class of unknown input switched linear systems via mode-dependent dwell time switchings. The distinguishing feature of the proposed method is that strong detectability condition of subsystems of the switched systems is unnecessarily required. First, a time-varying coordinate transformation is introduced to design a suitable reduced-order observer for each subsystem. Then, computable sufficient conditions on the synthesis of the observers are proposed in the framework of a mode-dependent dwell time technique. Since the observer of an individual subsystem cannot be designed due to unavailability of strong detectability condition of the subsystem, the state of the switched system is estimated under the condition of confining the dwell time by a pair of upper and lower bounds, restricting the growth of the Lyapunov function of the active subsystem and forcing “energy” of the overall switched system to decrease at switching instants. Finally, an example is presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The goal of this paper is to study the exponential stabilization problem for autonomous discrete-time switched linear systems (SLSs), where only the discrete mode can be controlled. Our approach is based on periodic control Lyapunov functions whose value decreases periodically instead of at each time step as in the classical control Lyapunov functions. Using periodic control Lyapunov functions, we develop stabilizability analysis and controller synthesis conditions that are less conservative than existing results in that they apply to a larger class of SLSs. Utilizing recent results on the switched optimal control problems, a constructive way to find periodic control Lyapunov functions is presented. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a new design method of discrete-valued control for continuous-time linear time-invariant systems based on sum-of-absolute-values (SOAV) optimization. We first formulate the discrete-valued control design as a finite-horizon SOAV optimal control, which is an extended version of \mathbbL^1 optimal control. We then give simple conditions that guarantee the existence, discreteness, and uniqueness of the SOAV optimal control. Also, we show that the value function is continuous, by which we prove the stability of infinite-horizon model predictive SOAV control systems. We provide a fast algorithm for the SOAV optimization based on the alternating direction method of multipliers (ADMM), which has an important advantage in real-time control computation. A simulation result shows the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper deals with model reduction by balanced truncation of switched linear systems (SLS). We consider switched linear systems whose dynamics, depending on the switching signal, switches between finitely many linear systems with a common state space. These linear systems are called the modes of the SLS. The idea is to seek for conditions under which there exists a single state space transformation that brings all modes of the SLS in balanced coordinates. As a measure of reachability and observability of the state components of the SLS, we take the average of the diagonal gramians. We then perform balanced truncation by discarding the state components corresponding to the smallest diagonal elements of this average balanced gramian. In order to carry out this program, we derive necessary and sufficient conditions under which a finite collection of linear systems with common state space can be balanced by a single state space transformation. Among other things, we derive sufficient conditions under which global uniform exponential stability of the SLS is preserved under simultaneous balanced truncation. Likewise, we derive conditions for preservation of positive realness or bounded realness of the SLS. Finally, in case that the conditions for simultaneous balancing do not hold, or we simply do not want to check these conditions, we propose to compute a suitable state space transformation on the basis of minimization of an overall cost function associated with the modes of the SLS. We show that in case our conditions do hold, this transformation is in fact simultaneously balancing, bringing us back to the original method described in this paper. [ABSTRACT FROM AUTHOR]

This paper is devoted to the problem of nonlinear state estimation under multirate sampling in presence of disturbance inputs. Considering a general description of a nonlinear sampled-data system, we establish a prescriptive framework for multirate observer design via an approximate discrete-time model of the plant. This framework is shown to be input-to-state stable in a semiglobal practical sense with respect to the estimation error for the unknown exact discrete-time model. A numerical example of an aerospace vehicle with input and output channels of various sampling rates demonstrates how the multirate observer can drastically improve performance compared with the single-rate observer. [ABSTRACT FROM PUBLISHER]

In this note, we present corrections to our previous paper “Switching rule design for switched dynamic systems with affine vector fields” refid="ref1"/, refid="ref2"/ . The correction is necessary to guarantee the stability of the system under sliding motion, which is not ensured from refid="ref1"/, refid="ref2"/ due to an error in the expressions (11) of the original paper refid="ref1"/. To correct the results it is necessary to add a new condition to the results of refid="ref1"/, refid="ref2"/. If there is no sliding motion or if the sliding motion dynamics, in the sense of Filippov, satisfies a quadratic stability condition, the additional condition is not necessary. The corrections in this note are restricted to the case of two operation modes. [ABSTRACT FROM PUBLISHER]

This paper introduces the concept of consistency for continuous-time switched linear systems having the switching function as a primary control signal to be designed. A switching control strategy is strictly consistent whenever it improves performance compared to the ones of all isolated subsystems. Conditions under which a min-type switching strategy is strictly consistent for the classes of \cal H2 and \cal H\infty performance indexes are determined. This property makes clear the importance of switching systems control design in both theoretical and practical application frameworks. Moreover, with this property it is not necessary to assume that all the subsystems are not stable in order to make a switching strategy design problem well posed. The theory is illustrated by means of several academic examples. [ABSTRACT FROM PUBLISHER]

This paper addresses the problem of controlling an uncertain time-varying plant by means of a finite family of candidate controllers supervised by an appropriate switching logic. It is assumed that, at every time, the plant consists of an uncertain single-input/single output linear system. It is shown that stability of the switched closed-loop system can be ensured provided that 1) at every time there is at least one candidate controller capable of potentially stabilizing the current time-invariant “frozen” plant model, and 2) the plant changes are infrequent or satisfy a slow drift condition. [ABSTRACT FROM AUTHOR]

This paper is concerned with the derivation of a model reference adaptive control (MRAC) scheme for multimodal piecewise-affine (PWA) and piecewise-linear systems. The control allows the plant to track asymptotically the states of a multimodal piecewise affine (or smooth) reference model. The reference model can be characterized by a number and geometry of phase space regions that can be entirely different from those of the plant. Numerical simulations on a set of representative examples confirm the theoretical derivation and proof of stability. [ABSTRACT FROM AUTHOR]

This paper considers asymptotic stability and transient performance of discrete-time piecewise affine systems. We propose a procedure to construct a nested sequence of finite-state symbolic models, each of which abstracts the original piecewise affine system and leads to linear matrix inequalities for guaranteed stability and performance levels. This sequence is in the order of decreasing conservatism, and hence gives us the option to pay more computational cost and analyze a finer symbolic model within the sequence in return for less conservative results. Moreover, in the special case where this sequence is finite, an exact analysis of stability and performance is achieved via semidefinite programming. [ABSTRACT FROM PUBLISHER]

We consider the problem of achieving input-to-state stability (ISS) with respect to external disturbances for control systems with quantized measurements. Quantizers considered in this paper take finitely many values and have an adjustable “center” and “zoom” parameters. Both the full state feedback and the output feedback cases are considered. Similarly to previous techniques from the literature, our proposed controller switches repeatedly between “zooming out” and “zooming in.” However, here we use two modes to implement the “zooming in” phases, which allows us to attenuate an unknown disturbance while using the minimal number of quantization regions. Our analysis is trajectory-based and utilizes a cascade structure of the closed-loop hybrid system. We further show that our method is robust to modeling errors using a specially adapted small-gain theorem. The main results are developed for linear systems, but we also discuss their extension to nonlinear systems under appropriate assumptions. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate distributed multi-agent tracking of a convex set specified by multiple moving leaders with unmeasurable velocities. Various jointly connected interaction topologies of the follower agents with uncertainties are considered in the study of set tracking. Based on the connectivity of the time-varying multi-agent system, necessary and sufficient conditions are obtained for set input-to-state stability and set integral input-to-state stability for a nonlinear neighbor-based coordination rule with switching directed topologies. Conditions for asymptotic set tracking are also proposed with respect to the polytope spanned by the leaders. [ABSTRACT FROM AUTHOR]

The concept of using multiple models to cope with transients which arise in adaptive systems with large parametric uncertainties was introduced in the 1990s. Both switching between multiple fixed models, and switching and tuning between fixed and adaptive models was proposed, and the stability of the resulting schemes was established. In all cases, the number of models needed is generally large (c^n where n is the dimension of the parameter vector and c an integer), and the models do not “cooperate” in any real sense. In this paper, a new approach is proposed which represents a significant departure from past methods. First, it requires (n+1) models (in contrast to c^n) which is significantly smaller, when “n” is large. Second, while each of the (n+1) models chosen generates an estimate of the plant parameter vector, the new approach provides an estimate which depends on the collective outputs of all the models, and can be viewed as a time-varying convex combination of the estimates. It is then shown that control based on such an estimate results in a stable overall system. Further, arguments are given as to why such a procedure should result in faster convergence of the estimate to the true value of the plant parameter as compared to conventional adaptive controllers, resulting in better performance. Simulation studies are included to practically verify the arguments presented, and demonstrate the improvement in performance. [ABSTRACT FROM PUBLISHER]

The twisting and supertwisting algorithms, generating important classes of second order sliding modes (SOSMs), are well-recognized for their finite time stability and robustness properties. In the present paper, a continuous modification of the twisting algorithm and an inhomogeneous perturbation of the supertwisting algorithm are introduced to extend the class of SOSM's that present the afore-mentioned attractive features. Thus modified, the twisting and supertwisting algorithms are utilized in the state feedback synthesis and, respectively, velocity observer design, made for the finite time stabilization of a double integrator if only output measurements are available. Performance and robustness issues of the resulting output feedback synthesis are illustrated by means of numerical simulations. [ABSTRACT FROM AUTHOR]